dislocations - purdue universitydislocations 2016 1 the dislocations conference focuses on...

DISLOCATIONSAn International Conference Dedicated to the Fundamentals of Plasticity of Crystalline Solids

SEPTEMBER 19-23, 2016 AT PURDUE UNIVERSITY

DISLOCATIONS 2016 1

The Dislocations conference focuses on dislocation-based plasticity. This complex phenomenon continues to chal-lenge researchers in the mechanics, metallurgy, physics, and computational science and mathematics communities. The past three decades have witnessed a major transition in this field that was induced by the development and maturation of the method of Dislocation Dynamics Simulations. Although this method now seems conceptually simple, it has bridged for the first time, and in a formal manner, the Theory of Dislocations and the Theory of Metal Plasticity. Most importantly, the development of the method of Dislocation Dynamics Simulations has created a reason to revisit, by modeling and experiments, a wide range of single-dislocation processes such as mobility, cross slip, formation of hard junctions, dislocation conversion through reactions, and the interaction of dislocations with lattice defects, precipitates, and homo- and hetero-phase interfaces. These efforts have placed the dislocations and plasticity community closer than ever to achieving a predictive understanding of metal deformation and failure. Progress in this direction stimulated much work in atomisitic and electronic scale modeling of dislocation and de-fects, high resolution electron microscopy, and the use of high energy, synchrotron generated X-ray beams to probe deformation of metals in three dimensions. Because of the role that the dislocation dynamics simulations method has played over the past three decades in motivating all these works, the Dislocations-2016 conference is being held under the theme’30 Years of Dislocation Dynamics Simulations.’

The Dislocations conference series focus on the latest advances in fundamentals of dislocations and plastic deforma-tion. The scope of the conference covers dislocations and plastic deformation of metals, semiconductors, crystalline compounds, and heterogeneous material systems. Contributions of theoretical, computational, and experimental nature were solicited, focusing on fundamental properties of dislocations, dislocation-based plasticity in bulk and at interfaces, the role of dislocations in fatigue and fracture of materials, dislocations in irradiated solids, and methods of characterization of dislocations and plasticity.

The Dislocations conference has been held every four years since the year 2000. Dislocations-2016 is held at The Stewart Center on the campus of Purdue University in West Lafayette, Indiana, USA, during the week 19-23 Septem-ber 2016. All editions of the conference have been held as a single oral session, augmented by one or two poster sessions. This year, the number of contributions has jumped significantly in spite of the fact that the conference comes only a few weeks prior the Multiscale Materials Modeling (MMM-2016) Conference in Dijon, France, October 9-14, 2016, where significant themes dedicated to dislocations and plasticity are arranged. Over 180 contributions were received of which slightly over 60 contributions were given oral slots while the rest of the contributions were accepted as invited posters. Such a significant level of interest shows that the dislocations community not only con-tinues to be distinct, as it has always been, but also has grown considerably. This level of interest also indicates that research on dislocations and plasticity is thriving worldwide.

As the Chairperson of Dislocations-2016, I have been honored by the opportunity to serve the highly dynamic and prolific dislocations and plasticity community. While working on the organization tasks, I got the chance to learn firsthand about the quantity and quality of research carried out in the field and multitude of techniques used by researchers. The successful organization of the conference could not have been possible without the support of Purdue’s College of Engineering Associate Dean for Research, Dr. Melba Crawford, The Chief Scientist of Purdue’s Discovery Park, Dr. Tomas Diaz de la Rubia, The Director of Purdue’s Energy Center, Dr. Maureen McCann, and the Head of the School of Materials Engineering, Dr. David Bahr. The tireless work of the staff at Purdue Conferences Di-vision (Stewart Center) is greatly appreciated. Mr. Ethan Kingery and his Information Technology assistants deserve a special mention. The input received from the Dislocations-2016 Executive Committee and Scientific Committee members regarding the organizational aspects and selection of invited speakers has been invaluable. Lastly, but not least, I wish to thank the members of the Local Organizing Committee for their enthusiasm and support. A spatial thank you is also due to the plenary speakers for accepting the duty of reviewing the key works in the field, to the invited speakers and all participants for making this meeting a memorable scientific event.

Anter El-AzabDislocations-2016 ChairmanPurdue University, West LafayetteSeptember 19, 2016

FOREWORD

2 DISLOCATIONS 2016

Anter El-Azab, ChairPurdueUnited States of America

David Bahr, Co-chairPurdueUnited States of America

Marisol KoslowskiPurdueUnited States of America

Ghadir HaikalPurdueUnited States of America

LOCAL ORGANIZING COMMITTEE

INTERNATIONAL EXECUTIVE COMMITTEE

Dallas TrinkleUIUCUnited States of America

Giacomo PoUCLAUnited States of America

Michael SangidPurdueUnited States of America

Alejandro StrachanPurdueUnited States of America

Grethe WintherTechnical University of DenmarkDenmark

Vasily BulatovLawrence Livermore National LaboratoryUnited States of America

Wei CaiStanford UniversityUnited States of America

Istvan GromaEötvös Loránd UniversityHungary

Benoit DevincreCNRS-ONERAFrance

Amine BenzergaTexas A&M UniversityUnited States of America

Erik BitzekFriedrich-Alexander University Erlangen-NurembergGermany

Steven FitzgeraldOxford UniversityUK

Marc LegrosCEMES-CNRS ToulouseFrance

Yoji ShibutaniOsaka UniversityJapan

DISLOCATIONS 2016 3

Michael ZaiserFriedrich-Alexander University Erlangen-NurembergGermany

Marc GeersEindhoven University of TechnologyThe Netherlands

Akiyuki TakahashiTokyo University of ScienceJapan

Lyle LevineNational Institute of Standards and Technology (NIST)United States of America

Dallas TrinkleUniversity of Illinois, Urbana-ChampaignUnited States of America

Alfonso NganHong Kong UniversityHong Kong

Hussein ZbibWashington State UniversityUnited States of America

Amit AcharyaCarnegie Mellon UniversityUnited States of America

Cynthia VolkertUniversity of GöttingenGermany

INTERNATIONAL SCIENTIFIC COMMITTEEBill CurtinÉcole polytechnique fédérale de LaUnited States of AmericanneSwitzerland

Mac FivelGrenoble Institute of TechnologyFrance

Jaafar El-AwadyJohns Hopkins UniversityUnited States of America

Thomas HochrainerBremen UniversityGermany

Erik van der GiessenUniversity of GroningenThe Netherlands

James ColeIdaho National LaboratoryUnited States of America

Daniel WeygandKarlsruhe Institute of TechnologyGermany

David RodneyUniversité Claude Bernard Lyon 1France

4 DISLOCATIONS 2016

Amit AcharyaCarnegie Mellon UniversityUnited States of America

“Crystal Plasticity Models and Connections with Dislocation theory”

Amit Acharya is a Professor in the Mechanics, Materials, and Computing group of the Department of Civil & Environmental Engineering at Carnegie Mellon University (CMU). He also holds a courtesy appointment in the Dept. of Materials Science and Engineering at CMU and a Visiting Professorship in the Dept. of Mathematical Sciences at the University of Bath, UK. He received a PhD degree in Theoretical & Applied Mechanics from the University of Illinois at Urbana-Champaign (UIUC) in 1994. Subsequently, he did post-doctoral work for a year at the University of Pennsylvania and then worked for HKS, Inc. in Providence, RI (now Simulia, Dassualt Systemes) from 1995-1998, spending most of his time as a senior research engineer in the ABAQUS Std Development group. There, he was the lead developer of the *Hysteresis nonlinear viscoelastic material model and the S4, fully-integrated finite strain shell element, that are still in use in the ABAQUS general-purpose FE code. From 1998-2000, he was a Research scientist at the DOE-ASCI funded Center for Simulation of Advanced Rockets at UIUC, before joining CMU in 2000. His honors include a Leverhulme Visiting Professorship from the Leverhulme Foundation, UK, a Rosi and Max Varon Visiting Professorship from the Weizmann Institute, Israel, and an IndAM Visiting Professorship to the University of Pavia, Italy. He has been an invited short-course lecturer at SISSA (Trieste, Italy) and has held visiting research positions at Oxford, Cambridge, Marseille, Edinburgh, and Metz. His broad research interests are in Continuum Mechanics, Mathematical Materials Science, and Applied Mathematics. Current emphasis is on theoretical and computational defect mechanics in crystalline, liquid crystalline, and metallic glass systems, coarse-graining of nonlinear time-dependent systems and the interplay of differential geometry and structural mechanics in the design and actuation of thin sheets.

Nasr GhoniemUniversity of CaliforniaLos Angeles, United States of America

“What physics have we learned from computer simulations of defect mechanics?”

Nasr Ghoniem holds the Distinguished Professor title of the University of California. He is currently professor of Mechanical and Aerospace Engineering, and is also of Materials Science & Engineering at UCLA. He has wide experience in the development of materials in severe environments (Nuclear, Mechanical and Aerospace). He developed some of main multiscale computational methods in defect physics and mechanics. He is a fellow of the American Nuclear Society, the American Academy of Mechanics, the American Society of Mechanical Engineers, the Japan Society for Promotion of Science, and The Materials Research Society. He was the general chair of the Second International Multiscale Materials Modeling Conference in 2004. He serves on the editorial boards of several journals, and has published over 350 articles, 10 edited books, and is the co-author of a two-volume book (Oxford Press) on the mechanics and physics of defects, computational materials science, radiation interaction with materials, instabilities and self-organization in non-equilibrium materials (Nasr Ghoniem and Daniel Walgraef, Instabilities and Self-Organization in Materials: Part I-Fundamentals of Nanoscience, and Part II-Applications in Materials Design and Nanotechnology, Oxford Press, 2007, 1100 pages.) He graduated 35 Ph.D. students and 25 post-doctoral scholars (14 are currently in faculty positions).

PLENARY SPEAKERS

DISLOCATIONS 2016 5

Michael ZaiserFriedrich-Alexander University Erlangen-NurembergGermany

“Statistically averaged dislocation dynamics”

Professor Zaiser received his PhD from the Max-Planck-Institute of Metals Research in Stuttgart, Germany. He has held positions in several European countries, among which the Chair of Mechanics of Materials at the University of Edinburgh, UK. He is currently Chair Professor and Head of Materials Simulation at the Department of Materials Science, FAU University of Erlangen-Nürnberg, Germany. He has published over 150 papers and supervised 18 PhD students, 6 of which are currently holding faculty positions at major research universities. Michael Zaiser is member of the Editorial Boards or Associate Editor of several international journals. His research is posited at the interface between Theoretical Physics and Computational Materials Science, drawing strongly on concepts and methods from Statistical Physics and Complexity Theory to develop novel approaches for the solution of materials problems, and has organized or co-organized several international events devoted to statistical mechanics approaches to materials deformation and failure. His work on dislocation theory combines discrete simulation with statistical analysis and methods drawn from the statistical mechanics of many-particle systems in order to develop new physically based continuum approaches towards crystal plasticity.

Ben Larson, EmeritusOak Ridge National LaboratoryUnited States of America

“Toward a Predictive Understanding of Deformation at the Mesoscale Combining Experiment and Theory”

Bennett C. Larson is presently Corporate Fellow, Emeritus, in the Materials Science & Technology Division at Oak Ridge National Laboratory (ORNL). He was Group Leader for X-Ray Diffraction in the Condensed Matter Sciences and Solid State Divisions at ORNL from 1973-2006 and Section Head from 1990-2003. His current research interests are in the development and application of submicron-resolution 3D x-ray microscopy (3DXM) using synchrotron x-rays; fundamental investigations of materials deformation, microstructure, and evolution on mesoscopic length scales, including direct comparison with finite-element and first principles modeling of deformation; radiation damage in metal alloys; and microscopic phonon physics of thermal transport in concentrated metal alloys and uranium dioxide. Other research interests have included the feasibility of real-time measurements of displacement cascade dynamics and evolution with sub-pico-second resolution using femto-second x-ray pulses; microsecond-resolution time-resolved x-ray studies of pulsed-laser deposition film growth, inelastic x-ray scattering investigations of the dynamical electronic structure of strongly correlated materials; and nanosecond resolution synchrotron x-ray investigation of pulsed laser melting in semiconductors. Larson was a guest scientist at the Jülich Forschungscentrum, Jülich, Germany during 1974. He was a recipient of the 1974 Sidhu Award for early career achievements by the Pittsburgh Diffraction Society; he received the 1985 Bertram Warren Diffraction Physics Award by the American Crystallographic Association for nanosecond-resolution synchrotron x-ray measurements of pulsed-laser melting in Si; and he was co-recipient of the 2015 Advanced Photon Source Arthur H. Compton Award for seminal developments advancing focusing monochromator design and spatial and temporal resolved synchrotron x-ray capabilities. He joined Oak Ridge National Laboratory in 1969 after receiving a PhD in Physics from the University of Missouri, Columbia, MO. Larson can be reached by e-mail at [email protected].

PLENARY SPEAKERS

6 DISLOCATIONS 2016

PLENARY SPEAKERSDavid RodneyUniversité Claude Bernard Lyon 1France

“Ab Initio Modeling of Dislocation Core Properties”

David Rodney is a Professor at the Institut Lumière Matière of the University of Lyon in France. Prior to this, he was an Associate Professor at the Institute of Technology of Grenoble. Prof. Rodney is an engineer of Paris School of Mines with a M.S. degree from Jussieu University in Paris in Solid State Physics. He received a Ph.D. in Materials Science for research performed at Caltech, Brown University and the CEA Saclay, and was a post-doctoral fellow at ONERA. Prof. Rodney has been an invited researcher at MIT and the University of Chicago. His research is focused on the modeling of materials at different length and time scales, with a particular emphasis on linking elementary processes at the atomic scale with meso- and macroscopic properties. He has published over 80 papers in scientific journals. Since 2012, he is an editor at Acta Materialia.

DISLOCATIONS 2016 7

INVITED SPEAKERSSylvie AubryLawrence Livermore National Laboratory

Amine BenzergaTexas A&M University

Joel BonnevilleUniversité de Poitiers

Vasily BulatovLawrence Livermore National Laboratory

Wei CaiStanford University

Bill CurtinEcole Polytechnique Federale de LaUnited States of Americanne

Michael DemkowiczTexas A&M University

Benoit DevincreLEM-CNRS/ONERA

Jaafar El-AwadyJohns Hopkins University

Alphonse FinelLEM-CNRS/ONERA

Marc FivelUniversity Grenoble Alpes

Claude FressengeasUniversite de Lorraine/CNRS

Vikram GaviniUniversity of Michigan

Maryam GhazisaeidiOhio State University

Istvan GromaEötvös University Budapest

Thomas HochrainerUniversity of Bremen

Darcy HughesFremont, CA

Christoph KirchlechnerMax-Planck-Institut für Eisenforschung

Lyle LevineNational Institute of Standards and Technology

Jamie MarianUniversity of California, Los Angeles

Alfonso NganUniversity of Hong Kong

Lucia NicolaDelft University of Technology

Shigenobu OgataOsaka University

Wolfgang PantleonTechnical University of Denmark

Catalin PicuRensselaer Polytechnic Institute

Giacomo PoUniversity of California, Los Angeles

Stefan SandfeldFriedrich-Alexander University of Erlangen-Nuremberg

Nobuhiro TsujiKyoto University

Erik Van der GiessenUniversity of Groningen

Daniel WeygandKarlsruhe Institute of Technology

Grethe WintherTechnical University of Denmark

8 DISLOCATIONS 2016

SCHEDULE AT-A-GLANCESunday Reception and Registration from 5:30pm - 7:30pm East and West Faculty Lounges, Purdue Memorial Union

Monday Tuesday Wednesday Thursday Friday

8:00-8:15 Opening RemarksSTEW 214ABCD

AnnouncementsSTEW 214ABCD




8:15-8:55 Plenary Plenary Plenary Plenary Plenary

9:00-10:30 Presentations Presentations Presentations Presentations Presentations

10:30-10:45 Coffee Break Coffee Break Coffee Break Coffee Break Coffee Break

10:45-12:15 Presentations Presentations Presentations Presentations Presentations

12:15-1:45 Lunch BreakPMU East/West

Faculty Lounges

Lunch BreakPMU East/West

Faculty Lounges

Committee Meeting

PMU Lafayette Room


Faculty Lounges


Faculty Lounges

Closing Remarks

1:45-3:15 PresentationsSTEW 214ABCD

PresentationsSTEW 214ABCD

Presentations STEW 214ABCD

Poster Introduction

PresentationsSTEW 214ABCD

3:15-3:30 Coffee Break Coffee Break 3:00-6:45pmFree Afternoon

(Planned Outing)

Coffee Break

3:30-5:15 Presentations

Poster Introduction

Presentations Presentations

Evening 6:45-8:45Invited Poster

Session I*STEW 218ABCD

6:45-8:45Invited Poster

Session II**STEW 218ABCD

6:00pm Reception and

BanquetPMU East/West

Faculty Lounges

Presentation Time: Plenary (40 min); Invited (25 min) ; Contributed (20 min)

*Authors are encouraged to leave posters up all day Monday and Tuesday.**Authors are encouraged to leave posters up all day Wednesday and Thursday.

DISLOCATIONS 2016 9

MONDAY, SEPTEMBER 19Time Corresponding

Author Title Remarks

8:00-8:15 Opening Remarks

8:15-8:55 Amit Acharya Crystal Plasticity Models and Connections with Dislocation Theory Plenary

9:00-9:25 Fressengeas Claude A crystal defect field theory for coupled plasticity and fracture Invited

9:25-9:50 Alfonso Ngan Dislocation-density function dynamics – an all-dislocation, full-dynamics approach for modeling dislocation structures at both intensive and extensive scales

Invited

9:50-10:10 Philip Eisenlohr Dislocation density-based crystal plasticity modeling of single crystal Niobium

Contributed

10:10-10:30 Jaehyun Cho Coupled 3D dislocation dynamics at nano- and micro-scales Contributed

10:30-10:45 Coffee Break

10:45-11:10 Jaime Marian Unraveling the temperature dependence of the yield strength in BCC metals from atomistically-informed crystal plasticity calculations

Invited

11:10-11:35 Catalin Picu Dislocations in Molecular Crystals: Role of Molecular Flexibility in Defining the Core Structure and Critical Stresses

Invited

11:35-11:55 Jonathan Amodeo Multi-scale modeling of plasticity under pressure: from dislocation core to texture evolution

Contributed

11:55-12:15 Kaila Bertsch In situ TEM analysis of dislocation interactions with grain boundaries in BCC Metals

Contributed

12:15-1:45 Lunch Break

1:45-2:10 Grethe Winther Prediction of dislocation boundary characteristics Invited

2:10-2:35 Michael Demkowicz Towards dislocation-based models of general interfaces in crystals Invited

2:35-2:55 Martin Crimp Characterization of Dislocation Motion Across Grain Boundaries in Commercially Pure Tantalum

Contributed

2:55-3:15 Michael Marx How to Measure a Dislocation’s Breakthrough Stress and the Grain Boundary Resistance against Slip Transfer Based on the DFZ-Model of Fracture

Contributed


3:30-3:50 Yinan Cui Temperature Insensitivity of the Flow Stress in Body-centered Cubic Micropillar Crystals

Contributed

3:50-4:10 Tomoaki Niiyama Atomistic Simulations for the Interaction between Grain Boundaries and Avalanche Motion of Dislocations

Contributed

4:10-5:15 Invited Poster Introduction (See List of Invited Posters for Session I)

5:15-6:45 Free Time

6:45-8:45 Invited Poster Session I

10 DISLOCATIONS 2016

TUESDAY, SEPTEMBER 20Time Corresponding


8:00-8:15 Announcements

8:15-8:55 Nasr Ghoniem What physics have we learned from computer simulations of defect mechanics?

Plenary

9:00-9:25 Amine Benzerga Analyses of Creep using High-Temperature Discrete Dislocation Plasticity

Invited

9:25-9:50 Benoit Devincre Modeling the Bauschinger Effect and cyclic hardening in Single Crystals from Dislocation Dynamics Simulations

Invited

9:50-10:10 Satish Rao Simulations of Orientation Dependence of Strain-Hardening, Strain-Burst Characteristics and Dislocation Microstructure Evolution in 20.6mm Size Ni Microcrystals

Contributed

10:10-10:30 Roman Gröger Slip activity in bcc metals under uniaxial load Contributed


10:45-11:10 Marc Fivel 3D Dislocation Dynamics Simulations of Nanoindentation: Application to Cu/graphene Bilayer System

Invited

11:10-11:35 Jaafar El-Awady Competition between Slipping, Twinning, and their Interactions on the Hardening Response of Magnesium: Temperature and Strain Rate

Invited

11:35-11:55 Joshua Crone Displacement-controlled nanoindentation simulations with dislocation dynamics

Contributed

11:55-12:15 Caizhi Zhou Analysis of Plastic Anisotropy in Nanotwinned Copper by a Statistical Grain Boundary Dislocation Model

Contributed


1:45-2:10 Sylvie Aubry Strength of hexagonal close-packed crystals Invited

2:10-2:35 Lucia Nicola Green’s function molecular dynamics meets discrete dislocation plasticity

Invited

2:35-2:55 Yang Xiang Dislocation Climb in Discrete Dislocation Dynamics Contributed

2:55-3:15 Michaël Texier Unusual room-temperature plasticity in silicon nanopillars Contributed


3:30-3:55 William A. Curtin The stability, dissociation and cross-slip of <c+a> dislocations in Mg and other hcp metals

Invited

3:55-4:20 Vasily Bulatov Probing the Ultimate Limits of Crystal Plasticity Invited

4:20-4:20 Bob Svendsen GENERIC-based coarse-graining of the dynamics of discrete dislocation line ensembles with variable orientation

Contributed

4:40-5:00 Hariprasath Ganesan Influence of Cottrell atmospheres on dislocation mobility in ferritic iron

Contributed

DISLOCATIONS 2016 11

WEDNESDAY, SEPTEMBER 21Time Corresponding


8:00-8:15 Opening Remarks Session honoring Istvan Groma on the occasion of his 60th Birthday

8:15-8:55 Michael Zaiser Statistically averaged dislocation dynamics Plenary

9:00-9:25 Erik Van der Giessen On the temporal scale transition from discrete dislocation to continuum plasticity

Invited

9:25-9:50 Alphonse Finel Mesoscale Theory of Dislocations : from the Discrete to the Continuum

Invited

9:50-10:10 Helena Van Swygenhoven

Following dislocation patterning during fatigue with in-situ Laue micro-diffraction

Contributed

10:10-10:30 Arttu Lehtinen Glassy avalanches in 3D dislocation systems Contributed


10:45-11:10 Thomas Hochrainer Thermodynamically Consistent Continuum Dislocation Dynamics

Invited

11:10-11:35 Stefan Sandfeld A Unifying Approach towards Dislocation Microstructure in Simulation and Experiment

Invited

11:35-11:55 Peter Nellist STEM Optical Sectioning for Imaging Edge and Screw Displacements in Dislocation Core Structures

Contributed

11:55-12:15 Peter Dusan Ispanovity

The role of dislocation density in micron-scale plastic deformation Contributed


1:45-2:20 Istvan Groma Dislocation pattern formation in a 2D continuum theory of dislocations

Keynote

2:20-3:00 Invited Poster Introduction (See List of Invited Posters for Session II)

3:00-6:45 Free Time / Planned Outing

6:45-8:45 Invited Poster Session II


THURSDAY, SEPTEMBER 22Time Corresponding


8:00-8:15 Announcements Session honoring Ben Larson on the occasion of his retirement

8:15-8:55 Ben Larson Toward a Predictive Understanding of Deformation at the Mesoscale Combining Experiment and Theory

Plenary

9:00-9:25 Christoph Kirchlechner

Insights Into Dislocation Grain-Boundary Interaction By X-Ray µLaue Diffraction

Invited

9:25-9:50 Lyle Levine Full Strain and Stress Tensors Measured from Individual Dislocation Cells in Severely Plastic Deformed Aluminum

Invited

9:50-10:10 Anders Clemen Jakobsen

Mapping Dislocations In Diamond Crystals Using Dark-Field X-ray Microscopy With 200 nm Resolution

Contributed

10:10-10:30 Shengxu Xia Dislocation Patterns under Monotonic Loading of FCC Crystals Oriented for Multiple Slip

Contributed


10:45-11:10 Wolfgang Pantleon Disorientations, dislocations and slip systems Invited

11:10-11:35 Darcy Hughes Exploring the limit of dislocation based plasticity in nanostructured metals

Invited

11:35-11:55 Ludovic Thilly In-situ deformation of micro-objects combined with x-ray diffraction as a tool to uncover the elementary plasticity mechanisms: on the role of dislocation nucleation in the brittle-to-ductile transition of semi-conductors and MAX phases

Contributed

11:55-12:15 Thomas Bieler Introduction of Precisely Controlled Dislocations into SRF Cavity Nb Sheet and Their Impact on Local Superconducting Properties

Contributed

End Larson Session


1:45-2:10 Daniel Weygand Analysis Of The Deformation Behavior Of Wires Under Torsion: Insights From Simulations And Experiments

Invited

2:10-2:35 Nobuhiro Tsuji Discontinuous Yielding in Ultrafine Grained Metals Invited

2:35-2:55 Bassem Barkia In situ TEM investigation of deformation micro-mechanisms and dislocation mobility in titanium

Contributed

2:55-3:15 Dan Mordehai Nanoindentation of Thin-Films and Nanoparticles Contributed



THURSDAY, SEPTEMBER 22

FRIDAY, SEPTEMBER 23

Time Corresponding Author Title Remarks

3:30-3:55 Wei Cai Work Hardening and Athermal Strain Rate Effects in Face-Centered Cubic Metals

Invited

3:55-4:20 Maryam Ghazisaeidi First principles modeling of <c+a> dislocation geometry and interactions with solutes in Mg alloys

Invited

4:20-4:20 Xinghang Zhang Deformation mechanisms of nanotwinned Al Contributed

4:40-5:00 Abigail Hunter The role of elastic anisotropy and the gamma-surface in mesoscale dislocation simulations

Contributed

6:00 Reception and Banquet

Time Corresponding Author Title Remarks

8:00-8:15 Announcements

8:15-8:55 David Rodney Ab Initio Modeling of Dislocation Core Properties Plenary

9:00-9:25 Joel Bonneville Experimental Atomic Scale Imaging of Slip Traces in BCC Crystals Invited

9:25-9:50 Vikram Gavini Electronic Structure Study of Dislocations in Aluminum Invited

9:50-10:10 Shigenobu Ogata Atomistic study of temperature and stress dependent dislocation nucleation properties from grain boundary

Contributed

10:10-10:30 Marisol Koslowski Dislocation cross-slip mechanism in FCC metals Contributed


10:45-11:10 Giacomo Po An anisotropic non-singular theory of dislocations with atomic resolution

Invited

11:10-11:35 Thomas Swinburne The Thermal Force on a Dislocation: Resolving Anomalies In The Phonon Coupling With Zwanzig’s Technique

Invited

11:35-11:55 Keonwook Kang Characterization of Misfit Dislocation at the Ferrite/Cementite Interface in Pearlitic Steel

Contributed

11:55-12:15 Dallas Trinkle Dislocations and hydrogen: Nanoscale hydrides and pipe diffusion in palladium

Contributed

12:15 Closing Remarks


MONDAY POSTER SESSION1 Yohich Kohzuki X-ray induced defects as obstacles to dislocation motion in NaBr and KBr single

crystals

2 Shengxu Xia Dislocation Patterning under Cyclic Loading of FCC Crystals Oriented for Multiple Slip

3 Shuai Wang Interstitial atom in abnormal lattice sites under elastic field of dislocation

4 Andrea Nicolas Effect of microstructure on strain localization in a 7050 Aluminum alloy: modeling for various textures

5 Laurent Proville Quantum softening of fcc solid solutions

6 Kyoung Eun Kweon Interaction of Point Defects with Dislocations in CdTe and Nucleation of Te Precipitates

7 Yasushi Kamimura Deformation Mechanism of bcc Ti-Nb-based Gum Metal

8 Yichao Zhu Homogenisation of a row of dislocation dipoles from discrete dislocation dynamics

9 Shuozhi Xu A Concurrent Atomistic-Continuum Study of Dislocation Slip Transfer across Twist Grain Boundaries

10 Shin Takeuchi Peierls Stresses of Dislocations in a Variety of Crystals Estimated via Peierls-Nabarro Model Using ab-initio Gamma-Surface and Their Comparison with Experimantally Estimated Values

11 Ronan MADEC Dislocation Strengthening in FCC and BCC Metals in the Athermal Regime using the MobiDiC Dislocation Dynamics Code

12 Fredric Granberg Multiscale Modeling Of Dislocation-Obstacle Interaction

13 Jacques Rabier The BDT and the Core Structures of Dislocations in Silicon

14 James Ramsey Dislocation dynamics simulations of precipitate hardening

15 Hao Wang Annihilation of Non-screw Dipolar Dislocations and Debris Evolution across Time Scales

16 Hareesh Tummala Collective influence of texture, grain shape, size and dislocation density on the plasticity of polycrystalline metallic thin films

17 Yiping Chen An Anisotropic Dislocation Loop Model for Simulation of Nanoindentation of Single Crystals

18 Sachiko Nakagawa Does phonon-like motion trigger a crystalline defect?

19 Si Gao Bauschinger effect in 99% purity Al having fine grain sizes

20 Xiaohan Zhang Field Dislocation Mechanics for Quasi-static, Supersonic Applications

21 Ghiath Monnet Modeling dislocation interaction with local and extended obstacles

22 Zhiliang Zhang Ductile mechanisms of representative transition metals containing pre-existing nanovoids

23 Markus Stricker Glissile Junctions And Their Role On The Plastic Deformation At The Microscale

24 Enrique Galindo-Nava

Predicting microstructure and strength in martensitic steels


MONDAY POSTER SESSION25 Srikanth

KrishnamoorthyDynamical Approach to Displacement Jumps In Load Controlled Nanoindentation

26 Ananthakrishna G Dynamical Approach to Intermittent Nanoindentation and Indentation Size Effect

27 Alexander Stukowski

Constructing an Atomistic Crystal from a Dislocation Line Network

28 Berengere Luthi Stabilization of the Hard Core Structure of Dislocations by Interstitial Solutes in BCC Metals: a New Key Player in the Blue Brittleness of Steels

29 Johanna Gagel Dislocation microstructure evolution under tribological contacts

30 Emmanuel Clouet First-Principles Modeling of Screw Dislocation Mobility in Zr and Ti

31 Lucile Dezerald Link Between Dislocation Trajectory And Schmid Law Deviation In BCC Crystals

32 John Rotella Grain Boundary Mechanics in Nickel-based Superalloys

33 Pierre-Antoine Geslin

Modeling thermally activated plasticity at the mesoscale: dislocation climb and unpinning.

34 Christoffer Zehnder Room temperature deformation mechanisms in the Mg2Ca Laves phase and a Mg-Mg2Ca alloy

35 Amit Samanta Ab initio Energy Landscape for Dislocation Motion in Tantalum

36 DOMINGOS LOPES DA SILVA JUNIOR

Structure and Energetics of Kinks on Partial Dislocations in Ice Ih

37 Mitsuhiro Itakura First-principles calculations of interaction between carbon atoms and edge dislocation in alpha iron

38 Akiyuki Takahashi Dislocation Dynamics Study on Dislocation-Precipitate Interaction Mechanism Transition from Cutting to Orowan Looping

39 Diwakar Naragani Investigation of Nonmetallic Inclusion-Driven Failures

40 ill Ryu Microscopic investigation of strain gradient plasticity under non-proportional loading

41 Takuya Suzuki Dislocation Dynamics Modeling of Material Strength Change in Spinodally Decomposed Ferritic Fe-Cr Alloys

42 Kartik Kapoor Investigating Microstructural Features In Ti-6Al-4V Using Crystal Plasticity Finite Element Modeling

43 Andrea Rovinelli Microstructurally-short crack growth driving force identification: combining DCT, PCT, crystal plasticity simulation and machine learning technique

44 Sebastian Schröders (Nano-)Mechanical properties and deformation mechanisms of the topologically closed packed µ-phase in the Fe-Mo system

45 Sung Youb Kim Dislocation induced stress drop in cubic metals

46 Ichiro YONENAGA Dislocation Processes in Deformation of Semiconductors

47 Eyal Oren Molecular Dynamics Simulations of Dislocation Kinematics and Dynamics in Copper


MONDAY POSTER SESSION48 Inga Gudem

RingdalenDislocation-precipitate interaction in aluminum alloys

49 Jan Fikar Interaction of Prismatic Dislocation Loops with Free Surfaces by Atomistic Simulations and Experiments

50 Aritra Chakraborty Systematic identification of crystal plasticity constitutive parameters in ß-Sn

51 Vicente Salinas In Situ Monitoring of Dislocation Proliferation using Ultrasound


WEDNESDAY POSTER SESSION1 Severin Schmitt On the Representation of Internal Length Scales at the Discrete-Continuum Transition

2 Christian Heinrich Predicting fatigue crack initiation in metals using dislocation dynamics simulations

3 Pierre Hirel From glissile to sessile: the fate of <110> dislocations in perovskites deformed at high temperature

4 Jonas Verschueren Dislocation mobility: an atomistic perspective

5 In-Chul Choi Transient Mechanical Behavior of Body-Centered Cubic Chromium Studied by High-Temperature Nanoindentation

6 Yang Su Grain Boundary Resistance in Alpha-titanium Quantified by Nanoindentation and Boundary-aware Crystal Plasticity Modeling

7 Veerappan Prithivirajan

Microstructure based fatigue modeling of IN 718 produced by DMLS

8 Amuthan Ramabathiran

Finite Temperature Quasicontinuum Analysis of Dislocations in Magnesium

9 Caizhi Zhou Atomistic Modeling of Plastic Deformation of Polycrystalline Metallic Nanolayered Composites

10 Thomas Bieler Microstructural evolution in SAC105 and SAC305 solder joints with different initial cooling rates and thermal cycling conditions using HE-XRD

11 Frederic Sansoz Atomistic mechanisms of dislocation nucleation and interactions with perfect and imperfect twin boundaries

12 Ajey Venkataraman Role Of Grain Boundary Sliding In Deformation Of Polycrystalline Materials

13 Alexander Barashev Dislocations in radiation damage of materials for nuclear energy applications

14 Christophe TROMAS Understanding of brittle to ductile transition in nano-lamellar phase: case of the Ti2AlN phase

15 Jeffrey Lloyd Non-linear elastodynamic effects of dislocation generation and motion in shock waves

16 Yifei Zeng, Marisol Koslowski

The influence of structural changes on the critical size of crystals upon mechanical milling

17 Eric Hintsala Back Stress Analysis of Hardening in Sub-50nm Si Nanocubes

18 Seunghwa Ryu Stability of Eshelby Dislocations in FCC Crystalline Nanowires

19 Leonardo Agudo Jácome

Three-dimensional Quantitative Dislocation Analysis and the High Temperature Creep Behavior of Ni-Base Single Crystal Superalloys

20 Hikmatyar Hasan Multi-scale modelling of high-temperature deformation mechanisms in Co-Al-W-based superalloys.

21 Aboozar Mapar Hydroforming and failure of a large grain pure niobium tube

22 Andreas Prahs A strain gradient plasticity theory accounting for multi-slip

23 Ryan Sills Orowan Looping with Platelet-like Precipitates in Overaged Aluminum-Copper Alloys


WEDNESDAY POSTER SESSION24 Thomas Bieler Subsurface Dislocation Slip Analysis using 3D Crystal Plasticity with a Non-local

Constitutive Description

25 Harsha Phukan Crystal Plasticity based Modeling and Experimental Analysis of Slip Transfer in Commercial Purity Titanium

26 Di Kang Identification of Activated Slip Systems in High Purity Single Crystal Niobium Used for Particle Accelerator Cavities

27 Philip Eisenlohr Boundary Layer Formation in Continuum Dislocation Dynamics

28 Vassili Vorontsov Determination of superlattice stacking fault energies in multi-component superalloys.

29 Zahra Molaeinia Dislocation Mediated Plasticity in Hydrogen Charged Metals: Coupled Non-Linear Finite Element and Discrete Dislocation Dynamics Simulations

30 Zhengxuan FAN Molecular dynamics simulation of surface cyclic slip irreversibility in vacuum and in oxygen environments in fcc metals

31 Christopher Barrett Dislocation Transmutation through twin interfaces in hexagonal close-packed materials

32 Stefanos Papanikolaou

Size effects and stochastic plastic flow during uniaxial crystal compression: a minimal discrete dislocation model

33 Alireza Ebrahimi Continuum Dislocation Dynamics Simulations of Micro-Scale Plasticity

34 Roman Kositski Strength of Fe Single-Crystalline Nanoparticles under Compression

35 Alon Malka-Markovitz

Stress-Dependent Activation Parameters for Cross-Slip in FCC Metals

36 Babak Kondori Effects of taper on micropillar compression: A discrete dislocation simulation

37 Mahmoud Mousavi Dislocation-based fracture within nonlocal anisotropic elasticity

38 Mehran Monavari Annihilation, Sources and Junctions in Continuum Dislocation Dynamics

39 Giacomo Po Mechanics of Defect Evolution Library (MoDELib)


Plasticity Models and connections with Dislocation Theory

Anish Roy1, Saurabh Puri2, Amit Das3, Akanksha Garg4, Xiaohan Zhang5,Amit Acharya6

6119 Porter Hall, Civil & Environmental Engineering, Carnegie Mellon University, Pittsburgh, PA 15215, USA, email: [email protected]; 1Loughborough University,U.K.; 2Simulia, Inc., USA; 3Indian Institute of Technology, Bombay, India; 4FM Global,

USA; 5Stanford University, USA.

ABSTRACT

We show how the structure of classical plasticity theory (including crystal plasticity) is a natural averaged picture of microscopic, time-dependent, dislocation dynamics, stated in the language of nonlinear partial differential equations; a brief history of this identification, starting from the elastic theory of continuously distributed dislocations will naturally be implicit in our presentation. Both the microscopic and meso-macroscopic models will be illustrated with selected results. Due to the nonlinearity, complexity, and time-dependence of any physically reasonable microscopic model of dislocation dynamics, understanding what may constitute meaningful and practical questions for developing a closed macroscopic model of crystal plasticity is in itself a subtle endeavor. We will outline one such set of questions directed towards deriving constitutive equations for the averaged macroscopic model described above and, time permitting, describe our present efforts in that direction.

It is a pleasure to acknowledge collaborations with Armand Beaudoin, Claude Fressengeas, Satya Varadhan, and Noel Walkington.

PLENARY SPEAKER ABSTRACTS


What physics have we learned from computer simulations of defect mechanics?

Nasr Ghoniem1, Giacomo Po1, Yinan Cui1, Tamer Crosby2, Andrew Sheng1, and Can Erel1

1University of California, Los Angeles, Los Angeles, CA 90095-1597, USA2 Alberta Innovates Technology Futures, Alberta, Canada

ABSTRACT

Computer simulations of defect mechanics have been developed over the past decade to be predictive, requiring minimal data input. Moreover, many experiments have been implemented to directly confront these computer simulations at the comparable time and length scales. Such advances have enabled higher levels of confidence in computer simulations as virtual laboratory tool that can be used to understand the underlying physics.Thus, the focus of defect physics and mechanics has shifted from predicting the macroscopicresponse of the material (such as the stress-strain behavior), to providing the database that can be used to construct simpler models based on the dominant physical mechanisms. In this presentation, we review the progress made in discrete defect mechanics, and how it has advanced to a predictive stage of both plastic deformation and complex fracture processes. We also discuss major physical insights that have emerged from such computer simulations,beyond predictions of macroscopic constitutive equations. The review include: theoretical connections between plasticity and fracture, the physics of plastic deformation of bcc metals at the micro scale, the phenomena associated with steady and cyclic deformation of fcc metals, the origins of strain bursts and dislocation avalanches, and the scaling laws of self-organized and tuned criticality of plastic flow, described as a complex dynamical system near criticality.

[1] [N.M. Ghoniem, S.-H. Tong, L. Sun, Parametric dislocation dynamics: a thermodynamics-based approach to investigations of mesoscopic plastic deformation, Phys. Rev. B 61 (2)(2000) 913.

[2] G. Po, N.M. Ghoniem, A variational formulation of constrained dislocation dynamics coupled with heat and vacancy diffusion, J. Mech. Phys. Solids 66 (2014) 103–116.

[3] G. Po, M. Mohamed, T. Crosby, C. Erel, A. El-Azab, N.M. Ghoniem, Recent progress in Discrete Dislocation Dynamics and its applications to micro plasticity, JOM – J. Miner. Met. Mater. Soc. 66 (10) (2014) 2108–2120.

[4] Tamer Crosby, Giacomo Po, Can Erel and Nasr Ghoniem, “The origin of strain avalanches in sub-micron plasticity of fcc metals,” Acta Materialia, 89 (2015) 123–132.

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, under Award Number DE-FG02-03ER54708, and the US Air Force Office of Scientific Research (AFOSR), under award number FA9550-11-1-0282.



Toward a Predictive Understanding of Deformation at theMesoscale Combining Experiment and Theory

Bennett C. Larson

Materials Science & Technology Div., Emeritus, Oak Ridge National Laboratory,Oak Ridge, TN 37831, USA, [email protected]

The formulation of a predictive understanding of mesoscale deformation in ductile materials represents both an experimental and computational grand challenge. Although the task remains formidable, broad advances toward understanding and predicting dislocation-mediated deformation have been made on both the experimental and computational fronts over the last 20 years. These advances have been enabled by the ongoing development of increasingly powerful electron and synchrotron x-ray based surface and three-dimensional microscopies along with concomitant progress in both theory and computational techniques. Progress toward the goal of afundamental and quantitatively predictive understanding of the statistical dynamics of interacting dislocations and dislocation densities on mesoscopic length scales in complex, heterogeneous materials microstructure will be highlighted and discussed, underscoring direct comparisons ofdeformation measurements with theory and computations. Experimental capabilities and deformation investigations including electron backscattering microscopy, high-energy monochromatic 3D x-ray microscopy (3DXM), and white beam 3D x-ray microscopy techniques will be considered and related to deformation simulations including finite-element modeling(FEM), discrete dislocation dynamics (DD), and continuum dislocation dynamics (CDD). The use of the dislocation density tensor introduced by Nye and Kröner will be discussed as a direct,quantitative, spatially resolved link between experimental measurements and deformation simulations on mesoscopic length scales. Examples of such linkages will be presented forsubmicron-resolution 3DXM studies of deformation in Cu at the Advanced Photon Source in relation to FEM simulations of spherical microindentation and both DD and CDD simulations of uniaxial strain in Cu, including an outlook for future mesoscale investigations.

This research was supported by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Science and Engineering Division and by the Center for Defect Physics an Energy Frontier Research Center. The Advanced Photon Source is supported by the Department of Energy, Scientific Users Facility Division.



Ab Initio Modeling of Dislocation Core Properties

David Rodney1, Emmanuel Clouet2, Lisa Ventelon2, Laurent Proville2, Lucile Dezerald3,Bérengère Lüthi2, François Willaime4

1Institut Lumière Matière, Université Lyon 1, CNRS, UMR 5306, 69622 Villeurbanne,France ; [email protected]; 2CEA, DEN, Service de Recherches de

Métallurgie Physique, 91191 Gif-sur-Yvette, France; 3Institut Jean Lamour, Université de Lorraine, SI2M, F-54011 Nancy, France; 4CEA, DEN, Département des Matériaux

pour le Nucléaire, 91191 Gif-sur-Yvette, France.

ABSTRACT

The modeling of dislocations and their mobility using ab initio density functional theory (DFT) calculations has made tremendous progress these past few years, in part thanks to an increase in computing power, but also because of methodological developments, including methods to correct the energy for elastic interactions between periodic images. In this talk, we will review recent advances in dislocation plasticity based on ab initio calculations, mainly in body centered cubic (BCC) and hexagonal close packed (HCP) metals. In BCC transition metals, we will discuss our new understanding of the screw dislocation two-dimensional Peierls potential and its close connection to the well-known deviations from the Schmid law. We will also see how a line tension model can be used to predict kink-pair energies from DFT data. Alloying effects on the dislocation core structure and mobility will be addressed; highlighting in particular how interstitial atoms can restructure the screw dislocation core. In HCP metals, we will show how DFT calculations identified stable and metastable dislocation cores, how these cores are related to slip in different slip systems and how an inversion of stability between a glissile and a sessile core explains the profoundly different plastic behaviors observed by in-situ TEM in Zr and Ti. Alloying effects will also be discussed in HCP metals. Finally, the talk will serve as a basis for discussion on the challenges and opportunities to bridge these small-scale simulations with higher-scale models and simulations.

David Rodney is a Professor at the Institut Lumière Matière of the University of Lyon in France. Prior to this, he was an Associate Professor at the Institute of Technology of Grenoble. Prof. Rodney is an engineer of Paris School of Mines with a M.S. degree from Jussieu University in Paris in Solid State Physics. He received a Ph.D. in Materials Science for research performed at Caltech, Brown University and the CEA Saclay, and was a post-doctoral fellow at ONERA. Prof. Rodney has been an invited researcher at MIT and the University of Chicago. His research is focused on the modeling of materials at different length and time scales, with a particular emphasis on linking elementary processes at the atomic scale with meso- and macroscopic properties. He has published over 80 papers in scientific journals. Since 2012, he is an editor at Acta Materialia.



Statistically Averaged Dislocation Dynamics

Michael Zaiser

FAU University of Erlangen-Nürnberg, Department of Materials Science, Institute for Materials Simulation WW8, Dr.-Mack-Str. 77, 90762 Fürth, Germany

ABSTRACT

On length scales above the dislocation core size, dislocations are commonly envisaged as discrete line-like objects whose evolution is described by discrete dislocation dynamics. On scales above the spacing of the discrete dislocations up to the macroscale, it is desirable to describe the same objects in terms of averaged, density-like variables whose evolution can be formulated in a continuum framework, thus establishing the link with continuum elasto-plasticity. We discuss the challenges faced in obtaining density-based formulations of dislocation dynamics by statistical averaging of the properties and evolution of discrete dislocation systems. We demonstrate a formal averaging procedure based upon ensemble averages that can be used to obtain statistically averaged descriptions of the geometry, kinematics, energetics and dynamics of systems of three-dimensionally curved dislocations in terms of density-like fields. An averaged energy functional is derived which expresses the elastic energy of a dislocation system in terms of these field variables. By combining this functional with the constraints and conservation laws that govern dislocation kinematics, we show how a class of thermodynammically consistent, closed theories of continuum dislocation dynamics can be derived which are rigorously founded in the underlying discrete dynamics of dislocation systems. The performance of such theories is demonstrated by comparison with the underlying discrete dynamics for various benchmarking examples. We discuss the relationship between our work and other density-based approaches towards dislocation microstructure evolution, ranging from the classical work of Mura and its recent extensions, over the very different but complementary work of Kocks and Mecking, to recent screw-edge theories of dislocation transport. In conclusion, open questions and intrinsic limitations of the approach are discussed.

[1] T. Hochrainer, S. Sandfeld, M. Zaiser and P. Gumbsch, Continuum dislocations dynamics: towards a physical theory of crystal plasticity. Journal of the Mechanics and Physics of Solids63, 167-178 (2014).[2] M. Zaiser, Local density approximation for the energy functional of three-dimensional dislocation systems, Physical Review B 92, 174120 (2015).[3] T. Hochrainer, Thermodynamically consistent continuum dislocation dynamics. Journal of the Mechanics and Physics of Solids, 88, 12-22 (2016).

This presentation is based upon joint work of various groups (M.Zaiser, T. Hochrainer, S. Sandfeld, P. Gumbsch and others) which is supported by DFG in the framework of the research unit FG-1650 “Dislocation based Plasticity” .



Dislocations in a quantum crystal

Sébastien Balibar1, John R. Beamish2, Andrew D. Fefferman3, Ariel Haziot4, Xavier Rojas5, Fabien Souris6

1Laboratoire Pierre Aigrain, Departement de Physique, Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex05, France, [email protected]

2 Department of Physics, University of Alberta, Edmonton, Canada T6G 2E13 Université Grenoble Alpes, Institut Néel, BP 166, 38042 Grenoble Cedex 9, France

4 Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA

5 Department of Physics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK

6 Department of Physics, University of Alberta, Edmonton, Canada T6G2E1

ABSTRACT

Solid helium is paradoxical: it is both a model and an exception. It is a model for crystalproperties mainly because of its extreme purity which makes universal phenomena simpler and easier to identify. It is also exceptional because the large quantum fluctuations of atoms around the nodes in their crystal lattice allow these phenomena to occur at vey low temperature with a large amplitude. The properties of helium 4 crystals illustrate how the motion of dislocations may reduce their shear elastic modulus, as it does in all hexagonal close packed (hcp) crystals including metals. But this motion takes place without anydissipation in the limit of T=0 and in the absence of impurities, which is now exceptional andleads to a very large elastic anomaly at low temperature, which was called "giant plasticity" by Haziot et al.[1]. More recently, we have discovered that, in helium 4 crystals, helium 3 impurities are not necessarily fixed pinning centers for dislocations. Even at relatively large velocities, dislocations are able to move dressed with impurities[2]. This illustrates what is really quantum in these crystals: it is mainly the dynamics of their dislocations and the behavior of impurities. We were also able to measure the dislocation density, their length distribution, their scattering with thermal phonons, the distribution in binding energy to helium 3 impurities[3], etc.

[1] A. Haziot, X. Rojas, A. D. Fefferman, J.R. Beamish, and S. Balibar, Phys. Rev. Lett. 110,035301 (2013).[2] A. Haziot, A.D. Fefferman, F. Souris, J. R. Beamish, H. J. Maris, and S. Balibar, Phys. Rev.B 88, 014106 (2013).[3] A. D. Fefferman, F. Souris, A. Haziot, J. R. Beamish, and S. Balibar, Phys. Rev. B 89, 014105 (2014).

We acknowledge support from NSERC (Canada) and from the European Research Council grant AdG 247258-SUPERSOLID.

Unraveling the temperature dependence of the yield strength in BCC metals from atomistically-informed crystal plasticity

calculations

Authors: D. Cereceda1,2, M. Diehl3, F. Roters3, D. Raabe3, Jaime Marian1

1 Department of Materials Science and Engineering, University of California Los Angeles, Los Angeles, CA 90095, USA

2 Department of Civil Engineering, Johns Hopkins University, Baltimore, MD 21218,USA

3 Theory and Simulation Group, Max-Planck-Institut für Eisenforschung, 40237Düsseldorf, Germany

ABSTRACT

The plastic behavior of body-centered cubic (BCC) single crystals is governed by screw dislocation glide on close-packed crystallographic planes. Screw dislocation motion occurs via thermally-activated nucleation and relaxation of so-called kink pairs on a periodic energy substrate known as the Peierls potential. A long standing puzzle regarding BCC plasticity has been the discrepancy between the measured values of the flow stress in tensile deformation tests and the calculated values of the Peierls stress at the atomistic scale. Here, we present a model that unifies both concepts and provides a justification for the differences in terms of the non-Schmid behavior displayed by BCC crystals. Our model consists of a crystal plasticity microstructural engine parameterized entirely using atomistic calculations, that includes full non-Schmid effects as well as a physically-consistent flow rule constructed on the basis of thermally activated screw dislocation glide. We apply the methodology to yielding in tungsten and show that available experimental measurements can be explained and reproduced by accounting for these two very important features of BCC plasticity. The validated methodology is used to predict strength as a function of several state variables in W single crystals.


Interstitial atom in abnormal lattice sites under elastic field of dislocation

Authors: Shuai Wang1, 2, 3, Ian M. Robertson1, 2, 3, and Petros Sofronis1, 4

Affiliations: 1International Institute for Carbon Neutral Energy Research (WPI-I2CNER), Kyushu University, 744 Moto-oka, Nishi-ku, Fukuoka 819-0395, Japan;

2Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison WI;

3 Department of Engineering Physics, University of Wisconsin-Madison, Madison, WI.4Department of Mechanical Science and Engineering, University of Illinois at Urbana-

Champaign, Urbana, IL.

ABSTRACTThe strain tensors of H, He atoms in body-centered cubic (BCC) iron were calculated byusing density functional theory, and the interaction energies of these atoms with the elastic field of edge and screw dislocations were obtained based on anisotropic linear continuum elasticity theory [1, 2]. Two type of trapping sites, octahedral site (O-site) and tetrahedral site (T-site) were investigated. Hydrogen and helium atoms should be trapped in T-site in a perfect BCC iron lattice, however, under the elastic field of a dislocation, all the atomstrapped in O-site are found to have stronger interaction with dislocation than in the T-site. For instance, by jumping from T-site to O-site, the interaction energy of the screw dislocation andH atom located 4b away changes from -0.013 eV to -0.12 eV, which is comparable with the edge dislocation case (-0.15 eV). This finding stresses the role of interstitial and screw dislocation interaction on modifying the mechanical property of body-centered cubic metals,and it may bring new understanding on the dislocation behavior with an accompanying soluteatmosphere.

[1] A.W. Cochardt, G. Schoek, H. Wiedersich, Interaction between dislocations and interstitial atoms in body-centered cubic metals, Acta Metallurgica. 3 (1955) 533–537.

[2] R.M. Douthwaite, J.T. Evans, Interaction between a tetragonal distortion and a 〈111〉screw dislocation in an anisotropic cubic crystal, Scripta Metallurgica. 7 (1973) 1019–1026.

The authors gratefully acknowledge the support of the International Institute for Carbon Neutral Energy Research (WPI-I2CNER), sponsored by the World Premier International Research Center Initiative (WPI), MEXT, Japan, and the support of the National Science Foundation through Award No. CMMI-1406462.

Solid Solution Hardening and Dynamic Strain Ageing in Fe-X Alloys (X = C, Si, Ni, Al, Cr)

Daniel Caillard

CEMES-CNRS, 29 rue Jeanne Marvig, BP94347, 31055 Toulouse, [email protected]

ABSTRACT

Iron is the perfect model material to study Peierls friction forces and the influence of solute atoms on mechanical properties, at low and high temperatures.Alloying induces a strong hardening close to room temperature which can be interpreted in terms of a Cottrell interaction between dislocations and immobile solute atoms. Which dislocations (screws or edges) are responsible for hardening remains however unclear.At high temperatures, dislocations interact dynamically with various interstitial or substitutional solute atoms, leading to dynamic strain ageing (DSA). Here again, the detailed mechanisms are not well understood. In particular, alloys containing carbon and substitutional atoms with no affinity with carbon exhibit DSA in the same temperature range as iron containing carbon only, whereas alloys containing carbon and substitutional atoms with strong affinity with carbon exhibit DSA at a much higher temperature. The respective roles of interstitial and substitutional atoms in DSA are thus to be determined.To interpret these properties, in situ straining experiments have been carried out in a JEOL 2010 transmission electron microscope, between 100K and 800K, in pure Fe and in various binary FeC, FeNi, FeSi, FeCr and FeAl alloys. The results show that solid solution hardening between 200K and 300K results from the pinning of screw dislocations at super-jogs formed by cross-slip in the vicinity of substitutional solute atoms [1]. The corresponding hardening has been clearly correlated to the density of pinning points and to the concentration of solute atoms.Dynamic strain ageing has also been studied above room temperature. The effect of interstitial carbon is characterized by two different dislocation-solute interactions in the jerky flow and serrated flow temperature domains, and by a surprisingly low mobility of screw dislocations controlled by a high-temperature resurgence of the Peierls mechanism [2]. Substitutional atoms can either move the domain of dynamic strain ageing to higher temperatures or not, depending on their chemical affinity for carbon. The results are interpreted by a shielding effect of carbon atoms connected to dislocations, inhibiting the interaction between dislocations and substitutional atoms [3].

[1] D. Caillard, Acta Mater: 61, 2793 and 2808 (2013).[2] D. Caillard and J. Bonneville, Scripta Mater: 95, 15 (2015).[3] D. Caillard submitted


Effect of microstructure on strain localization in a 7050 Aluminum alloy: modeling for various textures

Authors: Alberto W. Mello1, Andrea Nicolas1,*, Ricardo A. Lebensohn2, Michael D. Sangid1

Affiliations: 1 School of Aeronautics and Astronautics, Purdue University, 701 W. Stadium Ave, West Lafayette, IN 47907-2045, USA; 2 Materials Science and Technology

Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA;*Corresponding Author, e-mail address: [email protected]

ABSTRACT

The purpose of this study is to find the residual strain fields on the microstructure for different orientations and assess their predictability by means of Crystal Plasticity Fast Fourier Transform (CP-FFT) formulation. The microstructure for rolled Al7050-T7451 was experimentally obtained with an EBSD scanner along the rolling direction (L-T orientation), across the rolling direction (L-T orientation), and transverse the rolling direction (T-Sorientation), all of which were converted to columnar models by using Dream3D, and analyzed under uniaxial tension and release by using Lebensohn’s CP-FFT formulation with an imposed macroscopic strain rate. The residual strain fields found on the simulation were then compared to the fields found on the specimens via Digital Image Correlation (DIC), which used micro stamping along with the patterning protocol.The results showed that the levels of strain concentration predicted by the simulation were reasonable on all three specimens, however the match between both actual and predicted strain fields needs improvement. Further studies use columnar Al7050-T7451 on the experiments, consider slip system selective hardening on the mathematical model, and increase resolution on the micro stamped pattern size to improve the match between strain fields.

The authors gratefully acknowledge funding from the Office of Naval Research, N00014-14-1-0544. RAL acknowledges support from the Joint DoD/DOE Munitions Technology Programs. Also, the authors graciously acknowledge technical support and advice from Mr. Andrea Rovinelli (EVP-FFT) and Major Todd Book (EBSD). Drs. Jacob Hochhalter and Andrew Cannon are thanked for their help with the micro stamping design, development, and procedure.

Quantum softening of fcc solid solutions

M. Landeiros dos Reis1, A. Choudhury1 and L. Proville1

1CEA, DEN, Service de Recherches de Métallurgie Physique, Gif-sur-Yvette 91191, France.

ABSTRACT

Below one hundred Kelvin, the quantum fluctuations were found to decrease the Peierls stress of screw dislocations in various atomic-scale models for bcc Fe [1, 2]. We have found that the very same effect is also present in the glide of ½ <110>{111} dislocations in various fcc solid solutions. The zero point energy of the simulation cell is shown to vary opposite to the potential energy along the dislocation glide. As a result the computation for the critical shear stress is systematically lower when quantum fluctuations are taken into account thence yielding quantum softening. The present results allow us to expect that quantum softeningmay occur in a wide variety of materials.

[1] L. Proville, D. Rodney and M.C. Marinica, Nature Mater., 11, 845 (2012)[2] B. Barvinschi, L. Proville and D. Rodney, Modelling Simul. Mater. Sci. Eng. 22, 025006

(2014)


Investigation of post-irradiation fracture toughness responseusing 3D dislocation dynamics simulations

Christian Robertson1, Kadiri Gururaj2

1CEA, DEN, SRMA, Building-455, F91191 Gif-sur-Yvette, France; 2Materials Science Group, IGCAR, Kalpakkam, 603 102 Tamil Nadu, India.

ABSTRACT

Ferritic alloys are widely used as structural nuclear materials, thereby submitted to several dose-dependent evolutions. This paper focuses on the fracture toughness response evolutionsincluding: the Ductile to Brittle Transition Temperature (DBTT) shift and the Upper Shelve Toughness (UST) reduction. A screw dislocation mobility scheme is adopted first, based on kink-pair nucleation and their subsequent propagation at finite velocity, bearing in mind that «dislocation motion appears to be the factor defining the nature of the brittle-ductile transition». This approach ensures a gradual dislocation velocity evolution across the whole ductile to brittle transition. A set of parameters representative of Fe-Cr crystals is thenevaluated according to the selected mobility scheme, using experimental inputs. These parameters are then implemented in three-dimensional Dislocation Dynamics (DD)simulations, representative of irradiated and non-irradiated Fe-Cr bulk grains, strained atdifferent temperatures in the 50-300°K range. Our calculation results are consistent with a radiation-induced downshift of the apparent straining temperature «∆T», that proved comparable to the DBTT changes measured in the same irradiation conditions. The USTreduction is then analysed through its link with the work-hardening ability at the grain-scale.This investigation takes advantage of an original micro-mechanical model [1], accounting for experimental EBSD data on the grain size and grain orientation distributions.

[1] K. Gururaj, C. Robertson, M. Fivel, J. Nuclear Materials, 459, 194 2015.

Acknowledgement: This work has been carried out within the framework of the EUROfusionConsortium and has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 633053.

Interaction of Point Defects with Dislocations in CdTe and Nucleation of Te Precipitates

Kyoung E. Kweon and Vincenzo Lordi

Material Science Division, Lawrence Livermore National Laboratory, 7000 East Avenue, L-413, Livermore, CA 94550, USA (email: [email protected])

ABSTRACT

Cadmium telluride (CdTe) and its alloy cadmium zinc telluride (CZT) are among the highest performing semiconductor materials for room-temperature X-ray and γ-ray detectors. However, their performance has been limited by spatially non-uniform carrier trapping by deep-leveldefects. Dislocations are of particular interest, since point defects, impurities, and Te-rich secondary phases that are known to trap charge may be associated with dislocations, and dislocations also may trap carriers themselves. The distribution of dislocations in CdTe or CZT crystals often has been observed to be very non-uniform.

In this work, we determine the interaction of various point defects (Cd vacancies, Te interstitials, and Te anti-site defects) with 30° partial dislocations in CdTe using density functional theory(DFT). Our calculations predict that the defect formation energies decrease strongly as the defects get closer to the dislocation cores and that defects located in the dislocation core significantly modify the defect states associated with the dislocation. In addition, we calculate migration energies of the defects along the dislocation line and binding energies of multiple defects within the dislocation cores. We find that some defects are very mobile along the dislocation line, and defect–defect interactions promote clustering within or near the dislocations. Lastly, we investigate Te precipitation near dislocations using semi-empirical molecular dynamics simulations with large numbers of excess Te added to the defect–dislocationsystems, based on results from our DFT calculations. We show the role of dislocations on Te precipitation by comparing to the dynamics in the absence of dislocations. Better understanding of the properties of dislocations decorated with various point defects and Te precipitates can help devise growth and processing procedures for improved detector performance.

Prepared by LLNL under Contract DE-AC52-07NA27344 and funded by the U.S. DOE/NNSAOffice of Defense Nuclear Nonproliferation R&D.

LLNL-ABS-803713


Deformation Mechanism of bcc Ti-Nb-based Gum Metal

Y. Kamimura1, S. Katakura1, K. Edagawa1, S. Takeuchi2, S. Kuramoto3, T. Furuta4

1Institute of Industrial Science, The University of Tokyo, Meguro-ku, Tokyo 153-8505,Japan [email protected]; 2Tokyo University of Science, Kagurazaka, Shinjuku-

ku, Tokyo 162-8601, Japan; 3Ibaraki University, Hitachi, Ibaraki 316-8511, Japan; 4Toyota Central R & D Laboratory, Nagakute, Aichi 480-1192, Japan

ABSTRACT

Gum Metal was developed in Toyota Central Laboratory as an alloy having multi-functional properties [1]. The striking feature of cold-swaged Gum Metal is that the deformation mechanism has been interpreted to be a dislocation-free shear process at the ideal shear strength. However, the present authors have shown recently from the extensive deformation experiments,including thermal-activation analysis, on Gum Metal single crystal samples and cold-swaged polycrystalline samples that the deformation behavior is not at all special but quite consistent with the dislocation-glide controlled deformation mechanism of bcc alloys both for single crystals and cold-swaged samples; i.e., Peierls mechanism below the room temperature and alloy hardening mechanism above the room temperature. τχ-χ and ψ-χ relations of single crystals show typical asymmetry of slip in bcc crystal, indicating that Gum Metal belongs to {112} slip type as generally observed in B2 ordered bcc alloys. This means that due to partial B2 ordering in Gum Metal [2], screw dislocation core is necessarily of polarized type and translates zigzag changing the polarity alternately along {112} plane, as shown in computer modelling of dislocation motion in B2 crystal [3].

[1] T. Saito, T. Furuta, J.-H. Hwang, S. Kuramoto, K. Nishino, N. Suzuki, R. Chen, A. Yamada, K. Ito, Y. Seno, T. Nonaka, H. Ikehara , N. Nagasako, C. Iwamoto, Y. Ikuhara, T. Sakuma, Science, 300, 464 (2003).

[2] J.-P. Liu, Y.-D. Wang, Y.-L. Hao, Y. Wang, Z.-H. Nie, D. Wang, Y. Ren, Z.-P. Lu, J. Wang, H. Wang, X. Hui, N. Lu, M. J. Kim, R. Yang, Scientific Rep. 3, 2156 (2013).

[3] S. Takeuchi, Philos. Mag. A, 41, 541 (1980),

Dislocation Climb in Discrete Dislocation Dynamics

Authors: Yang Xiang1, Yejun Gu2, David J. Srolovitz3

Affiliations: 1Department of Mathematics, Hong Kong University of Science andTechnology. Email: [email protected]; 2Nano Science and Technology Program, Hong

Kong University of Science and Technology; 3Department of Materials Science andEngineering & Department of Mechanical Engineering and Applied Mechanics,

University of Pennsylvania.

ABSTRACT

We derive a Green's function formulation for the climb of curved dislocations and multiple dislocations in three-dimensions. In this new dislocation climb formulation, the dislocationclimb velocity is determined from the Peach–Koehler force on dislocations through vacancydiffusion in a non-local manner. The long-range contribution to the dislocation climb velocityis associated with vacancy diffusion rather than from the climb component of the well-known,long-range elastic effects captured in the Peach–Koehler force. Both long-range effects areimportant in determining the climb velocity of dislocations. Analytical and numericalexamples show that the widely used local climb formula, based on straight infinitedislocations, is not generally applicable, except for a small set of special cases. We alsopresent a numerical discretization method of this Green's function formulation appropriate forimplementation in discrete dislocation dynamics (DDD) simulations. In DDDimplementations, the long-range Peach–Koehler force is calculated as is commonly done,then a linear system is solved for the climb velocity using these forces. This is also donewithin the same order of computational cost as existing discrete dislocation dynamicsmethods.

[1] Y.J. Gu, Y. Xiang, S.S. Quek, and D.J. Srolovitz, Three-dimensional formulation of dislocation climb, J. Mech. Phys. Solids, 83, 319-337, 2015.

[2] Y.J. Gu, Y. Xiang, and D.J. Srolovitz, Relaxation of low angle grain boundary structure by climb of the constituent dislocations, Scripta Mater., to appear, 2015.

This work was partially supported by the Hong Kong Research Grants Council General Research Fund 16302115.


Strain and rotation fields about dislocations in graphene: Theories and experiments

Authors: Luis L. Bonilla1, Ana Carpio2, Chungchen Gong3, Jamie H. Warner3

Affiliations: 1G. Millán Institute, Universidad Carlos III de Madrid,[email protected]; 2Applied Mathematics Dept., Universidad Complutense de

Madrid; Dept. of Materials, University of Oxford.

ABSTRACT

Strain fields, dislocations and defects may be used to control electronic properties of graphene. By using advanced imaging techniques with high-resolution transmission electron microscopes, we have measured the strain and rotation fields about dislocations in monolayer graphene with single-atom sensitivity [1]. These fields differ qualitatively from those given by conventional 2D linear elasticity. To explain the measurements, we have found the exact strain and rotation field about dislocations in 2D hyperstress theory [2] and solved numerically two different continuum theories regularized by using finite differences on a hexagonal lattice and periodizing differences along primitive directions: 2D linear elasticity and the Föppl-von Kármán plate equations [1]. The latter provides the best agreement with measurements and yields information on out-of-plane atomic displacements. Even at atomic distances, continuum theories regularized on the graphene lattice give surprisingly good quantitative descriptions of the measured strains and rotations provided these fields are calculated by geometric phase analysis of atomic positions based on the displacement vector of dislocations, and not by the usual formulas for strain and rotation.

[1] L.L. Bonilla, A. Carpio, C. Gong, J.H. Warner, Measuring strain and rotation fields at the dislocation core in graphene, Physical Review B, 92, 155417 (2015)

[2] R.D. Mindlin, Micro-structure in Linear Elasticity, Arch. Rat. Mech. Anal. 16, 51-78(1964).

Atomistic study of temperature and stress dependent dislocation nucleation properties from grain boundary

Shigenobu Ogata1,2 and Junping Du1

1Department of Mechanical Science and Bioengineering, Osaka University,1-3 Machikaneyama-cyo, Toyonaka, Osaka 560-8531, JAPAN

E-mail: [email protected] Strategy Initiative for Structural Materials, Kyoto University,

Sakyo, Kyoto 606-8501, JAPAN

ABSTRACT

The mechanical response of ultrafine grained metals, which may have limited number of dislocation source in the grains, are dominated by the dislocation nucleation from grain boundary (GB). The dislocation nucleation from GB has been frequently studied using molecular dyanamis (MD) to reveal atomistic details and energetics of the dislocation nucleation events. However, since usual MD simulation has limited timescale of nanoseconds, the dislocation nucleation processes with low frequency at low temperature and stress has not been discussed yet. To extend the timescale of MD simulation, we use an accelerated MD mothod, such as the adaptive-boost MD, which has recently been developed in our group. In the present research, we figure out the dislocation nucleation mechanism map of a symmetric tilt GBs with structural unit of ‘E’ in FCC Cu. The nucleation event is accelerated to the time-scale of experiments, such as nucleating one dislocation per second at 300K. It is found that the nucleation process is governed by atomic shuffling-assisted dislocation nucleation below a critical stress, which can only be studied by adaptive-boost MD at the time-scale of second. With increasing uniaxial tensile stress, the dislocation nucleation mechanism changes from the diffusive (local atomic shuffling) to displasive (collective nucleation without shuffling) mode. The critical stress for the mechanism transition dramatically decreases with increasing temperature. Based on the temperature- and stress-dependent critical stress, a dislocation nucleation map is obtained for the tilt GBs containing ‘E’ structural unit. This study explored the dislocation nucleation mechanisms over a wide range of grain boundaries and time-scales.


Temperature Insensitivity of the Flow Stress in Body-centered Cubic Micropillar Crystals

Yinan Cui, Giacomo Po, Nasr Ghoniem

Mechanical and Aerospace Engineering Department, University of California at Los Angeles (UCLA), Los Angeles, CA 90095, U.S.A. [email protected]

ABSTRACT

Plasticity of body-centered cubic (BCC) crystals is known to have a strong dependence on temperature, as a direct consequence of the thermally-activated process of kink pair nucleation and migration with a high energy (Peierls) barrier. Here we demonstrate that, in the sub-micron size scale, such strong temperature dependence of the flow stress must disappear. We explore the flow stress and hardening behavior of micro-pillar sizes in the range 200-2000 nm at temperatures of 150-900 K. Discrete Dislocation Dynamics (DDD) simulations reveal that the weak temperature sensitivity can be rationalized in terms of the weak role of screw dislocations in controlling plasticity; unique to small crystals of finite size. It is shown that finite, sub-micron samples have limited ability to store screw dislocations. The necessity of applying high stress in sub-micron crystals is demonstrated to greatly enhance the mobility of screw dislocations, rendering it close to that of edge dislocations. In the sub-micron size scale, we show that, because dislocation mobility transitions from being kink dominated to being phonon-drag dominated, the flow stress becomes insensitive to temperature. A dislocation mechanism map in the temperature-size space is proposed to further illustrate this phenomenon in tungsten micropillars.

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, under Award Number DE-FG02-03ER54708, and the US Air Force Office of Scientific Research (AFOSR), under award number FA9550-11-1-0282. We would like to thank Prof. Jaime Marian and Prof. Jonathan A. Zimmerman for inspiring comments and discussions.

Homogenization of a Row of Dislocation Dipoles from Discrete Dislocation Dynamics

Authors: S. J. Chapman1, Y. Xiang1, Y. C. Zhu2

Affiliations: 1Department of Mathematics, University of Oxford; 2Department of Mathematics, the Hong Kong University of Science and Technology.

ABSTRACT

Permanent deformations of crystalline materials are known to be carried out by a large number of atomist line defects, i.e. dislocations, and a good understanding of the collective behavior of dislocation systems can boost the discovery of high-end materials. However, due to crystallographic constraints, existing particle-averaging approaches struggle to generate a plasticity theory of dislocation continua that is consistent with the underlying discrete dynamics. To address such difficulties, the author discusses the homogenization of a system consisting of a row of dislocation dipoles, which would be equivalent to a dislocation-free state if conventional averaging approaches are employed [1]. The method automatically classifies the variables representing material microstructures into two groups, according to the time scales on which they naturally evolve. Based on such hierarchy in evolution time scales, the discrete dislocation dynamics can be upscaled to a coarse-grained level, where the variation of the fast-varying variables is considered quasi-statically on the time scale associated with the slow-varying variables. This time-scale separation method paves a way for properly incorporating dipole-like (zero net Burgers vector but non-vanishing) dislocation structures, known as the statistically stored dislocations (SSDs) into macroscopic models of crystal plasticity in three dimensions.

[1] S. J. Chapman, Y. Xiang, Y. C. Zhu, Homogenization of a row of dislocation dipoles from discrete dislocation dynamics. To appear in SIAM J. Appl. Math., (2016)

This work was partly supported by EPSRC through grant EP/D048400/1, and by the Hong Kong Research Grants Council through General Research Fund 606313.


Towards dislocation-based models of general interfaces in crystals

Michael J. Demkowicz

Materials Science and Engineering, Texas A&M University, 400 Bizzell St., College Station, TX 77840; [email protected]

ABSTRACT

Solid-state interfaces are ubiquitous in materials science. As awareness of their far-reaching influence on materials behavior grows, so does interest in predicting and controlling their structure and properties. Dislocations provide a basis for building versatile models of general homo- and heterophase interfaces in crystalline solids without resorting to full-scale, atomistic descriptions. I will describe progress towards building dislocation-based models of general crystalline interfaces and give examples of applications to grain boundaries and heterophase interfaces in metal composites. Our method compares well with full atomistic models, both in terms of interface structure and energy. It is also computationally inexpensive, enabling us to scan over a wide range of interface characters in search of interfaces with desired structures or properties. I will describe applications of this model to predicting interfacial precipitation patterns as well as sink strengths of interfaces under irradiation.

This work was supported by an NSF CAREER award under grant number 1150862.

X-ray induced defects as obstacles to dislocation motion in NaBr and KBr single crystals

Y. Kohzuki1 and T. Ohgaku2

1Department of Mechanical Engineering, Saitama Institute of Technology, 1690 Fusaiji, Fukaya, Saitama 369-0293, Japan

e-mail: [email protected] school of Natural Science and Technology, Kanazawa University,

Kakumamachi, Kanazawa 920-1192, Japan

ABSTRACT

When NaBr and KBr single crystals are exposed to X-ray (W-target, 30kV, 20mA), the crystals harden because the defects induced by it obstruct dislocation motion. Strain-rate cycling tests associated with ultrasonic oscillation were carried out for the crystals at 77 to 293K. As presented in the Dislocations-2008 Conference [1], stress decrement ( τ∆ ) due to oscillation and stress change due to strain-rate cycling have been measured during plastic deformation. The relative curve of τ∆ and strain-rate sensitivity (SRS) of flow stress has a stair-like shape also for the two kinds of crystal. That is to say, the curve has two bending points and is divided into three regions: two plateau regions and the region between the two bending points, where SRS decreases gradually with increasing τ∆ . The first region is a plateau at the small τ∆ . This implies that X-ray induced defects have the weak interaction with dislocation and act as obstacles to dislocation motion. Furthermore, dependence of stress decrement ( pτ ) at the first bending point on the activation volume (V) obtained from the difference between SRS in the first and second plateau regions reflects the interaction between dislocation and defects induced by the X-irradiation. The activation energy for the break-away of a dislocation from the defect can be obtained on the basis of pτ -V curve fitting the Barnett model to the experimental results. Then, the activation energy is 0.76 and 0.81eV for NaBr and KBr, respectively.

Reference[1] T. Ohgaku and T. Matsunaga, Interaction between dislocation and divalent impurity in

KBr single crystals, Dislocations-2008 IOP Conf. Ser.: Mater. Sci. Eng., 3, 012021 (2009)

Preference: Poster presentationPresenter: Y. Kohzuki


Experimental Atomic Scale Imaging of Slip Traces in BCC Crystals

B. Douat, J. Bonneville , C. Coupeau, M. Drouet

Université de Poitiers, Institut P’, CNRS-UMR 6630, ENSMABd Marie et Pierre Curie, Bât. SP2MI, 86962 Futuroscope Chasseneuil, FRANCE.

email: [email protected]

ABSTRACT

Scanning tunnelling microscopy (STM) is an experimental technique now currently used for assessing surface features of metallic materials at the atomic scale. In this context, we recently developed a unique experimental device that permits such a high-resolution surface imaging by in situ STM on strained samples at temperatures between 90K and 600K under ultra high vacuum conditions. This equipment is particularly well-suited to characterise the surface patterning of metals resulting from plastic deformation. When moving dislocations emerge at crystal surfaces, they generally produce steps that appear in the form of lines closely related to both the crystal structure and the elementary dislocation processes by which they are produced. Atomic scale observations of slip traces obtained on Nb single crystals using the equipment mentioned above will be reported. Compression tests were performed along the [ ] axis with an ( ) observation surface for STM. This symmetrical orientation yields highest Schmid factor for the �[111]( ) and �[ ](011) slip systems. Two temperatures were investigated, 200K and 290K. The {111} surface of Nb exhibits a (22) atomic reconstruction, which somewhat complicates the atomic scale analysis of slip trace crystallographic directions. At this ultimate resolution level, slip traces predominantly belong to the two <110> slip planes, but they may at some places deviate to correspond to <112> slip planes or even very locally to non-well-defined crystallographic planes. Dislocation dipoles in the form of opposite ending slip lines are also frequently observed. These atomic scale observations, which to our knowledge are the only ones ever obtained for bcc metals, will be discussed in the framework of the models that have been proposed over the years to explain the plasticity of bcc metals with a special emphasis on the latest simulations of dislocation cores, which are supposed to control their mobility.

Dislocation Patterning under Cyclic Loading of FCC Crystals

Oriented for Multiple Slip

Authors: Shengxu Xia1, Anter El-Azab2

Affiliations: 1School of Materials Engineering, Purdue University, Email: [email protected]

2School of Materials Engineering, Purdue University, Email: [email protected]

ABSTRACT

We report on the prediction of the dislocation patterns in FCC crystals under cyclic loading using continuum dislocation dynamics theory published in the authors’ early work [1]. In this density-based framework, the dislocation density evolution is governed by the transport, cross-slip and reactions of dislocations, which are captured by kinetic equations derived based on statistical mechanics principles. A novel finite element method customized to adapt to FCC single crystals has been used to solve the dislocation kinetic equations coupled with crystal mechanics. Within this framework, the cross slip process and dislocation-dislocation reactions at short range are treated using a Monte Carlo approach in the continuum frame. The continuum model is illustrated to have the ability to take the data obtained from discrete dislocation simulation as parameters in the curl-type kinetic equations to address cross-slip and short range reaction issues. Simulation results for the cyclic stress-train curve, the average dislocation density evolution, and emerging dislocation and slip patterns will be presented. Aspecial attention is given to the analysis of the observed dislocation patterns and comparison with TEM observation in the literature.

[1] S. Xia, A. El-Azab, Computational modeling of mesoscale dislocation patterning and plastic deformation of single crystals, Modelling and Simulation in Materials Science and Engineering, 23, 055009 (2015)


Experimental Atomic Scale Imaging of Slip Traces in BCC Crystals

B. Douat, J. Bonneville , C. Coupeau, M. Drouet

Université de Poitiers, Institut P’, CNRS-UMR 6630, ENSMABd Marie et Pierre Curie, Bât. SP2MI, 86962 Futuroscope Chasseneuil, FRANCE.

email: [email protected]

ABSTRACT

Scanning tunnelling microscopy (STM) is an experimental technique now currently used for assessing surface features of metallic materials at the atomic scale. In this context, we recently developed a unique experimental device that permits such a high-resolution surface imaging by in situ STM on strained samples at temperatures between 90K and 600K under ultra high vacuum conditions. This equipment is particularly well-suited to characterise the surface patterning of metals resulting from plastic deformation. When moving dislocations emerge at crystal surfaces, they generally produce steps that appear in the form of lines closely related to both the crystal structure and the elementary dislocation processes by which they are produced. Atomic scale observations of slip traces obtained on Nb single crystals using the equipment mentioned above will be reported. Compression tests were performed along the [ ] axis with an ( ) observation surface for STM. This symmetrical orientation yields highest Schmid factor for the �[111]( ) and �[ ](011) slip systems. Two temperatures were investigated, 200K and 290K. The {111} surface of Nb exhibits a (22) atomic reconstruction, which somewhat complicates the atomic scale analysis of slip trace crystallographic directions. At this ultimate resolution level, slip traces predominantly belong to the two <110> slip planes, but they may at some places deviate to correspond to <112> slip planes or even very locally to non-well-defined crystallographic planes. Dislocation dipoles in the form of opposite ending slip lines are also frequently observed. These atomic scale observations, which to our knowledge are the only ones ever obtained for bcc metals, will be discussed in the framework of the models that have been proposed over the years to explain the plasticity of bcc metals with a special emphasis on the latest simulations of dislocation cores, which are supposed to control their mobility.

Dislocation Patterning under Cyclic Loading of FCC Crystals





ABSTRACT

We report on the prediction of the dislocation patterns in FCC crystals under cyclic loading using continuum dislocation dynamics theory published in the authors’ early work [1]. In this density-based framework, the dislocation density evolution is governed by the transport, cross-slip and reactions of dislocations, which are captured by kinetic equations derived based on statistical mechanics principles. A novel finite element method customized to adapt to FCC single crystals has been used to solve the dislocation kinetic equations coupled with crystal mechanics. Within this framework, the cross slip process and dislocation-dislocation reactions at short range are treated using a Monte Carlo approach in the continuum frame. The continuum model is illustrated to have the ability to take the data obtained from discrete dislocation simulation as parameters in the curl-type kinetic equations to address cross-slip and short range reaction issues. Simulation results for the cyclic stress-train curve, the average dislocation density evolution, and emerging dislocation and slip patterns will be presented. Aspecial attention is given to the analysis of the observed dislocation patterns and comparison with TEM observation in the literature.



Dislocation-density Function Dynamics – an All-dislocation, Full-dynamics Approach for Modeling Dislocation Structures at Both

Intensive and Extensive Scales

Alfonso H.W. Ngan and H.S. Leung

Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, P.R. China (email of corresponding author: [email protected])

ABSTRACT

A successful strategy for computational plasticity will have to bridge across the meso scale in which the interactions of high quantities of dislocations dominate. In recent years, there has been considerable interest in density representations of dislocations. Compared to discrete dislocation dynamics (DDD), density approaches have the potential advantage of being more up-scalable for handling larger systems with higher plastic strains, in which the quantity of dislocations may become intractable by DDD.

Previously proposed density-based schemes, however, suffer from one or more of the following shortcomings. First, some schemes assume evolution laws of the Walgraef-Aifantis type, but thesewould not be applicable to 3D dislocations since their movement would not be fully representableby a simple “dislocation flux”. For 3D dislocations, their evolution needs to be derived from a well posed coarse-graining scheme which clearly defines the relationship between the discrete-line and density representations of the dislocation microstructure. Secondly, some schemes treat the evolution of GNDs rigorously via the Nye tensor in an elasto-plastic framework, but SSDs are handled via less rigorous phenomenological laws of, for example, the Kock-Mecking type. In reality, SSDs are usually present in larger quantities than GNDs and their presence affects the GNDs via mutual interactions. Thirdly, some schemes employ only ad hoc or phenomenological treatments for elastic interactions between dislocations.

In this work, a new meso-scale scheme based on the full dynamics of dislocation-density functions is presented. In this scheme, the evolution of the dislocation-density functions is derived from a coarse-graining procedure which clearly defines the relationship between the discrete-line and density representations. Dislocation generation is considered as a consequence of dislocations to maintain their connectivity, and a special scheme is devised for this purpose. Full dynamics of the dislocation-density functions are considered based on an “all-dislocation” concept in which SSDsare preserved and treated in the same way as the GNDs. Elastic interactions between dislocations are treated in accordance with Mura’s formula for eigen stress.

Electronic Structure Study of Dislocations in Aluminum

Authors: Sambit Das1, Mrinal Iyer1 , Vikram Gavini2,

Affiliations: 1Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA; 2Department of Mechanical Engineering, Department of

Materials Science and Engineering, University of Michigan, Ann Arbor, MI 48109, USA.

ABSTRACT

This talk presents the development of an efficient real-space formulation of orbital-free density functional theory using higher-order finite-element discretization. Orbital-free DFT using density dependent kernel kinetic energy functionals is shown to be in very good agreement with Kohn-Sham DFT for the Al-Mg materials system on a wide range of benchmark problems [1]. The developed real-space formulation, which enables consideration of complex geometries and general boundary conditions, is employed to study the energetics of isolated edge and screw dislocations in Aluminum. The core-size of the dislocation in Aluminum, as determined by the extent to which electronic structure effects are significant, is found to be around 8-10 times the magnitude of the Burgers vector [2]. This result is in stark contrast to the widely accepted notion that continuum descriptions of dislocation energetics are accurate beyond 1-3 Burgers vector from the dislocation line. Further, our study revealed a significant influence of macroscopic deformations on the core-energy of the dislocation. We show that this dependence of the core-energy on macroscopic deformations results in an additional force on dislocations, beyond the Peach-Koehler force, that is proportional to strain gradients. Further, we demonstrate that this force from core-effects can be significant and can play an important role in governing the dislocation behavior in regions of inhomogeneous deformations.

[1] S. Das, M. Iyer, V. Gavini, Real-space formulation of orbital-free density functional theory using finite-element discretization: The case for Al, Mg, and Al-Mg intermetallics,Phys. Rev. B, 92, 014104 (2014).

[2] M. Iyer, B. Radhakrishnan, V. Gavini, Electronic structure study of an edge dislocation in aluminum and the role of macroscopic deformations on its energetics, J. Mech. Phys. Solids 76, 260-275 (2014).


A Study of Grain and Grain-Boundaries Based on a Finite-Deformation Gradient Crystal-Plasticity Model

Habib Pouriayevali1, Baixiang Xu1

1 Mechanics of Functional Materials Division, Institute of Material Science, Technische Universitat Darmstadt, Petersenstrasse 32, D-64287 Germany,

[email protected]

ABSTRACT

In this study, a well-defined finite-deformation gradient crystal-plasticity model which has been proposed by Gurtin [1] is employed and represented with respect to the referenceconfiguration to study size-dependent hardening behavior of a single crystal. The thermodynamically consistent constitutive model is based on microscopic force balances. A recoverable defect-energy which incorporates geometrically necessary dislocation (GND) density is introduced and results in a rate-dependence non-local flow rule in a form of partial differential equation. The flow rule is derived from principle of virtual power and comprises energetic and dissipative gradient-strengthenings as well as self- and latent-hardening in a multi slip-system crystal. The constitutive model is implemented in the finite-element software ABAQUS via a user-defined subroutine (UEL). A plain-strain quadratic element in which displacement components and dislocation densities are treated as nodal degrees of freedom is defined. The primary aim of the current study is an understanding of effect of energetic and dissipative gradient-strengthenings as well as self- and latent-hardening in stress-strain response of a single crystal. Rate and size-dependent responses along with Bauschinger-like behavior under a cyclic simple-shear loading are investigated. Moreover, plastic flows in predefined slip systems and accumulation of GNDs are distinctly observed.This constitutive model is further developed for multicrystals. Penetration of dislocations through soft boundaries and accumulation of GNDs at hard boundaries are also investigated.

[1] Gurtin, M. E. (2008). "A finite-deformation, gradient theory of single-crystal plasticity with free energy dependent on densities of geometrically necessary dislocations." International Journal of Plasticity 24(4): 702-725.

A Concurrent Atomistic-Continuum Study of Dislocation Slip Transfer across Twist Grain Boundaries

Shuozhi Xu1, Liming Xiong2, Youping Chen3, David L. McDowell1,4

1GWW School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA

2Department of Aerospace Engineering, Iowa State University, Ames, IA 50011, USA3Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville,

Florida 32611, USA4School of Material Sciences and Engineering, Georgia Institute of Technology, Atlanta,

Georgia 30332, USA

ABSTRACT

Sequential slip transfer across grain boundaries (GB) plays an important role in grain size-dependent plastic deformation in polycrystalline metals. In spite of extensive studies in modeling individual phases and grains, well accepted criteria of slip transfer across GBs and models of predicting irreversible GB structure evolution are still lacking. Moreover, behavior of twist GBs is less explored than their tilt GB counterparts. Slip transfer is inherently multiscale since both the atomic scale structure of the interface and the long range fields of dislocation pile-ups come into play. Although a few concurrent multiscale methods have beendeveloped and employed to investigate GB slip transfer, these methods are limited by the need to pass defects from a continuum dislocation dynamics domain to the atomistic region near the interface or by the need for very significant computational effort devoted to adaptive remeshing to admit dislocations. In this work, large scale concurrent atomistic-continuum (CAC) simulations [1,2] are performed to address the slip transfer of dislocation pile-ups across twist GBs in Cu and Ni. Results suggest the viability of the CAC method to describe the interface reactions with fully-resolved atomistics while preserving the net Burgers vector and associated long range stress fields of curved dislocations. In addition, we explore the role of specific twist GB structures and dislocation character in interface absorption-desorption reactions, including evolution of the structure of the interface. The history effect of asequence of dislocation reactions with the interface is also identified in light of irreversible evolution of the GB with each encounter.

[1] L. Xiong, G.J. Tucker, D.L. McDowell et al., Coarse-grained atomistic simulation of dislocations, J. Mech. Phys. Solids, 59, 160 (2011)

[2] S. Xu, R. Che, L. Xiong, et al., A quasistatic implementation of the concurrent atomistic-continuum method for FCC crystals, Int. J. Plast., 72, 91 (2015)


Strength of hexagonal close-packed crystals

Sylvie Aubry, Moono Rhee, Mark Messner, and Athanasios Arsenlis

Lawrence Livermore National Laboratory, PO Box 808Livermore, CA 94551-0808

ABSTRACT

Metals and alloys with hexagonal close-packed (HCP) crystal structure show considerable variations in mechanical and physical properties essential for their technological applications. These materials have been used in the aerospace, the medical, and the automotive industry for their strength and lightweight properties. However, the highly anisotropic mechanical properties and, in particular, limited ductility of beryllium and magnesium alloys have so far restrained their practical uses. A new strength model approach, that makes use of an information-passing paradigm: simulation results from lower length-scale calculations are used to define functional forms and parameters at the next larger length scale, is proposed to model HCP crystals. The multiscale hierarchy includes calculations performed with molecular dynamics, dislocation dynamics and crystal plasticity models. The essential role of <c+a> dislocations in the ductility of HCP materials is studied using dislocation dynamics and isdiscussed.

[1] Sylvie Aubry, Moono Rhee, Gregg Hommes, Vasily Bulatov, and Athanasios Arsenlis,"Dislocation dynamics in hexagonal close-packed crystals," Journal of the Mechanics and Physics of Solids, submitted Sept. 2015.

[2] Mark C. Messner, Moono Rhee, Athanasios Arsenlis, and Nathan R. Barton. "A crystal plasticity model for slip resistance and junction formation in HCP metals,” submitted to Acta Mater, 2015.

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Peierls Stresses of Dislocations in a Variety of Crystals Estimated via Peierls-Nabarro Model Using ab-initio γ-surface and Their Comparison with

Experimentally Estimated Values

Y. Kamimura1, K. Edagawa1, A. Iskandarov1, M. Osawa1, Y. Umeno1, S. Takeuchi2

1Institute of Industrial Science, The University of Tokyo, Meguro-ku, Tokyo 153-8505,2Tokyo University of Science, Shinjuku-ku, Tokyo 162-8601, Japan

[email protected]

ABSTRACT

In a previous paper, we have estimated Peierls stresses of dislocations in a variety of crystals experimentally by extrapolating CRSS vs. T curve to absolute zero temperature [1]. The results showed that Peierls stresses normalized by the shear modulus distribute over four-orders of magnitude, but those of the same group of crystals are within an order of magnitude. To rationalize such homologous nature of the Peierls stress, we have calculated Peierls stresses via Peierls-Nabarro (P-N) model of the dislocation. In the P-N model, the essential quantities determining the Peierls stress are geometrical factor of h/d (h: lattice spacing of glide plane; d:period of Peierls potential), and the generalized stacking fault energy function or γ-surface. In the original P-N model, Peierls stress was formulated for edge dislocation (d=b) and sinusoidal γ-surface [2]. Foreman et al. showed that the shape of the γ-surface plays a decisive role in the Peierls stress [3]. So, we first determined γ-surface by ab-initio calculation for a variety of crystals: fcc metals, bcc metals, NaCl type ionic crystals, CsCl type ionic crystals and tetrahedrally-coordinated crystals. Then, the Peierls stress of each slip system has been calculated numerically according to the P-N model. The calculated Peierls stresses have a strong correlation with those of experimental values except for fcc metals, reflecting the homologous nature of the γ−surface, but the former values are generally larger than the latter ones by a factor of four on the average. The discrepancies between calculated and experimental Peierls stresses will be discussed.

[1] Y. Kamimura, K. Edagawa, S. Takeuchi, Acta Mater. 61, 294 (2013)[2] R.E. Peierls, Proc. Phys. Soc. 52 (1940) 34; F.R.N. Nabarro, Proc. Phys. Soc. 59, 256 (1947).[3] A.J. Foreman, M.A. Jaswon, J.K. Wood, Proc. Phys. Soc. 64, 156 (1951).


Strength of hexagonal close-packed crystals

Sylvie Aubry, Moono Rhee, Mark Messner, and Athanasios Arsenlis

Lawrence Livermore National Laboratory, PO Box 808Livermore, CA 94551-0808

ABSTRACT

Metals and alloys with hexagonal close-packed (HCP) crystal structure show considerable variations in mechanical and physical properties essential for their technological applications. These materials have been used in the aerospace, the medical, and the automotive industry for their strength and lightweight properties. However, the highly anisotropic mechanical properties and, in particular, limited ductility of beryllium and magnesium alloys have so far restrained their practical uses. A new strength model approach, that makes use of an information-passing paradigm: simulation results from lower length-scale calculations are used to define functional forms and parameters at the next larger length scale, is proposed to model HCP crystals. The multiscale hierarchy includes calculations performed with molecular dynamics, dislocation dynamics and crystal plasticity models. The essential role of <c+a> dislocations in the ductility of HCP materials is studied using dislocation dynamics and isdiscussed.

[1] Sylvie Aubry, Moono Rhee, Gregg Hommes, Vasily Bulatov, and Athanasios Arsenlis,"Dislocation dynamics in hexagonal close-packed crystals," Journal of the Mechanics and Physics of Solids, submitted Sept. 2015.

[2] Mark C. Messner, Moono Rhee, Athanasios Arsenlis, and Nathan R. Barton. "A crystal plasticity model for slip resistance and junction formation in HCP metals,” submitted to Acta Mater, 2015.


Peierls Stresses of Dislocations in a Variety of Crystals Estimated via Peierls-Nabarro Model Using ab-initio γ-surface and Their Comparison with

Experimentally Estimated Values

Y. Kamimura1, K. Edagawa1, A. Iskandarov1, M. Osawa1, Y. Umeno1, S. Takeuchi2

1Institute of Industrial Science, The University of Tokyo, Meguro-ku, Tokyo 153-8505,2Tokyo University of Science, Shinjuku-ku, Tokyo 162-8601, Japan

[email protected]

ABSTRACT

In a previous paper, we have estimated Peierls stresses of dislocations in a variety of crystals experimentally by extrapolating CRSS vs. T curve to absolute zero temperature [1]. The results showed that Peierls stresses normalized by the shear modulus distribute over four-orders of magnitude, but those of the same group of crystals are within an order of magnitude. To rationalize such homologous nature of the Peierls stress, we have calculated Peierls stresses via Peierls-Nabarro (P-N) model of the dislocation. In the P-N model, the essential quantities determining the Peierls stress are geometrical factor of h/d (h: lattice spacing of glide plane; d:period of Peierls potential), and the generalized stacking fault energy function or γ-surface. In the original P-N model, Peierls stress was formulated for edge dislocation (d=b) and sinusoidal γ-surface [2]. Foreman et al. showed that the shape of the γ-surface plays a decisive role in the Peierls stress [3]. So, we first determined γ-surface by ab-initio calculation for a variety of crystals: fcc metals, bcc metals, NaCl type ionic crystals, CsCl type ionic crystals and tetrahedrally-coordinated crystals. Then, the Peierls stress of each slip system has been calculated numerically according to the P-N model. The calculated Peierls stresses have a strong correlation with those of experimental values except for fcc metals, reflecting the homologous nature of the γ−surface, but the former values are generally larger than the latter ones by a factor of four on the average. The discrepancies between calculated and experimental Peierls stresses will be discussed.

[1] Y. Kamimura, K. Edagawa, S. Takeuchi, Acta Mater. 61, 294 (2013)[2] R.E. Peierls, Proc. Phys. Soc. 52 (1940) 34; F.R.N. Nabarro, Proc. Phys. Soc. 59, 256 (1947).[3] A.J. Foreman, M.A. Jaswon, J.K. Wood, Proc. Phys. Soc. 64, 156 (1951).


Dislocation Strengthening in FCC and BCC Metals

in the Athermal Regime

using the MobiDiC Dislocation Dynamics Code

Ronan Madec1, Ladislas P. Kubin2

1CEA, DAM, DIF, F-91297 Arpajon, France, [email protected]; 2LEM (CNRS/ONERA), 29 Avenue de la Division Leclerc, BP 72, 92322 Châtillon Cedex,

France.

ABSTRACT

The Mobile Dislocation Colony (MobiDiC) dislocation dynamics simulation was used to revisit dislocation strengthening for a selection of FCC crystals and of BCC crystals at temperatures above the so-called athermal transition. MobiDiC allows handling complex slip geometries, includes a careful treatment of the line tension at the triple nodes of junctions and is well suited for extensive studies on large clusters. In the case of BCC metals, it incorporates {110} and {112} slip systems in order to develop a comprehensive study of the coefficients of interaction between slip systems. The present work is devoted to two effects that have not been investigated as yet. The first one is the effect of the effective Poisson coefficient on the strength of dislocation reactions and the second one is the double degeneracy of some interaction coefficients when the active and forest slip systems are exchanged. Preliminary results on the coefficients that determine the dislocation mean free paths will also be discussed. They are part of an ongoing work on a generalized storage-recovery model for strain hardening in BCC metals at high temperatures.

Atomistic Modeling of Hardening in Thermally-Aged Fe-Cr Binary Alloys

Tomoaki Suzudo1, Yasuyoshi Nagai2, Alfredo Caro3

1Center for computational science and e-systems, Japan atomic energy agency, 2-4Shirane Shirakata, Tokai-mura 319-1195, Japan; 2The Oarai center, Institute for materials research, Tohoku university, 2145-2 Narita-cho, Oarai 311-1313, Japan;

3Materials science and technology division, Los Alamos national laboratory, P.O. box 1663, Los Alamos, NM 87545, United states

ABSTRACT

It is widely known that Iron-chromium (Fe-Cr) binary alloys with Cr concentration more than ~20% undergo spinodal decomposition when they are thermally aged. This microstructural evolution causes hardening and loss of ductility of the material; this is also called “475°C embrittlement.” Origin of the hardening can be ascribed to dislocations interacting obstacles, i.e. Cr-rich phases. Since the dislocation motion in such heterogeneous media is extremely complicated, the quantitative prediction of the hardening remains as an unsolved problem. The present study [1] is about the first attempt to tackle this problem by exploiting atomistic modeling techniques. We apply Monte Carlo simulation to creating spinodally-decomposed microstructure and molecular dynamics to simulating edge dislocations moving through thismicrostructure by imposing shearing deformation. We then measure the critical stress as a measure of hardness for many cases over the progress in spinodal decomposition, and succeedin reproducing an experimentally-discovered proportionality between the phase separationparameter (or the variation parameter) and the hardening. The result supports the validity ofour computational methods, and we believe that we made an important step towards the quantitative prediction of this mechanical degradation.

[1] T. Suzudo, Y. Nagai, D. Schwen and A. Caro, “Hardening in thermally-aged Fe-Cr binary alloys: Statistical parameters of atomistic configuration,” Acta Materialia 89, 116 (2015)

This work includes the result of "Research and development on degradation prediction of structural materials in nuclear reactors based on microstructural damage mechanisms" entrusted to Tohoku university by Education, Culture, Sports, Science and Technology of Japan (MEXT). A. Caro acknowledges support from the Center for Materials under Irradiation and Mechanical Extremes, a DOE-OBES Energy Frontier Research Center.


Glassy avalanches in 3D dislocation systems

Authors: Arttu Lehtinen1,Giulio Costantini2, Mikko J. Alava1, Stefano Zapperi1,2,3,4, and Lasse Laurson1

Affiliations: 1COMP Centre of Excellence, Department of Applied Physics, Aalto University, P.O.Box 11100, FI-00076 Aalto, Espoo, Finland; 2Center for Complexity and biosystems,

Department of Physics, University of Milano,via Celoria 26, 20133 Milano, Italy; 3ISI Foundation, Via Alassio 11/C, 10126 Torino, Italy; 4CNR-IENI, Via R. Cozzi 53, 20125

Milano, Italy .

ABSTRACT

Crystal plasticity occurs by deformation bursts due to the avalanche-like motion of dislocations. In order to study the statistical properties of these avalanches, we have performed extensive numerical simulations of Al with three-dimensional dislocation dynamics code ParaDis [1]. We have modified the default version of the code by adding a quasistatic stress loading feature where the stress-rate is controlled by the average velocity of the dislocations. Our results show that dislocation avalanches are power-law distributed and display peculiar stress and sample size dependence: The average avalanche size grows exponentially with the applied stress, and the amount of slip increases logarithmically with the system size. These results suggest that intermittent deformation processes in materials with FCC crystal structure exhibit an extended critical-like phase in analogy to glassy systems, instead of originating from a non-equilibrium phase transition critical point.

[1] A.Arsenlis, W. Cai, Me. Tang, M. Rhee, T. Oppelstrup, G. Hommes, T. G. Pierce, and V.V. Bulatov. "Enabling strain hardening simulations with dislocation dynamics." Modelling and Simulation in Materials Science and Engineering, 15, 6, (2007)

Dislocation plasticity: an exemplar of self-organised-criticality

L. M. Brown1

1Cavendish Laboratory, J. J Thompson Ave., Cambridge, U.K., CB3 0HE

[email protected]

ABSTRACT

The complex phenomena of work-hardening can be understood as manifestations of self-organised criticality (SOC) applied to a system of ellipsoidal slip bands, each slightly tilted away from the crystallographic slip plane [1]. Cross-slip and secondary slip play vital roles as in traditional theories. Details of the plastic flow, such as when and where slip bands will form, are no more predictable than earthquakes, but the emergent properties of the system typically obey power laws relating intensive variables (e.g. stress) to extensive variables (e.g. plastic displacement, strain). Recognition of SOC allows the experimentally observed exponents inthe power laws to be rationalised. The exponents range from -2 (statistics of acoustic emission) through 1/3 (Andrade creep) to +1 (linear hardening in Stage II). In some cases, the absolute values of the constants in the laws can be calculated and compared with experiment. A telling counterexample is logarithmic transient creep, which nevertheless confirms an equation of state based on SOC. This view of plasticity suggests a type of computer simulation in which there is no attempt made to calculate detailed arrangements of structural components, but categories of structure are quantified and are stored in the programme: e.g. statistics of angular misorientation of subgrains, and their size; dipole arrays; distribution of internal stress. Such a programme might facilitate alloy design relating to metal forming and fatigue.

[1] L. M. Brown, Constant intermittent flow of dislocations: central problems in plasticity, Mat. Sci. and Tech., 28, 1209 (2012)


How to Measure a Dislocation’s Breakthrough Stress and the Grain Boundary Resistance against Slip Transfer Based on the DFZ-Model of

Fracture

Florian Schäfer, Michael Marx, Christian Motz

Saarland University, Department 8.4 - Materials Science and EngineeringBuilding D22, 66123 Saarbruecken, Germany

[email protected]

ABSTRACT

In recent studies, the interaction of dislocations and grain boundaries is investigated by bi-crystall- and micro-specimen-experiments and supplementary simulations by discrete dislocation dynamics. However, quantitative data for the grain boundary resistance against slip transfer are still missing. In this study, we use FIB-initiated stage-I-fatigue cracks as highly localized sources for dislocations with well-known Burgers vectors to quantify the interaction between these dislocations in the plastic zone in front of the crack tip and selected grain boundaries. In case of a blocked slip band, the dislocations pile up at the grain boundary and cause a local stress concentration. The dislocation density distribution is measured from slip trace height profiles measured by AFM. Then the distribution of the local stresses is calculated with the dislocation-free zone model of Chang and Ohr [1]. The resulting critical local stress intensity factor is compared with the grain boundary resistance values calculated from common geometric models. Hence, it is possible to quantify the grain boundary resistance and to combine geometric and stress approach for grain boundary resistance against slip transfer to a self-contained concept. Thereby, the grain boundary resistance can be calculated based on a critical stress concept with the knowledge of the geometric parameters of the grain boundary only, namely the orientations of both participating grains and the orientation of the grain boundary plane [2]. This is necessary to understand the plastic deformation of polycrystalline materials and the fluctuating crack growth in the short crack regime.

[1] S.J. Chang, S.M. Ohr, Dislocation‐free zone model of fracture, J. Appl. Phys. 52 (12) 7174-7181 (1981)

[2] F. Schaefer, A.F. Knorr, M. Marx, H. Vehoff, Stage-I fatigue crack studies in order to validate the dislocation-free zone model of fracture for bulk materials, Phil. Mag. 95 (8)819-843 (2015)

This work was supported by the Deutsche Forschungsgemeinschaft (MA3322/7, MO2672/1).

3D Dislocation Dynamics Simulations of Nanoindentation: Application to Cu/graphene Bilayer System

Marc Fivel1, Mohammad Hammad2, 3, Hosni Idrissi2,4, J.P. Raskin3, Thomas Pardoen2

1 Laboratoire Science et Ingénierie des Matériaux et Procédés, University Grenoble Alpes / CNRS, F-38000 Grenoble, France

2 Institute of Mechanics, Materials and Civil Engineering (IMMC), Université catholique de Louvain, Place Sainte Barbe 2, B-1348 Louvain-La-Neuve, Belgium

3 Information and Communications Technologies, Electronics and Applied Mathematics (ICTEAM), Université catholique de Louvain, Place du Levant 3, B-1348 Louvain-la-

Neuve, Belgium4 Electron Microscopy for Materials Science (EMAT), Department of Physics, University

of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium

ABSTRACT

Discrete dislocation dynamics (DDD) simulations revealed to be a powerful numerical tool to relate the mechanical behavior of crystalline materials to the dislocation microstructure [1]. However, the method is computationally challenging so that most of the applications need to focus on small plastic strain studies or confined plasticity. Nanoindentation is a typical case were DDD simulations can help to better understand the measurements since strain amplitude is quite small and plasticity remains confined beneath the indenter [1-3].In this paper, nanoindentation simulations of (111) Cu single crystals are performed using a spherical indenter of radius 30nm. The boundary conditions relevant to the nanoindentation loading are enforced using the superposition principle based on a coupling of the DDD code with finite elements. Displacement boundary conditions are imposed within the contact area. Traction free conditions are imposed on the remaining indented surface. A nucleation algorithm based on Molecular Dynamics simulations is implemented in order to generate the dislocation during the loading. It consists in introducing as many interstitial prismatic loops as required in order to match the indenter position. Then, dislocations are allowed to move in the simulation box and the indenter displacement is further increased when the dislocation segments have all reached a stable position. Two situations have been investigated: (i) the case of a pure single crystal of copper from which the dislocation can escape through the free surface, printing a step at the slip plane intersection, (ii) the case of a graphene cap layer deposited on the Cu single crystal which prevent dislocation crossing at the free surface. Experimentally, it was observed that the pop-in events for these two cases are very different. In the case of the pure copper, the latter the pop-in event, the bigger the plastic burst. On the opposite, the graphene layer shows plastic burst with a similar amplitude independent of the indenter depth. The DDD results are analyzed in order to explain these experimental observations.

[1] M.C. Fivel, C.F. Robertson, G.R. Canova and L. Boulanger, 3D modeling of indent-induced plastic zone at a mesoscale, Acta Materialia, 46 (17), pp 6183-6194, (1998)

[2] H.-J. Chang, M. Fivel, D. Rodney and M. Verdier, Multiscale modelling of indentation in fcc metals: from atomic to continuum, CR–Physiques, 11, pp. 285-292, (2010).

[3] M. Fivel, Multiscale modeling of indentation : from atomic to continuum, in "Plasticity of Crystalline Materials. From Dislocation to Continuum" edited by I.R. Ionescu, S. Bouvier, O. Cazacu and P. Franciosi, ISBN 978-1-84821-278-7, pp.37-56, (2011)


Parametric Model of Dislocation Cross-Slip Driven by Geodesic Curvature Flow

Miroslav Kolář1, Michal Beneš1, Jan Kratochvíl2

1Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00, Prague 2,

[email protected], [email protected],2Department of Physics, Faculty of Civil Engineering, Czech Technical University in

Prague, Thákurova 7, 166 29, Prague, [email protected].

ABSTRACT

This contribution deals with the problem of dislocation cross-slip, which is considered as an elementary dislocation process. In our approach, dislocations are modeled as smooth curves evolving on a two dimensional surface. Their motion is driven by the geodesic curvature flow

Bv T Fκ= + ,Where ν denotes the normal velocity, κ is the geodesic curvature and F is the normal component of all external forces. In this model B denotes the drag coefficient and T stands for the line tension. The cross-slip phenomenon is considered to be a deterministic, stress driven process. The sharp edges between the primary planes and the cross-slip plane are regularized to ensure the C2 smoothness of the whole glide surface. For numerical simulations, we employ the parametric description of the evolving curves and semi-implicit flowing finite volume method enhanced with the tangential redistribution of the discretization points [2]. Overcoming of a spherical obstacle by double cross-slip is presented as an illustrative example. The results of computational experiments are compared with the results obtained by the projection method proposed in [3].

[1] M. Kolář, M. Beneš, D. Ševčovič, and J. Kratochvíl, Mathematical Model and Computational Studies of Discrete Dislocation Dynamics, IAENG International Jornal of Applied Mathematics, 45, 3 (2015)

[2] M. Kolář, M. Beneš, J. Kratochvíl, and P. Pauš, Numerical Simulations of Glide Dislocations in Persistent Slip Band, Acta Physica Polonica A, 128, 4 (2015)

[3] P. Pauš, J. Kratochvíl, and M. Beneš, A dislocation dynamics analysis of the crtical cross-slip anihilation distance and the cyclic saturation stress in fcc single crystals at different temperatures, Acta Materialia, 61, 20 (2013)

This work has been supported by the project No. 14-36566G Multidisciplinary research centre for advanced materials of the Grant Agency of the Czech Republic.

Multiscale Modeling Of Dislocation-Obstacle Interaction

Fredric Granberg1, Arttu Lehtinen2, Lasse Laurson2, Mikko Alava2, Kai Nordlund1

1Accelerator Laboratory, Department of Physics, University of Helsinki, P.O. Box 43, FIN-00014 University of Helsinki, Finland. E-mail: [email protected]

2COMP Center of Excellence, Department of Applied Physics, Aalto University School of Science, P.O. Box 11100, FIN-00076, Aalto, Espoo, Finland.

ABSTRACT

The mechanical properties of materials are mainly determined by the movement of dislocations, and their interaction with defects. In this study we investigated the interaction of edge dislocations with different carbides in BCC Fe, by means of Molecular Dynamics (MD).We identified the needed unpinning stress as well as the unpinning mechanism. To be able to investigate larger systems, we implemented a new class of obstacles in the Discrete Dislocation Dynamics (DDD) code ParaDiS. The new class of obstacles are interacting with the dislocations by a Gaussian potential with adjustable strength. With the obtained results from MD, we parametrized the newly implemented obstacles in DDD, and obtained the same mechanism and unpinning stress as in MD. With the DDD method parametrized this way, we simulate the interactions of dislocations with multiple obstacles and loops.

[1] F. Granberg, D. Terentyev, K. Nordlund, Interaction of Dislocations with Carbides in BCC Fe studied by Molecular Dynamics, Journal of Nuclear Materials, 460, 23-29 (2015)

[2] A. Lehtinen, F. Granberg, L. Laurson, K. Nordlund, M. Alava, Multi-Scale Modeling of Dislocation-Precipitate Interactions in Fe; from Molecular Dynamics to Discrete Dislocations, Submitted (2015)

This research was funded by the Academy of Finland project SIRDAME (grant No 259886 and 260053). We thank the IT Center for Science, CSC, for granted computational resources. This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.


Slip transmission in fcc/fcc bilayers using phase field dislocation dynamics (PFDD)

Yifei Zeng1, Abigail Hunter2, Irene J. Beyerlein3, Marisol Koslowski1

1School of Mechanical Engineering, Purdue University, West Lafayette, IN 47097, USA;2X Computational Physics Division, Los Alamos National Laboratory, PO Box 1663 MS

T086, Los Alamos, NM 87545, USA, [email protected]; 3Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.

ABSTRACT

This research presents the formulation of a phase field dislocation dynamics model designed to treat a system comprised of two materials differing in moduli and lattice parameters, meeting at a common interface. We use it to investigate the critical stress required to transmit a perfect dislocation across a bimaterial interface with a cube-on-cube orientation relationship. The calculation of the critical stress accounts for the effects of: 1) the stresses induced at the interface due to the lattice mismatch (misfit or coherency stresses), 2) the elastic moduli mismatch (Koehler forces or image stresses) and 3) the formation of the residual dislocation. Our results show that the critical stress associated with the transmission of a dislocation from material 1 to 2 is not the same as from material 2 to 1. We find that the transmission from the material with the lower shear modulus is easier than the reverse and the degree of asymmetry in critical stress is directly proportional with the lattice mismatch. Ananalytical model for the critical stress is also presented. It is based on the formation energy of the residual dislocation and shows good comparison with the simulated results in the limit of large mismatch for coherent interfaces. The analytical model predicts a scaling factor for the critical stress that is based on the shear moduli and lattice parameters of both materials.

The BDT and the Core Structures of Dislocations in Silicon

Jacques Rabier

Pprimme Institute, UPR 3346 CNRS – Université de Poitiers –ENSMA, Département Physique et Mécanique des Matériaux,

BP30179, F-86962 Chasseneuil Futuroscope Cedex, France

ABSTRACT

Although being one of the more studied material and considered as a model material for studying the relations between dislocation velocity and plasticity of bulk materials, a lot of problems are still pending about plasticity and dislocations in silicon. This is the case of the Brittle to Ductile Transition (BDT). Since the experimental evidence that plastic deformation of silicon below the usual BDTT is controlled by perfect shuffle dislocations [1], it is now admitted that perfect shuffle dislocations control the plasticity in the high stress low temperature domain and dissociated glide dislocations in the high temperature low stress domain. The BDT appears then relevant to the transition between these two domains where several core configurations can be operative. Unlike dissociated glide dislocations, core computations of perfect dislocations show that various forms of core can exist for a given dislocation. Some of these cores are sessile and differently from metals these sessile dislocations cannot be mobilized under stress, which promote nucleation of crack [2]. TEM experiments on plastically deformed silicon at high stress have shown that perfect dislocations nucleated in the brittle domain possess strong pinning points the density of which increases with temperature [2], [3]. Those pinning points appear to be intrinsic and can be associated either to a local transition between shuffle and glide cores or to some parts of sessile perfect dislocation cores. It is found that those pinning points are due to segments of sessile core rather than to glide core segments. This induces a shut off of the perfect dislocations sources and a severe discontinuity in the apparent mobility of available dislocations close to the BDT, the consequences of which will be discussed.

[1] J Rabier, P Cordier, T Tondellier, J L Demenet, H Garem Dislocation microstructures in Si plastically deformed at RT, Journal of Physics: Condensed Matter 12, 10059 (2000)

[2] J. Rabier, L. Pizzagalli, J. L. Demenet, Dislocations in Silicon at High Stress, “Dislocations in solids”, Elsevier B. V., 16, 47 (2010)

[3] T. Okuno, H. Saka, Electron microscope study of dislocations introduced by deformation in Si between 77 and 873 K, Journal of Materials Science, 48, 115 (2013)


Dislocation Dynamics Simulation of Precipitate Hardening

Lynn B. Munday, Joshua C. Crone, James J. Ramsey, Jaroslaw Knap

U.S. Army Research Laboratory, Aberdeen Proving Grounds, MD, 21005, [email protected]

ABSTRACT

Hexagonal close packed (hcp) crystals exhibit an anisotropic plastic response to loading, limiting their manufacturability and use in structural applications. Alloying hcp materials can drastically modify their plastic response through precipitate hardening. Computationalmodeling and simulation tools based on the phase-field method are beginning to provide the ability to predict the evolution of the precipitate’s size, shape and distribution due to heat treatment and alloy composition. However, a crystal plasticity constitutive model needed to predict the overall plastic response can only be parameterized to capture the effect of the precipitate structure; necessitating the need for a lower length scale model capable of predicting the discrete nature of plasticity occurring near the precipitates due to the motion of individual dislocations. For this reason, we integrate microstructure directly into a discrete dislocation dynamics (DDD) framework [1,2,3] in order to explicitly model the elastic interactions of dislocations with crystalline microstructure. This DDD framework allows us to characterize the influence of different precipitate structures on the evolution of the dislocation density which, in turn, is used to parameterize crystal plasticity models based on Orowan’s relation. In this presentation, we describe the use of this DDD framework to predict the dislocation density evolution and hardening in Mg-Nd alloys hardened by beta precipitates. We report the effect of precipitate elastic constants, shape, size and distribution on the predicted hardening. We also identify cross-slip as a locally activated dislocation process occurring near precipitates that induces strain rate effects on the dislocation density evolution. We will also report on our recent work extending this DDD framework to the simulations of polycrystalline materials.

[1] E. van der Giessen and A. Needleman, MSMSE 3, 689 (1995).[2] A. Arsenlis et al., MSMSE 15, 553 (2007).[3] J.C. Crone et al., MSMSE 22, 3 (2014).

Annihilation of Non-screw Dipolar Dislocations and Debris Evolution

across Time Scales

Hao Wang1,*, David Rodney2, Dongsheng Xu1, Rui Yang1

1 Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, P. R. China2 Institut Lumière Matière, Université Lyon 1, CNRS, UMR 5306, F-69622 Villeurbanne, France

ABSTRACT

Dislocation annihilation is one of the most important processes during fatigue. While the annihilation of screw dislocations in face-centered metals was thoroughly studied in the beginning of this century, the annihilation of non-screw dislocations hasreceived far less attention, despite the profuse existence of edge dipoles in deformed metals. This raises questions on the reliability of certain phenomenological parame-ters, e.g., the minimum annihilation distance. In the present work, interaction betweennon-screw dipolar dislocations and subsequent debris evolution are systematically studied in metals and alloys, covering a variety of lattice structures, dislocation orien-tations, dipole heights and temperatures. Direct molecular dynamics simulations indi-cate that dipolar dislocations transform into individual defects depending on dipoleheight, orientation and temperature; reconstructed configurations are formed at low temperature, while vacancy clusters, stacking fault tetrahedra and interstitial loops at high temperature. Employing saddle-point search methods, activation energies of the atomic processes therein are obtained and the lifetime of the above by-products is es-timated, showing the stability of certain clusters and loops on the experimental time-scale. Using objective kinetic Monte Carlo simulations, debris evolution and the re-sulting microstructure, as well as their influence on metal properties are revealed. Representative processes are stacking fault tetrahedron formation in Cu upon disloca-tion annihilation; pentavacancy as the key nucleus for vacancy clustering in Al; tem-perature-dependent defect evolution under irradiation in Ni; and interstitial loop strengthening upon deformation in Al.

Keywords: Dislocation annihilation; Point defect; Cluster; Dislocation loop; Mul-tiscale simulation

* E-mail: [email protected]. Patrick Veyssière (1947-2011) initiated and contributed to the research.


Collective influence of texture, grain shape, size and dislocation density on the plasticity of polycrystalline metallic thin films

Authors: Hareesh Tummala1, 2, Marc Fivel1, Thomas Pardoen2, Laurent Delannay2,Guerric Lemoine2

Affiliations: 1SiMaP-GPM2, Universit�́�𝒆𝒆𝒆 Grenoble Alpes / CNRS, F 38000 Grenoble, France; 2iMMC, Universit�́�𝒆𝒆𝒆 catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium

ABSTRACT

Freestanding metallic thin films often show a sharp crystallographic texture and columnar nanosized grains with mostly one grain along the thickness [1]. Enhanced strength and fatigue resistance of such nanocrystalline thin films are often accompanied by a lack of ductility. However, recently, moderate to high ductility of thin films has been reported [2]. This raises some fundamental questions about the deformation mechanisms that are active and also onthe modeling using classical dislocation based hardening approaches. In this paper, we study the collective influence of texture, grain shape, grain size and dislocation density distributions on strain hardening behavior; and on the transition from dislocation based to grain boundary nucleation based hardening. Thereby, providing some insight into the experimentally measured high ductility [3]. Firstly, we perform three dimensional discrete dislocation dynamics simulations on individual grains of same volume but different aspect ratios to understand the influence of the grain shape on the slip system activity and on the back stresses produced. Then, polycrystalline version of the dislocation dynamics code, TRIDIS coupled[4] with a finite element methods, is used to perform simulations of a film multi-crystal by accounting the essential characteristics from the literature. Results reveal the importance ofgrain size and dislocation density distributions on strain hardening and on the plastic transition regime in metallic thin films.

[1] W. D. Nix, Elastic and plastic properties of thin films on substrates, MSEA, 234-236, 37-44 (1997)

[2] M. -S. Colla et al., High strength-ductility of thin nanocrystalline palladium films with nanoscale twins, Acta Mater., 60, 1795-1808 (2012)

[3] T. Pardoen, Size and rate dependent necking in thin metallic films, Jr. Phys. Mech. Solids,62, 81-98 (2014)

[4] M. C. Fivel and G. R. Canova, Developing rigorous boundary condition to simulations of discrete dislocation dynamics, MSMSE, 5-7, 753 (1999)

An Anisotropic Dislocation Loop Model for Simulation of Nanoindentation of Single Crystals

Jiapei Guo Yiping Chen Qiao Ni

[email protected] of Mechanics, Huazhong University of Science and Technology

430074 Wuhan, China

ABSTRACT

An anisotropic dislocation loop model is proposed for simulation of nanoindentation of single crystals based on the recently available solution of the elastic displacement and stress fieldsdue to a polygonal dislocation within an anisotropic homogeneous half-space [1]. The present investigation is a direct extention of the approach established by Mura et al. [2], and its recent application to triangular dislocation loop model [3], which is only capable of describing the indentation processes of isotropic materials, thus ruling out the possibility of characterizing the nanoindentation of elastically anisotropic single crystals. By following Mura’s procedure, we adopt square and triangular prismatic dislocation loops as building blocks and with Burgers vectors normal to the free surface to simulate the Vickers and Berkovich indentation,respectively. However, we place all the dislocation loops within a semi-ellipsoidal volume rather than a semi-spherical region as adopted by Mura after analysing the existing simulation results based on dislocation density formulation. The nanoindentation is performed in [001] and [111] crystallographic directions employing Vickers and Berkovich indentors,respectively, and different magnitude of pile-up, sink-in and spring-back is observed in different directions, clearly demonstrating the elastic anisotropy of the indented single crystals, hence an further improvement of Mura’s model.

[1] H. J. Chu, E. Pan, J. Wang, I. J. Beyerlein, Elastic displacement and stress fields induced by a dislocation of polygonal shape in an anisotropic elastic half-space, Journal of Applied Mechanics, 79, 021011-1 to 021011-9(2012)

[2] T. Mura, N. Yamashita, A dislocation model for hardness indentation problems, Int. J. Engng Sci., 27(1), 1-9 (1989)

[3] S. Muraishi, Triangular dislocation loop model for indented material, Mechanics of Materials, 56, 106-121 (2013)

Acknoledgement The project is supported by National Natural Science Foundation Of China NSFC (11272129)


Dislocation 2016 USA , Sep 29-23 Abs up to 12/15 up to 300 words

Does phonon-like motion trigger a crystalline defect?

S T.Nakagawa.

1-1 Ridai-cho, Graduate School of Science, Okayama Univ. of Science, Japan,[email protected]

ABSTRACT

Self-interatsial atoms (SIA) often produce a specific “crystalline defect”, rather than simply smear out by recombination with vacancies. Such a crystalline defect is depicted using crystallographic notation. For example, the {311} platelet in c-Si is made of 110 linear defects composed of SIAs by aligning them along the orientation of 332 [1]. This formation process is the current issue of us, which undergoes at a high temperature as 723 K. In such system where high temperature is essential, a molecular dynamics (MD) simulation traces all the atoms, and a crystallographic analysis called Pixel Mapping (PM) method [2]analyses both crystalline defects and the phase (in terms of the long-ranger-order (LRO) parameter). The PM reveals the existence of wide gap between two sets of {311} double layers and mathematical lattice frame laying in the gap space, which we confirmed to be the platform for SIAs to be trapped [3]. We monitored such annealing process using MD after randomly scattering Frenkel pairs (FP) in bulk of c-Si [3]. Because of the presence of FPs, the time-series of LRO parameter showed us the slow phase transition as critical slowing-down phenomenon first. The annealing was started since then. Unexpected result was that the defect density was not proportional to the initial concentation of FPs, espetially at low concentation below 3 atomic %. Moreover, a cooperative and oscillatory movement of target atoms looked to promote the formation of the specific {311} defect made of SIAs. Here we show the nonlinear correlation between SIAsand surrounding atoms through its time-series of LRO parameter.References[1] S. Takeda and T. Kamino: Phys. Rev. B 51, 214 (1995).[2] S. T. Nakagawa: Phys. Rev. B 75, 205406 (2002).[3] S. T. Nakagaw: Rad. Effect Defect Solids, (2014). doi: 10.10 80/10420150.2014.984613.

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Bauschinger effect in 99% purity Al having fine grain sizes

Authors: Si Gao1, Akinobu Shibata1,2, Yoshihisa Kaneko3, Nobuhiro Tsuji1,2

Affiliations: 1 Dept. Materials Science and Engineering, Kyoto University, 606-8501,Kyoto, Japan;

2 Elements Strategy Initiative for Structural Materials (ESISM), Kyoto University3 Dept. Mechanical Engineering, Osaka City University, Japan;

A commercial purity Al (99% purity: 2N-Al) with various grain sizes ranging from 0.5 µm to 18 µm was fabricated by Equal Channel Angular Pressing (ECAP) and subsequent annealing processes. The microstructure of the specimen was observed by SEM-EBSD and TEM. Monotonic tension and compression test revealed that the yield stress and flow stress were significantly higher in the specimens having grain sizes smaller than 2 μm than those having larger grain sizes. Tension-compression tests were carried out to measure the Bauschinger effect of the 2N-Al at different stages of plastic deformation by using a dumbbell-like specimen. Then, the back stress at different plastic strains was measured from the stress-strain curves obtained from of the tension-compression test. It was found that the exceptionally high back stress accounted for a great portion of the total flow stress in the fine grained specimens. The large back stress is discussed based on the grain size and dislocation pile-ups in the material [1].

[1] C. W. Sinclair et al, Scripta Materialia 55 (2006) 739–742


Plasticity in nanolayered crystals - Combining nanomechanical testing, electron microscopy and density functional theory

calculations

Sandra Korte-Kerzel1, Christoffer Zehnder1, Sebastian Schröders1, Bernd Meyer²,Tobias Klöffel²

1 Institute of Physical Metallurgy and Metal Physics, RWTH Aachen University, Aachen 52074, Germany

² Interdisciplinary Center for Molecular Materials and Computer-Chemistry-Center, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91052 Erlangen, Germany

ABSTRACT

Many atomically layered crystals have been found to possess extraordinary mechanical properties, like high hardness and modulus paired with appreciable ductility facilitated by slip on one particularly soft layer within the stacking. The MAX phases are the most prominent example of this class of materials, but other crystals are also being investigated, for example X2BC boron carbides. Among these kinds of structures, dislocation motion is expected and most commonly observed to take place parallel to the atomic stacking along the basal planes.Taking Mo2BC, a promising coating material, as an example two major gaps in our understanding are addressed here: Firstly, while slip takes place within the basal plane, it not obvious in which of the parallel layers this should occur, and, secondly, there has so far been no characterization of any alternative slip systems. To address these aspects,microcompression has been used to activate individual slip systems while suppressing cracking by reducing the sample size. In correlation with EBSD and TEM, (041} planes have been identified as alternative slip planes where the Schmid factor on the basal plane systems is low. In order to identify the exact slip planes parallel to the basal orientation and potential Burgers vectors on (041}, DFT calculations were used to obtain gamma surfaces and assess the shear strength. It is shown that the combination of small scale testing, electron microscopy and DFT is well suited to investigate the mechanisms of plasticity in complex and brittlecrystals. The potential of this approach is extended even further when combined with high temperature nanomechanical testing which not only allows the measurement of thermal activation to relate 0 K calculations to ambient temperatures but can also reveal changes in deformation mechanism in atomically layered crystals, as shown here in nanoindentation at temperatures of up 800 °C.

Title: Atomic Scale Study of Twinning Dislocations in Zirconium

Authors: Olivier MacKain1, Maeva Cottura1, David Rodney2 and Emmanuel Clouet1

Affiliations: 1CEA, DEN, Service de Recherches de Métallurgie Physique, F-91191 Gif-sur-Yvette, [email protected]; 2Institut Lumière Matière, UMR5206 Université de

Lyon 1 – CNRS, F-69622 Villeurbanne

ABSTRACT

Plasticity in zirconium, as well as in many other hexagonal close-packed metals, is controlled by the glide of dislocations with <a> Burgers vectors. Those dislocations can however not explain any deformation along the <c> axis and at low temperatures twinning is activated to accommodate such a strain. In this work, we focus on the mechanisms controlling twin growth using atomistic simulations relying either on an empirical interatomic potential of the EAM type or on ab initio calculations. The four different twinning systems, which can be activated in zirconium depending on the temperature or the applied strain, are modeled. We first study the perfect twin boundaries showing the ability of the EAM potential to predict their structures and relative energies taking the ab initio calculations as a reference. We then focus on the disconnections, i.e. the twinning dislocations which are responsible of the twin growth. For a given twinning system, several disconnections of different Burgers vectors, different heights and different core structures exist. Considering all these disconnections, we calculate their formation and migration energies using the NEB method. The elastic interactions between the defects and their periodic images are computed using linear inhomogeneous anisotropic elasticity, allowing to extract disconnection core energies that are intrinsic properties of the disconnections, independent of the cell dimensions. We use this information to develop a kinetic model of twin growth and study the competition between the different growth modes under various stress states.


Plasticity in nanolayered crystals - Combining nanomechanical testing, electron microscopy and density functional theory

calculations

Sandra Korte-Kerzel1, Christoffer Zehnder1, Sebastian Schröders1, Bernd Meyer²,Tobias Klöffel²


² Interdisciplinary Center for Molecular Materials and Computer-Chemistry-Center, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91052 Erlangen, Germany

ABSTRACT

Many atomically layered crystals have been found to possess extraordinary mechanical properties, like high hardness and modulus paired with appreciable ductility facilitated by slip on one particularly soft layer within the stacking. The MAX phases are the most prominent example of this class of materials, but other crystals are also being investigated, for example X2BC boron carbides. Among these kinds of structures, dislocation motion is expected and most commonly observed to take place parallel to the atomic stacking along the basal planes.Taking Mo2BC, a promising coating material, as an example two major gaps in our understanding are addressed here: Firstly, while slip takes place within the basal plane, it not obvious in which of the parallel layers this should occur, and, secondly, there has so far been no characterization of any alternative slip systems. To address these aspects,microcompression has been used to activate individual slip systems while suppressing cracking by reducing the sample size. In correlation with EBSD and TEM, (041} planes have been identified as alternative slip planes where the Schmid factor on the basal plane systems is low. In order to identify the exact slip planes parallel to the basal orientation and potential Burgers vectors on (041}, DFT calculations were used to obtain gamma surfaces and assess the shear strength. It is shown that the combination of small scale testing, electron microscopy and DFT is well suited to investigate the mechanisms of plasticity in complex and brittlecrystals. The potential of this approach is extended even further when combined with high temperature nanomechanical testing which not only allows the measurement of thermal activation to relate 0 K calculations to ambient temperatures but can also reveal changes in deformation mechanism in atomically layered crystals, as shown here in nanoindentation at temperatures of up 800 °C.

Title: Atomic Scale Study of Twinning Dislocations in Zirconium

Authors: Olivier MacKain1, Maeva Cottura1, David Rodney2 and Emmanuel Clouet1

Affiliations: 1CEA, DEN, Service de Recherches de Métallurgie Physique, F-91191 Gif-sur-Yvette, [email protected]; 2Institut Lumière Matière, UMR5206 Université de

Lyon 1 – CNRS, F-69622 Villeurbanne

ABSTRACT

Plasticity in zirconium, as well as in many other hexagonal close-packed metals, is controlled by the glide of dislocations with <a> Burgers vectors. Those dislocations can however not explain any deformation along the <c> axis and at low temperatures twinning is activated to accommodate such a strain. In this work, we focus on the mechanisms controlling twin growth using atomistic simulations relying either on an empirical interatomic potential of the EAM type or on ab initio calculations. The four different twinning systems, which can be activated in zirconium depending on the temperature or the applied strain, are modeled. We first study the perfect twin boundaries showing the ability of the EAM potential to predict their structures and relative energies taking the ab initio calculations as a reference. We then focus on the disconnections, i.e. the twinning dislocations which are responsible of the twin growth. For a given twinning system, several disconnections of different Burgers vectors, different heights and different core structures exist. Considering all these disconnections, we calculate their formation and migration energies using the NEB method. The elastic interactions between the defects and their periodic images are computed using linear inhomogeneous anisotropic elasticity, allowing to extract disconnection core energies that are intrinsic properties of the disconnections, independent of the cell dimensions. We use this information to develop a kinetic model of twin growth and study the competition between the different growth modes under various stress states.


Field Dislocation Mechanics for Quasi-static, Supersonic Applications

Authors: Xiaohan Zhang1, Amit Acharya2

Affiliations: 1Mechanical Engineering, Stanford University. [email protected];2Civil and Environmental Engineering, Carnegie Mellon University.

[email protected]

ABSTRACT

We have developed a model based on continuum mechanics that reduces the study of a significant class of problems of discrete dislocation dynamics to questions of the modern theory of continuum plasticity. The physical phenomena explored correspond to behavior of individual and a collection of few dislocations, in particular, phenomena complementary to what can be dealt with Discrete Dislocation Dynamics methodology in a fundamental manner. Numerically we have explored: 1) the question whether Peierls stress exists in a translationalinvariant continuum mechanics theory, which has been believed impossible if inferred from aclassical static argument without considerations of the onset dynamic shape change of dislocation cores; 2) dislocation annihilation and dissociation as consequences of fundamental kinematics and energetics and not targeted constitutive rules for such phenomena; 3) finite speed propagation effects of elastic waves vis-à-vis dislocation dynamics with nonlinear elasticity. The kinetic relationship between dislocation velocity and applied load is shown to be qualitatively consistent with MD simulations [1]. 4) Dislocation pile ups in parallel slip planes in a single crystal. For example, a few classical pile up problems are solved in our model and compared to analytical solutions made possible in Eshelby, Frank and Nabarro [2].Stress-strain curve is also analyzed.

[1] P. Gumbsch, H. Gao, Dislocations faster than the speed of sound, Science, 283, 965 (1999)

[2] J.D. Eshelby, F.C. Frank, F.R.N. Nabarro, The equilibrium of linear arrays of dislocations.Philos. Mag., 42, 351 (1951)

On The Temporal Scale Transition From Discrete Dislocation To Continuum Plasticity

Erik Van der Giessen

University of Groningen, Zernike Institute for Advanced Materials, Nijenborgh 4, 9747AG Groningen, the Netherlands

ABSTRACT

In a multi-scale picture of metal plasticity, coarse-graining from an individual dislocation to continuum plasticity involves a number of scale transitions in space and time. Somewhere along this chain of scale transitions, continuum slip emerges as the `smeared-out’ result of the motion of many discrete dislocations. Starting from the classical laws of Orowan and Kröner, formal spatial averaging procedures have been developed in the past two decades by Groma, Zaiser and co-workers. The time scale, however, is unaffected by these approaches, thus leaving coarse-graining in time as one of the last conundrums in multi-scale plasticity.

This objective of this work is to study how small timescale fluctuations at the level of discrete dislocations average out to a much longer time scale that is characteristic of continuum slip. Simulations will be reported of the single-slip response of edge dislocations, each governed by two timescales: for dislocation nucleation and linear viscous drag. The results reveal that the collective dislocation behavior at high densities gives rise to an approximate power law dependence of the overall slip rate on applied stress with an exponent on the order of 10.


Modeling dislocation interaction with local and extended obstacles

Ghiath Monnet

EDF – R&D, MMC, Avenue des Renardières, 77818 Moret sur Loing, France. E-mail address: [email protected].

ABSTRACT

It is well known that hardening is controlled by obstacle nature, size, density and distribution.Recent Dislocation Dynamics (DD) simulations [1] show that hardening induced by randomly distributed precipitates can be predicted by a simple constitutive equation involving the precipitate strength, size and density. The equation is inspired from the seminal work of Bacon et al [2] on the Orowan hardening, who were the first to reveal the dipolar interaction effects of the line tension and to apply Friedel statistics on impenetrable obstacles. Although the equation seems to predict hardening over a large range of precipitate size, density and strength, it does not seem to apply in the case of small dislocation loops [3]. Atomistic simulations show that loops are invariably absorbed by edge dislocations and form helical turns on screw dislocations.The intense line relaxation pins strongly screw dislocations and confers a non-local (extended) character to the defect. Implementing these features into large scale DD simulations [3] show that hardening induced by small loops can be expressed using the Taylor equation with a constant coefficient α = 0.5. Now the constitutive description of hardening induced by local and extended defects can be established, the effect of their superposition on the flow stress is still unknown. New DD simulations involving a large number of precipitates and dislocation loops were carried out in order to determine the appropriate description of the resulting hardening. It is shown that strong precipitates restrict line relaxation during helical turn formation, which results in a surprising superposing effect.

[1] G Monnet, Acta Materialia, 95, 302-311 (2015)[2] DJ Bacon, UF Kocks, RO Scattergood, Philosophical Magazine, 28, 1241-1263 (1973) [3] G Monnet, Scripta Materialia, 100, 24-27 (2015)

Title: The Thermal Force on a Dislocation: Resolving AnomaliesIn The Phonon Coupling With Zwanzig’s Technique

Authors: Thomas D. Swinburne1, Sergei L. Dudarev1

Affiliations: 1CCFE, Culham Science Centre, Abingdon, Oxon, OX14 3DB, UK

ABSTRACT

Elasticity theory gives the force acting on an elastic singularity in a linear continuum, but realcrystal defects are localised deformations in a discrete, non-linear crystal. Phonon scatteringtheories based on elasticity theory predict that the defect-phonon coupling should rise linearlywith temperature, but atomistic simulations of nanoscale defects find the coupling is oftentemperature independent. This anomalous coupling is indicative that elasticity theory isinsufficient to capture the important thermal dynamics of crystal defects.

We have derived an exact equation of motion for a crystal defect, treated only as a localiseddeformation, from the Newtonian dynamics of the host crystal[1,2]. Our analytical approachuses Zwanzig’s technique, giving a clear form for the total force acting on a crystal defect. Atzero temperature one can show the defect force reduces to the Peach-Koehler force, but at finitetemperature the defect force is stochastic, with the defect-phonon coupling related to the defectforce autocorrelation.

Our computational method can extract the formally exact defect position, velocity and forcedirectly from the atomistic positions, velocities and forces for the first time. We show how forceaverages converge much faster than position or velocity averages, and compare these results toanalytic expansions. Our numerical and analytical results allow direct comparison betweenVineyard and Kramer’s transition state theories and resolve anomalies in the defect-phononcoupling by showing how scattering theories erroneously assume crystal defects conservemomentum.

[1] T. D. Swinburne, S. L. Dudarev and A. P. Sutton, PRL, 113, 215501 (2014)[2] T. D. Swinburne and S. L. Dudarev, PRB, 92, 134302 (2015)


Ductile mechanisms of representative transition metals containing pre-existing nanovoids

Kai Zhao1, Inga G. Ringdalen2, Jianying He1, Zhiliang Zhang1*

1NTNU Nanomechanical Lab, Department of Structural Engineering, Norwegian University of Science and Technology (NTNU), Trondheim 7491, Norway;

2SINTEF Materials and Chemistry, Trondheim 7465, Norway.

*Corresponding author: [email protected]

ABSTRACT

The ductile mechanism based on dislocation emission and propagation in monocrystalline Cu and Fe are investigated by molecular dynamics simulation. The dislocation activity in Cu is controlled by the collective interaction of stacking faults along the pyramid structure consisting of four (111) planes. The dislocation configuration in nanovoided Cu is strongly dependent on the void size and strain rate. Vacancy generation is observed in Cu specimens due to the intersection of more than two stacking faults. Three dominant mechanisms of void growth in Fe are identified: (i) for smaller void, nucleation of twinning boundaries; (ii) for intermediate void, emission of shear loops; (iii) for larger void, stacking faults nucleate at the void surface and then degenerate into shear loops. The generation of vacancies in Fe is attributed to the jog dragging of the screw dislocations. The predicted slip-twinning transition rate of Fe at room temperature agrees well with atomistic simulations. Since previous models [1,2] can only predict the effect of void size on the yield stress, an analytical model based on nudged elastic band calculation is proposed to include the strain rate dependence of the incipient yielding. This new model demonstrates the critical radius of shear loop in Cu sample under 108 s-1 loading is about on the magnitude of Burgers vector.

[1] V.A. Lubarda, M.S. Schneider, D.H. Kalantar, B.A. Remington, M.A. Meyers, Void growth by dislocation emission, Acta Materialia, 52, 1397 (2004)

[2] Y. Tang, E.M. Bringa, M.A. Meyers, Ductile tensile failure in metals through initiation and growth of nanosized voids, Acta Materialia, 60, 4856 (2012)

Title: Glissile Junctions And Their Role On The Plastic Deformation At The Microscale

Authors: Markus Stricker1, Daniel Weygand1

Affiliations: 1Institute for Applied Materials (IAM), Karlsruhe Institute of Technology (KIT), Engelbert-Arnold-Str. 4, 76131 Karlsruhe, Germany; [email protected],

phone: +49 721 608 48499

ABSTRACT

Dislocation junction formation is in general considered as primary hardening mechanism in plastic deformation. Here it is shown that glissile junctions act as an effective dislocation source. They change the topology of the dislocation network and strain paths in micrometer sized specimen [1]: Depending on sample size, dislocation density and an increasing number of activated slip systems, the density fraction of dislocations generated by multiplication from glissile junctions and their contribution to the macroscopic plastic deformation reach 30-60%. Furthermore, a correlation between the formation of glissile junctions and stress drops is observed. These findings are included in a rate formulation for a crystal plasticity model [2]. A comparison between Discrete Dislocation Dynamics simulations [3] and the crystal plasticity model is shown. Although the glissile junction mechanism does not significantly alter the macroscopic behavior (e.g. stress-strain curve), the way in which a specific structure relaxes the externally applied strain is different. This change in the local relaxation behavior is attributed to the formation of weaker sources during straining, which should be included in continuum plasticity frameworks.

[1] M. Stricker, D. Weygand, Dislocation multiplication mechanisms – Glissile junctions and their role on the plastic deformation at the microscale, Acta Mater., 99, 130 (2015)

[2] A. Ma, F. Roters, A constitutive model for fcc single crystals based on dislocation densities and its application to uniaxial compression of aluminium single crystals,

Acta Mater., 52, 3603 (2004)[3] D. Weygand, L.H. Friedman, E. Van der Giessen, A. Needleman, Aspects of boundary

value-problem solutions with three-dimensional dislocation dynamics, Model. Simul.



Enrique I. Galindo-Nava, Pedro E.J. Rivera-Díaz-del-Castillo

[email protected] of Cambridge

Department of Materials Science and Metallurgy27 Charles Babbage Road, Cambridge

CB3 0FS, United Kingdom

ABSTRACT

A new modelling framework for describing the microstructure of martensitic steels is presented. The structure of lath martensite in Fe-C steels is described in terms of ahierarchical arrangement by decomposing it in prior austenite grains, packets, blocks and laths [1]. The first three microstructural features are intrinsically related to crystallographic orientations of the martensite with respect to the prior-austenite phase, whilst the lath patterning is related to the lattice distortions produced during the phase transformation. The dislocation density is obtained by considering the lattice distortion energy being equal to the strain energy of dislocations at the lath boundaries. The transition from lath- to plate-like structure in martensite with carbon content higher than 0.6 wt% is also described [2]: In addition to the energy stored by dislocations, finely spaced transformation twins crossing throughout the plates (midribs) accommodate the excess lattice distortion energy induced by the highcarbon content. These microstructural features act as the main strength contributors in high-C steels. Tempering effects are introduced by estimating the extent of carbon diffusing away from dislocations and twin boundaries; this mechanism relaxes the Cottrell atmospheres of lath dislocations and coarsens the boundaries. Descriptions of the dislocation and grain boundary density allow us to postulate a unified description of the hardness in martensitic steels for a wide range of carbon contents. Strength contributions of lath and plate martensite, precipitates and retained austenite are included, and possible scenarios for microstructural optimisation are explored. It is shown that a peak in hardness is usually observed for carbon contents ranging 0.6-1wt% as a result of a compromise between the strength of martensite, and the increase in retained austenite.

[1] E.I. Galindo-Nava, P.E.J. Rivera-Díaz-del-Castillo. A model for the microstructure behaviour and strength evolution in lath martensite. Acta Materialia 98 (2015) 81-93[2] E.I. Galindo-Nava, P.E.J. Rivera-Díaz-del-Castillo. Understanding the factors controlling the hardness in martensitic steels. Scripta Materialia 110 (2016) 96-110

This research was supported by the grants EP/L014742/1 and EP/L025213/1 from the UK Engineering and Physical Sciences Research Council (EPSRC).

Dynamical Approach to Displacement Jumps In Load Controlled Nanoindentation

K. Srikanth1 and G. AnanthakrishnaMaterials Research Centre, Indian Institute of Science, Bangalore-560012,

India

ABSTRACT

We extend the recently developed dislocation dynamical model [1] to explain displacement jumps in load controlled experiments as an alternate theoretical approach to simulations. We set-up a system of coupled nonlinear evolution equations for the mobile and forest dislocationdensities. These equations are coupled to an equation describing the load rate condition. We include nucleation, multiplication, and propagation threshold mechanisms for mobile dislocations apart from other well-known dislocation transformation mechanisms between the mobile and forest dislocations. The commonly used Berkovitch indenter is considered. The ability of the approach is illustrated by adopting experimental parameters such as the indentation rates, the geometrical quantities defining the Berkovitch indenter including the nominal tip radius and other parameters. We demonstrate that the model predicts all the generic features of nanoindentation such as the existence of an initial elastic branch followed by several displacement jumps of decreasing magnitudes, and residual plasticity after unloading. More specifically, we show that the model reproduces load-displacement curve for Al thin films [2]. The stress corresponding to the maximum force on the Berkovitch elastic branch is close to the theoretical yield stress. The predicted values for all the quantities are close to those reported by experiments. We explicitly demonstrate that the displacementjumps arise due to a competition between the applied load rate and the rate at which area increases due to plastic deformation. We also elucidate the ambiguity in defining hardness at nanometre scales where displacement jumps dominate. The approach also provides insights into several open questions.

[1] G. Ananthakrishna, R. Katti and K. Sriknath, Dislocation dynamical approach to force fluctuations in nanoindentation experiments, Phys. Rev. B 90, 094104, (2014)[2] A. Gouldstone, H. J. Koh, K. Y. Zeng, A. E. Giannakopoulos and S. Suresh, Discrete and continuous deformation during nanoindentation of thin films, Acta Mater., 48, 2777, (2000)


Dynamical Approach to Intermittent Nanoindentation and Indentation Size Effect

G. Ananthakrishna1 and K. Srikanth Materials Research Centre, Indian Institute of Science, Bangalore-560012,

India

ABSTRACT

Dynamical methods offer a natural platform to describe instabilities. Recently, we developed a dislocation dynamical model [1] to explain load drops in displacement controlled (DC) experiments and displacement jumps in load controlled (LC) experiments with a view to develop an alternate theoretical approach to simulations. We set-up a system of coupled nonlinear evolution equations for the mobile and forest dislocation densities. We include nucleation, multiplication, and propagation threshold mechanisms for mobile dislocations apart from other well known dislocation transformation mechanisms between the mobile and forest dislocations. The evolution equations are coupled to relevant equation defining the loading condition. The model predicts not just the generic features of nanoindentation, but numbers that closely match experiments. For instance, the model predicts the existence of an initial elastic branch followed by load drops in the case of DC experiments or several displacement jumps in the case of LC experiments and residual plasticity after unloading. The approach has been extended to explain well-known features of indentation size effect (ISE). For instance, our model predicts that a plot of the square of indentation hardness as a function of the inverse of the indentation depth is linear up to a tenth of micrometer but shows a tendency for saturation for nanometer scales. Our approach uses experimental parameters such as the indentation rates, the geometrical quantities defining the indenter etc. The approach offers a way of describing ISE based on dislocation evolution equations and does not require information about dislocation densities from other sources. The approach also provides insights into several open questions.

[1] G. Ananthakrishna, R. Katti and K. Sriknath, Dislocation dynamical approach to force fluctuations in nanoindentation experiments, Phys. Rev. B 90, 094104, (2014); K. Srikanth and G. Ananthakrishna, Dynamical approach to displacement jumps in nanoidentation experiments, under review in Acta Materialia


Authors: Alexander Stukowski1, Wei Cai2, Vasily V. Bulatov3

Affiliations: 1Institute of Materials Science, Darmstadt University of Technology, 64289Darmstadt, Germany, [email protected]; 2Department of Mechanical

Engineering, Stanford University, Stanford, CA 94305-4040, USA; 2Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550, USA

ABSTRACT

While the problem of automatically identifying dislocation defects in atomistic crystal models was solved a few years ago with the development of the dislocation extraction algorithm(DXA) [1], the converse, i.e. the construction of an atomistic model from a given network of dislocation lines and corresponding Burgers vectors, is still unsolved. We report on an effort to develop a practical solution to this problem and describe a computational method toconvert a line representation of dislocations to a fully atomistic one. Besides being a very useful tool, which greatly simplifies the construction of initial configurations for atomistic simulations, such an algorithm could enable a full round-trip from molecular dynamics (MD) to discrete dislocation dynamics (DD) and back to MD, e.g,, to bypass the time and lengthlimitations of MD or to overcome DD’s inability to describe the spontaneous formation of dislocations.Our approach is based on a Delaunay tetrahedralization and decomposition of the input linenetwork into triangular loops (of prismatic and glide type), for which the elastic displacement field can be computed [2]. A challenge lies in the fact that, in general, the result depends on the decomposition and the order in which cut surfaces are being introduced in the crystal. However, the deformation history that led to a particular dislocation network and the sequence of cuts are typically unknown. Thus, this information must be synthesized by the algorithm in a meaningful way. Furthermore, we discuss how overlaps and gaps in the material, which may arise from cut surface intersections, can be dealt with to construct fault-free atomistic crystals.

[1] A. Stukowski, K. Albe, Extracting dislocations and non-dislocation crystal defects from atomistic simulation data, Modelling Simul. Mater. Sci. Eng., 18, 085001 (2010)

[2] D.M. Barnett, The displacement field of a triangular dislocation loop, Phil. Mag. A, 51,383 (1985)


Unusual room-temperature plasticity in silicon nanopillars

A. Merabet1, M. Texier*1, C. Tromas2, M. Verdier3, A. Talneau4, O. Thomas1, J. Godet2

* Corresponding author : [email protected] 1 Aix-Marseille Université, CNRS, Université de Toulon, IM2NP UMR 7334, F-13397

Marseille, France 2 Institut Pprime, UPR3346 CNRS – Université de Poitier, F-86962 Futurscope –

Chasseneuil du Poitou Cedex, France 3 SIMaP, Université Joseph Fourier, CNRS, UMR5266, F-38402 Saint Martin-d'Héres,

France 4 Laboratoire de Photonique et de Nanostructures, CNRS, F-91460 Marcoussis, France

ABSTRACT

Over the last years, progresses in nanomaterials design and manufacturing has revolutionized technology and opened up prospects for many scientific researches. The investigations of material properties (electrical, optical, electronic, ...) at small scales have revealed amazing behaviors, different from those currently observed in bulk samples. More recently, a few studieshave revealed that the mechanical behavior of semiconducting materials is also affected by the sample size . For instance, silicon, which is known to behave at room temperature as a brittle material, shows an unexpected ductile behavior when the sample size decreases below few hundreds of nanometers [1]. The mechanisms leading to this phenomenon remain, however, poorly understood. In this context, this research project aims at investigating in more details the deformation behavior of silicon nanopillars by combining experimental techniques (SEM, FIB, HRTEM) and molecular dynamics simulations. In this work various nanopillars, with different orientations (<110>, <100>, <123>) and diameters (from 100 nm to 1 µm), were patterned by RIE and FIB micromachining in SOI (Silicon On Insulator) 340 nm layers, these pillars were then compressed with a slow-strain-rate (10-4 s-1) at room temperature using a nano-indentor equipped with a flat punch and which allow control both displacement and applied force. The measured stress-strain curves evidence the first stages of plastic deformation (pop-in events). Post mortem observations of deformed nanopillars performed by SEM and TEM reveal the activation of different slip systems. The comparison between HRTEM experimental images and simulations notably evidence the simultaneous propagation of partial and perfect dislocations in {111} planes. In addition, unexpected plastic events have also been evidenced in {113} planes. Various possible deformation mechanisms involved during the nano-compression of the pillars will be described, based on the microscopic observations. [1] F. Östlund et al., Brittle-to-Ductile Transition in Uniaxial Compression of Silicon Pillars at

Room Temperature, Adv. Func. Mat., 19, p1(2009). This work is performed within the framework of the ANR-funded research project « BrIttle-to-Ductile Transition in Silicon at Low dimensions » (project n° 12-BS04-0003, SIMI4 program).

Stabilization of the Hard Core Structure of Dislocations by Interstitial Solutes in BCC Metals: a New Key Player in the Blue Brittleness of Steels

Bérengère Lüthi1, Lisa Ventelon1, David Rodney2, François Willaime3

1CEA, DEN, Service de Recherches de Métallurgie Physique, 91191 Gif-sur-Yvette, France; [email protected]; 2Institut Lumière Matière, Université Lyon 1, CNRS,

UMR 5306, 69622 Villeurbanne, France; 3CEA, DEN, Département des Matériaux pour le Nucléaire, 91191 Gif-sur-Yvette, France.

ABSTRACT

The core structure of screw dislocations in pure BCC transition metals has been the object of extensive studies and debates for several decades. Thanks in particular to DFT calculations, there is now a general consensus that the dislocation core adopts a symmetrical configuration, the easy core configuration, centered on a triangle of first-neighbor <111> atomic columns,where helicity is reversed with respect to the bulk. The other core configurations – the asymmetric core, the hard core and the split core – are all unstable in pure BCC metals [1].The case of alloys has however so far been rarely addressed. In this work, we investigate the effect of interstitial solute atoms on the ½<111> screw dislocations in BCC metals using ab initio calculations. First considering the case of Fe(C), our DFT calculations show that, when a row of solute atoms is added in the neighborhood of the dislocation core, both the dislocation and the solute atoms reorganize towards a low-energy configuration, where, surprisingly, the dislocation adopts a hard-core configuration. The solute atoms are at the center of regular trigonal prisms formed by the Fe atoms inside the three <111> core atomic columns [2], a local configuration similar to the building unit of cementite. We obtain the same core reconstruction with other solutes (B, N, O) in Fe and in other metals (W, Mo).NEB calculations show that the mobility of the transformed dislocations is very low. This agrees with recent in-situ TEM observations, which show that in the regime of dynamical strain ageing of steels, often referred as blue brittleness, the mobility of screw dislocations is strongly reduced [3].

[1] L. Dézerald et al., Phys. Rev. B 89, 024104-13 (2014)[2] L. Ventelon et al., Phys. Rev. B 91, 220102(R) (2015)[3] D. Caillard, J. Bonneville, Scripta Mater. 95, 15 (2015)


Prediction of dislocation boundary characteristics

Author: Grethe Winther

Affiliation: Department of Mechanical Engineering, Technical University of Denmark, [email protected]

ABSTRACT

Plastic deformation of both fcc and bcc metals of medium to high stacking fault energy is known to result in dislocation patterning in the form of cells and extended planar dislocation boundaries. The latter align with specific crystallographic planes, which depend on the crystallographic orientation of the grain [1]. For selected boundaries it has been experimentally verified that the boundaries consist of fairly regular networks of dislocations, which come from the active slip systems [2]. The networks have been analyzed within the framework of Low-Energy-Dislocation-Structures (LEDS) and it is found that to a large extent the dislocations screen each other’s elastic stress fields [3].The present contribution aims at advancing the previous theoretical analysis of a boundary on a known crystallographic plane to actual prediction of this plane as well as other boundary characteristics, such as the dislocation content and misorientation. The prediction is based on the expected active slip systems and assumptions of mutual stress screening. In general, networks of dislocations with three linearly independent Burgers vectors fulfilling the criterion of mutual stress screening may form on any plane. Crystal plasticity calculations combined with the hypothesis that these boundaries separate domains with local differences in the slip system activity are introduced to address precise prediction of the experimentally observed boundaries. The presentation will focus on two cases from fcc metals: boundaries aligned with a {111} slip plane and boundaries, which bisect the angle between two slip planes. Finally, the effect of long-range plastic strain gradients is also discussed.

[1] X. Huang, G. Winther, Dislocation structures. Part I. Grain orientation dependence, Phil. Mag., 87, 5189 (2007)

[2] C. S. Hong, X. Huang, G. Winther, Dislocation content of geometrically necessary boundaries aligned with slip planes in rolled aluminum, Phil. Mag, 93, 3118 (2013)

[3] G. Winther, C. S. Hong, X. Huang, Low-Energy Dislocation Structure (LEDS) character of dislocation boundaries aligned with slip planes in rolled aluminium, Phil.Mag., 95,1471 (2015)

Dislocation microstructure evolution under tribological contacts

Johanna Gagel1, Daniel Weygand1, Peter Gumbsch1,2

1Institute of Applied Materials, Karlsruhe Institute of Technology, Karlsruhe, Germany [email protected]

2Fraunhofer IWM, Freiburg, Germany

ABSTRACT

Tribological contact properties are determined by the elastic and plastic response of the material. The investigation of the evolution of the plasticity near the surface is clearly a question where a detailed local resolution of the plastic activity is needed. However, incipient stages of plastic deformation are difficult to access experimentally and are not well understood. Therefore a three dimensional Discrete Dislocation Dynamics tool [1] is adapted for contact problems. The initial contact problem consists of indentation problem with a spherical indenter. The indentation simulations show how extended prismatic or helical dislocations structures can be formed from preexisting dislocations [2], which have also been found in experiments [3]. The simulations can be rationalized by a simple model, taking into account the complex stress field underneath the indenter. Furthermore simulations of sliding contacts give insights in how the dislocation microstructure changes with respect to the static case. Depending on the crystallographic orientation dislocation are transported by the moving contact and grain boundaries change the resulting surface roughness.

[1] D. Weygand, L. H. Friedman, E. Van der Giessen, A. Needleman, Aspects of boundary-value problem solutions with three-dimensional dislocation dynamics, Modelling and Simulation in Materials Science and Engineering 10 (4) (2002) 437

[2] J. Gagel, D. Weygand, P. Gumbsch, to be submitted[3] S. Graca, P. A. Carvalho, R. Colaco, Journal of Physics D: Applied Physics 44 (33)

(2011) 335402

The financial support by the Deutsche Telekom Stiftung, Bonn, Germany, is gratefully acknowledged.


First-Principles Modeling of Screw Dislocation Mobilityin Zr and Ti

Emmanuel Clouet1, Nermine Chaari1, David Rodney2, and Daniel Caillard3

1 CEA, DEN, Service de Recherches de Métallurgie Physique, 91191 Gif-sur-Yvette, France; [email protected] 2 Institut Lumière Matière, Université Lyon 1, CNRS UMR 5306, 69622 Villeurbanne, France; 3 CEMES-CNRS, 29 rue Jeanne Marvig, BP

94347, 31055 Toulouse cedex, France.

ABSTRACT

Titanium and zirconium have a close plastic behavior arising from their hexagonal close-packed crystallography and from their similar electronic structure. In particular, plasticity in these two transition metals is controlled by screw dislocations gliding in the prism planes, with cross-slip in the first-order pyramidal planes or in the basal planes activated at high enough temperature and a strong hardening associated with O addition. We use ab initio calculations and NEB method to study core properties of the screw dislocations and their mobility in both metals. These calculations show that screw dislocations may adopt different cores that are dissociated either in a prism or in a pyramidal plane, in agreement with the existence of stable stacking faults in these two planes [1]. The prismatic core easily glides in its habit plane, whereas the pyramidal core needs to overcome an important energy barrier to glide. The prismatic glissile core is the most stable in Zr, but the dislocation ground state in Ti corresponds to the pyramidal core. As a consequence, dislocation glide is easy and confined in the prismatic planes at low temperature in pure Zr, whereas a locking-unlocking mechanism operates in Ti where the locked periods correspond to a slow and limited glide in pyramidal planes and the unlocked periods to a rapid and extended glide in prismatic planes, in agreement with in situ TEM straining experiments [2]. Calculations in Zr also reveal that basal glide of the screw dislocation shares the same thermally activated process as pyramidal glide. Finally, we study the interaction of an oxygen atom with these different configurations of the screw dislocation. Ab initio calculations evidence a strong repulsion with the oxygen repelling the stacking fault ribbon, thus inducing dislocation cross-slip.

[1] N. Chaari, E. Clouet and D. Rodney, Phys. Rev. Lett. 112, 075504 (2014)[2] E. Clouet, D. Caillard, N. Chaari, F. Onimus and D. Rodney, Nature Materials 14, 931

Link Between Dislocation Trajectory And Schmid Law Deviation In BCC Crystals

Lucile Dezerald1,2, David Rodney3, Emmanuel Clouet2, Lisa Ventelon2 and François Willaime4

1Institut Jean Lamour, Université de Lorraine, SI2M, F-54011 Nancy, France;[email protected]; 2CEA, DEN, Service de Recherches de Métallurgie

Physique, F-91191 Gif-sur-Yvette, France; 3Institut Lumière Matière, Université Lyon 1 - CNRS, F-69622 Villeurbanne, France; 4CEA, DEN, Département des Matériaux pour

le Nucléaire, F-91191 Gif-sur-Yvette, France

ABSTRACT

Body-centered cubic (BCC) metals are known to display an atypical plasticity at low temperature. One of their most surprising properties is a marked dependence of the elastic limit on crystal orientation, in clear violation of the Schmid law. This effect is known to originate from the motion of ½<111> screw dislocations that are subjected to a high lattice resistance, which can be described through the two-dimensional energy landscape of the dislocation in the {111} plane, the so-called 2D Peierls potential. Here we use ab initiocalculations based on the Density Functional Theory (DFT) to investigate the 2D Peierls potential in the following BCC transition metals: V, Nb, Ta, Mo, W and Fe [1]. The Peierls potentials are found asymmetrical with respect to the {110} plane of average dislocation motion in all elements. Consequently, the dislocation trajectory is not straight between neighboring equilibrium positions, but systematically deviates towards the twinning region. We propose a modification of the Schmid law based on a projection of the applied stress on the deviated trajectory rather than on the average glide plane [2]. The proposed law agrees with both experimental and DFT measurements of the Peierls stress. This work thus enables predicting Schmid law deviations in all BCC crystals from simple atomistic calculations and provides a physical explanation for this well-known property characteristic of BCC plasticity.

[1] L. Dezerald, L. Ventelon, E. Clouet, C. Denoual, D. Rodney and F. Willaime, Ab initiomodeling of the two-dimensional energy landscape of screw dislocations, Physical Review B, 89, 024104 (2014).

[2] L. Dezerald, D. Rodney, E. Clouet, L. Ventelon, and F. Willaime, Plastic anisotropy and dislocation trajectory in BCC metals, under review (2015).


The stability, dissociation and cross-slip of <c+a> dislocations in Mg and other hcp metals

Z. Wu1 ,2 and W. A. Curtin1*

1Institute of Mechanical Engineering, Ecole Polytechnique Federale de Lausanne, Lausanne CH-1015, Switzerland ; 2Institute of High Performance Computing, 1

Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore.*[email protected]

ABSTRACT

Mg, Ti, Zr and their alloys are technologically critical structural metals in lightweight, high strength or high resistance to corrosion applications. These metals all have hcp structure and exhibit strongly anisotropic, multiple slip behaviors, which are highly complicated and distinctly different from those of well-established fcc and bcc metals. Despite their importance, our understanding on their fundamental plastic deformation is very limited. Here, we present a comprehensive, atomistic study on the most mysterious yet crucial <c+a> dislocations in Mg. First, both the <c+a> edge dislocation on the pyramidal II plane and <c+a> mixed dislocation on the pyramidal I plane are metastable. They undergo thermally-activated, stress-dependent climb-dissociations into basal oriented sessile structures, which cannot contribute to plastic straining and serve as strong obstacles to the motion of all other dislocations. These dissociations are intrinsic to Mg, driven by reduction in dislocation energy and predicted to occur at very high frequencies at room temperature, thus eliminating all major dislocation slip systems able to contribute to c-axis strain [1]. Second, the <c+a> screw dislocation dissociates into partials of pure screw character on both pyramidal I and II planes, making its cross-slip relatively easy and occur without dislocation constriction. The cross-slip energy barrier is controlled by the steps/jogs energy and the near-core dislocation energy difference on the two pyramidal planes. The near-core energy difference can be influenced by non-Schmid stresses, leading to tension-compression asymmetry and change of absolute stable planes for the screw dislocation. The cross-slip process is governed by features of the generalized stacking fault energy surfaces of pyramidal planes and thus expected to be general to all hcp metals. More broadly, the mechanistic insights on the edge, mixed, and screw <c+a> dislocations behaviors obtained in Mg are consistent with a wide range of experiments on other hcp metals and alloys.

[1] Z. Wu, W.A. Curtin, The Origins of High Hardening and Low Ductility in Magnesium, Nature, 526, 62 (2015)

Title: Grain Boundary Mechanics in Nickel-based Superalloys

Authors: John Rotella, Michael Sangid

Affiliations: Purdue University, 701 W. Stadium Ave. [email protected].

ABSTRACTMechanical behavior of structural materials are governed by their grain boundaries. Annealing twins have been shown as favorable boundaries to enhance strength and ductility. Through the process of Grain Boundary Engineering (GBE), we have the ability to tailor the volume fraction of the annealing twins to improve the mechanical behavior of the material. In this work, concurrent electron backscatter diffraction and digital image correlation will be used to study the heterogeneous strain of GBE nickel-based superalloys. Specifically, superalloys with various grain sizes and contents of annealing twins are cyclically loaded to determine the role of microstructure on strain evolution and accumulation. Grain boundary serrations will also be studied, specifically their role on sliding mechanisms.



Pierre-Antoine Geslin1, Benoit Appolaire2, Alphonse Finel2, Riccardo Gatti2, Benoit Devincre2, Francesca Boioli1, David Rodney1

1Institut Lumière Matière, Université Lyon 1 - CNRS, 69622 Villeurbanne, France; [email protected];

2Laboratoire d'Etude des Microstructures, Onera/CNRS, 92322 Châtillon, France.

ABSTRACT

The study of thermally activated mechanisms is of great importance to understand the evolution of metals and metallic alloys with temperature. At high temperature, vacancy diffusion is thermally activated and dislocations climb by vacancy absorption/emission. Most approaches [1,2] consider that climb occurs homogeneously along the dislocation. However, vacancies are emitted/absorbed at jogs, defects along the line that can present a low density, influencing significantly the climb process. In a recent contribution [3], we propose an analytical solution for the climb rate of a jogged dislocation, accounting for attachment-detachment kinetics of vacancies to the dislocation core, as well as pipe diffusion between jogs. In a multiscale approach, we then propose a phase-field model for dislocation climb that couples dislocation movements with the evolution of the vacancy field. We show how the model can be parametrized to reproduce the climb rate of jogged dislocations, allowing to study quantitatively the climb behavior of complex assemblies of dislocations. Secondly, we have implemented the nudged elastic band method into a dislocation dynamics framework to study the formation of persistent slip bands (PSB) during cyclic deformation and their evolution with temperature [4]. In particular, we investigate the minimum energy paths when a dislocation escapes from a PSB wall, bringing insights into the temperature stability of these structures.

[1] J.P. Hirth, J. Lothe, Theory of Dislocations, 1968.[2] S.M. Keralavarma, T. Cagin, A. Arsenlis, and A.A. Benzerga, Phys. Rev. Lett. 109,

265504 (2012).[3] P.-A. Geslin, B. Appolaire, A. Finel, Phys. Rev. Lett. in press (2015).

Room temperature deformation mechanisms in the Mg2Ca Laves phase and a Mg-Mg2Ca alloy

Christoffer Zehnder1, Sebastian Schröders1, James Gibson1, Stefanie Sandlöbes1,Sandra Korte-Kerzel1


ABSTRACT

In order to improve the creep resistance of magnesium alloys and thereby increase their operating temperature, hard intermetallic phases can be incorporated in the microstructure. In particular the addition of Al or Ca to Mg results in the formation of a skeleton-like intermetallic structure at the grain boundaries. This structure consists predominately of Laves phases, which reduces the minimum creep rate by a few orders of magnitude. In bulk, these Laves phases are extremely brittle at low temperatures, limiting our understanding of the underlying mechanisms of plasticity. Additionally, the small size of the microstructural features in technical alloys make bulk-scale tests unsuitable for studying these phases. Using nanomechanical testing (nanoindentation and microcompression) in individual grains, cracking can be suppressed and plastic deformation can be observed [1]. Micropillars were milled using FIB in individual grains of a polycrystalline specimen, and orientations determined by EBSD to activate and interrogate slip systems. These data have then been combined with slip line analysis around indents. Such an approach reveals the presence ofboth basal and prismatic slip at ambient conditions. Critical resolved shear stresses for these slip systems have been calculated, and TEM analysis of the deformation microstructure performed. In order to investigate the deformation behaviour of the alloy, i.e. the co-deformation of Mg and the Mg2Ca Laves phase, ECCI and DIC have been applied to deformed Mg-Al-Ca alloys. This reveals dislocation substructures and strain partitioning between the Mg matrix and the intermetallic phase. This work therefore exemplifies how nanomechanical testing in conjunction with electron microscopy can extend the current knowledge of plasticity in macroscopically brittle crystals.

[1] S. Korte, W.J. Clegg, Studying Plasticity in Hard and Soft Nb–Co Intermetallics, Advanced Engineering Materials, 14, No. 11 (2012), 991-997



Pierre-Antoine Geslin1, Benoit Appolaire2, Alphonse Finel2, Riccardo Gatti2, Benoit Devincre2, Francesca Boioli1, David Rodney1

1Institut Lumière Matière, Université Lyon 1 - CNRS, 69622 Villeurbanne, France; [email protected];

2Laboratoire d'Etude des Microstructures, Onera/CNRS, 92322 Châtillon, France.

ABSTRACT

The study of thermally activated mechanisms is of great importance to understand the evolution of metals and metallic alloys with temperature. At high temperature, vacancy diffusion is thermally activated and dislocations climb by vacancy absorption/emission. Most approaches [1,2] consider that climb occurs homogeneously along the dislocation. However, vacancies are emitted/absorbed at jogs, defects along the line that can present a low density, influencing significantly the climb process. In a recent contribution [3], we propose an analytical solution for the climb rate of a jogged dislocation, accounting for attachment-detachment kinetics of vacancies to the dislocation core, as well as pipe diffusion between jogs. In a multiscale approach, we then propose a phase-field model for dislocation climb that couples dislocation movements with the evolution of the vacancy field. We show how the model can be parametrized to reproduce the climb rate of jogged dislocations, allowing to study quantitatively the climb behavior of complex assemblies of dislocations. Secondly, we have implemented the nudged elastic band method into a dislocation dynamics framework to study the formation of persistent slip bands (PSB) during cyclic deformation and their evolution with temperature [4]. In particular, we investigate the minimum energy paths when a dislocation escapes from a PSB wall, bringing insights into the temperature stability of these structures.

[1] J.P. Hirth, J. Lothe, Theory of Dislocations, 1968.[2] S.M. Keralavarma, T. Cagin, A. Arsenlis, and A.A. Benzerga, Phys. Rev. Lett. 109,

265504 (2012).[3] P.-A. Geslin, B. Appolaire, A. Finel, Phys. Rev. Lett. in press (2015).

Room temperature deformation mechanisms in the Mg2Ca Laves phase and a Mg-Mg2Ca alloy

Christoffer Zehnder1, Sebastian Schröders1, James Gibson1, Stefanie Sandlöbes1,Sandra Korte-Kerzel1


ABSTRACT

In order to improve the creep resistance of magnesium alloys and thereby increase their operating temperature, hard intermetallic phases can be incorporated in the microstructure. In particular the addition of Al or Ca to Mg results in the formation of a skeleton-like intermetallic structure at the grain boundaries. This structure consists predominately of Laves phases, which reduces the minimum creep rate by a few orders of magnitude. In bulk, these Laves phases are extremely brittle at low temperatures, limiting our understanding of the underlying mechanisms of plasticity. Additionally, the small size of the microstructural features in technical alloys make bulk-scale tests unsuitable for studying these phases. Using nanomechanical testing (nanoindentation and microcompression) in individual grains, cracking can be suppressed and plastic deformation can be observed [1]. Micropillars were milled using FIB in individual grains of a polycrystalline specimen, and orientations determined by EBSD to activate and interrogate slip systems. These data have then been combined with slip line analysis around indents. Such an approach reveals the presence ofboth basal and prismatic slip at ambient conditions. Critical resolved shear stresses for these slip systems have been calculated, and TEM analysis of the deformation microstructure performed. In order to investigate the deformation behaviour of the alloy, i.e. the co-deformation of Mg and the Mg2Ca Laves phase, ECCI and DIC have been applied to deformed Mg-Al-Ca alloys. This reveals dislocation substructures and strain partitioning between the Mg matrix and the intermetallic phase. This work therefore exemplifies how nanomechanical testing in conjunction with electron microscopy can extend the current knowledge of plasticity in macroscopically brittle crystals.



Ab initio Energy Landscape for Dislocation Motion in Tantalum

Amit Samanta, Luis Zepeda-Ruiz, Vasily V. Bulatov

Lawrence Livermore National Laboratory 7000 East Avenue, Livermore, CA 94550

[email protected]

ABSTRACT

Motion of screw dislocations is known to control many important features of plastic deformation in BCC materials. Consequently, in the last few decades numerous studies using empirical and first principles methods have focused on understanding the stability of the various core structures, namely the easy core (E), the hard core (H) and the soft core (S). In this talk, we will present results from ab initio and empirical potential calculations for BCC metal tantalum. We show that the unavoidably small periodic supercell sizes used in DFTcalculations necessitate careful accounting for non-linear elasticity and that, once the latter is indeed accounted for, dislocation core energies can be extracted with very high precision, below 1 meV. We predict that the ground state of the screw dislocation in tantalum should remain the same non-polarized E-core within a wide range of pressures, from 0 to 7 Mbar. Together with an in depth analysis of the relative stability of the H, E and S-core structures, we are able construct a potential energy landscape from ab initio calculations that can describe the motion of screw dislocations in tantalum.



Christoph Kirchlechner, Nataliya Malyar, Gerhard Dehm

Max-Planck-Institut für Eisenforschung, Düsseldorf, Germany

ABSTRACT

The deformation behavior of metallic single crystals is size dependent [1], as shown by several studies during the last decade [2-4]. Nevertheless, real structures exhibit different interfaces like grain, twin or phase boundaries. Due to the possibly higher stresses at the micron scale, the poor availability of dislocation sources and the importance of diffusion in small dimensions the mechanical behavior of samples containing interfaces can considerable differ from bulk material.

In the talk we show the first in situ µLaue compression experiments on micron sized, bi-crystalline samples [5]. Three different grain-boundary types will be presented and discussed (i) Large Angle grain Boundaries (LAGBs) acting as strong obstacle for dislocation slip transfer; (ii) LAGBs allowing for easy slip transfer and (iii) coherent Σ-3 twin-boundaries in various orientations.While the bi-crystalline samples of (i) show strong hardening caused by pile-up stresses, the bi-crystalline samples of (ii) behave comparable to single crystals. However, in case of (ii) a large amount of dislocations is laid down at the grain-boundary leading to a significant change in grain-boundary character. Since (ii) does not store geometrically necessary dislocations within the crystal, the size scaling behavior is similar to a single crystalline reference. Finally, similar results will be presented for the coherent Σ-3 boundary (iii).The talk will focus on pile-up of dislocations, slip transfer mechanisms, storage of dislocations and dislocation networks at the LAGB.

[1] M.D. Uchic, D.M. Dimiduk, J.N. Florando and W.D. Nix, Science 305 (2004) p. 986.[2] J.R. Greer and J.T.M. De Hosson, Progress in Materials Science 56 (2011) p. 654.[3] O. Kraft, P.A. Gruber, R. Mönig and D. Weygand, Plasticity in confined dimensions, in Annual Review of Materials Research, 2010, p. 293.[4] M.D. Uchic, P.A. Shade and D.M. Dimiduk, Annual Review of Materials Research 39(2009) p. 361.[5] N. Malyar, J.S. Micha, G. Dehm and C. Kirchlechner, Acta Mater. in preparation (2015).

The authors want to acknowledge funding by the DFG within the project KI-1889/1 as well as ESRF for allocation of beamtimes MA-2488 and MA-2096. The authors thank Jean-Sébastien Micha for the superior support during the experiment.



Domingos L. Silva Junior1 and Maurice de Koning 2

1Instituto de Física e Química, Universidade Federal de Goiás, Regional Catalão, UFG, Av. Lamartine Pinto de Avelar, 1120 Setor Universitário - CEP 75704-020, Catalão,

Goiás, Brazil, [email protected] de Física "Gleb Wataghin", Universidade Estadual de Campinas, UNICAMP,

CEP 13083-859, Campinas, São Paulo, Brazil, [email protected]

ABSTRACT

We use Density Functional Theory (DFT) to investigate mobility properties in proton-disordered hexagonal ice, so called ice Ih. As in most crystalline materials, the plasticity in ice Ih is governed by the motion of lattice dislocations. In ice Ih the water molecules are connected by hydrogen bonds, which are highly directional. This characteristic, combined with proton disorder, is responsible for a large Peierls barrier in this structure. In crystals with a large Peierls barrier, dislocation glide takes place by thermally activated nucleation and propagation of kinks [1]. Therefore, kink structure and the formation and migration energetics play a central role in the plastic properties of ice Ih. In a previous work [2] we observed that the structure of partial dislocations in ice Ih are very similar to the 30o and 90o partial dislocations found in silicon [3]. In this context, we investigate the structure as well as the formation and migration energetics of kinks on 30o and 90o partial dislocations in ice Ih.

[1] V. V. Bulatov and W. Cai, Computer Simulations of Dislocations, Oxford University Press, Oxford (2006).[2] D. L. Silva Junior and M. de Koning, Phys. Rev. B 85, 024119 (2012).[3] V. V. Bulatov, et al., Philos. Mag. A. 81, 1257 (2001).

D.S. and M.K. gratefully acknowledge support from the Brazilian agencies CNPq, CAPES, FAPEG, FAPESP, CENAPAD-SP and the Center for Computational Engineering and Sciences - Fapesp/Cepid no. 2013/08293-7.

Title: Exploring the limit of dislocation based plasticity in nanostructured metals

Authors: Darcy A. Hughes

Affiliations: Fremont CA, USA 94539 [email protected]

ABSTRACT

A twofold decrease to an unexplored scale of 5 nm was produced in Cu by applying a large sliding load in liquid nitrogen, thereby breaking the grain size barrier for dislocation plasticity [1]. Sliding contact imposes a gradient in deformation and structure with depth, due to the interaction with surface asperities [2]. The structure is stabilized by small alloying additions of Fe and the formation of interconnected medium and high angle boundaries during sliding. In the subsurface layers, 5 nm scale grains/crystallites form due to high deformation. A continuously coarser size scale develops as the deformation decreases with increasing depth from the surface. This graded structure enables a direct and quantitative characterization of the structural scale over several orders of magnitude. Statistical and universal scaling analyses of deformation induced high angle boundaries, dislocation boundaries, and individual dislocations observed by high resolution electron microscopy reveal that dislocation processes dominate over the entire size scale. Quantitative analyses of the preferred crystal orientations further corroborate this result. These results are compared to large strain structures that develop under different deformation modes at smaller strains to illustrating this univesal behavior. Dislocation based plasticity continues at size scales far below the transition suggested by experiment and molecular dynamics simulations, with a limit below 5 nm. Mechanical properties in the subsurface can be predicted from the measured and quantified structural parameters. Very high strength metals i.e., >2.5 GPa, may emerge based on this enhanced structural refinement, with applications to wear resistant components for wind energy.

[1] D. A. Hughes, N. Hansen, Exploring the limit of dislocation based plasticity in nanostructured metals, Phys. Rev. Lett. 112, 135504 (2014)[2] D. A. Hughes, N. Hansen, Graded Nanostructures Produced by Sliding and Exhibiting Universal Behavior , Phys. Rev. Lett. 87, 135503 (2001)

Work performed while D. A. H. was at Sandia, was supported by the Office of Basic Energy Sciences, Division of Materials and Engineering Sciences, U. S. Department of Energy. Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’sNational Nuclear Security Administration under Contract No. DE-AC04-94AL85000. N. Hansen and support of a Danish Research Foundation Grant No. DNR F86-5 are also acknowledged.


Dislocations in Molecular Crystals: Role of Molecular Flexibility in Defining the Core Structure and Critical Stresses

Catalin R. Picu, Anirban Pal, Nithin Mathew

Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180; [email protected].

ABSTRACT

Molecular crystals, such as some food components, pharmaceuticals and energetic materials, are common occurrences in everyday life and in engineering. Their mechanics is significantly more complex than that of monatomic crystals due to the low symmetry of such crystals and to the coupling between dislocation motion and intra-molecular deformation. In this work we study the effect of molecular flexibility on the structure, critical stresses and mobility of dislocations in Cyclo Trimethylene Trinitramine (RDX) which is an energetic crystal widely used in military and civilian applications. We identify the most important slip systems and determine the core structure of dislocations using atomistic models at zero and finite temperature [1]. The slip systems are ranked based on their critical stresses and results are compared with experimental observations. We observe that molecules rotate in specific positions inside the core and determine that such rotated molecules are actually stable point defects that may exist outside of the core [2]. They have a finite lifetime once the dislocation that created them moves away and may interact with other mobile dislocations on the same glide plane. Further, the effect of artificially reducing the molecular flexibility on critical stresses and dislocation mobility is investigated using a set of coarse grained models withincreasing degree of coarsening. It is concluded that even a small reduction of the molecular flexibility increases the Peierls stress to unrealistic values and hence the interaction between glide and molecular distortion is essential in the mechanics of these cyrstals [3].

[1] N. Mathew, R.C. Picu, P.W. Chung, Peierls stress of dislocations in molecular crystal RDX, J. Phys. Chem. A, 117, 5326 (2013)

[2] A. Pal, R.C. Picu, Rotational defects in the RDX crystal, J. Chem. Phys. 140, 044512 (2014)[3] A. Pal, R.C. Picu, Towards coarse grained models of RDX crystals, J. Phys. Chem. A,

submitted (2015).

Probing the Ultimate Limits of Crystal Plasticity

Vasily V. Bulatov

Lawrence Livermore National LaboratoryL-367, PO Box 808, Livermore, CA 94550

[email protected]

ABSTRACT

Dislocations are ubiquitous in metals where their motion presents the dominant and often the only mode of plastic response to straining. However, under certain conditions depending on the material, dislocations' own activity becomes insufficient to prevent other modes of inelastic response from triggering (often) leading to catastrophic material failure. High strain-rate deformation, e.g. laser-driven shock and shockless compressions, is one such case where response mechanisms other than dislocation multiplication and motion are known to become active. Given that dislocations do not move with velocities in excess of the sound velocity and that the initial dislocation line density can be fairly low, it is of interest to find under what conditions of straining does dislocations' own ability to relieve stress become overwhelmed. And, when indeed dislocation motion is no longer sufficient, what other mechanisms of response are triggered and how and what are the critical parameters - straining rate, initial dislocation microstructure, temperature, pressure, etc. - that define the limits of dislocation mediated plasticity. Here I will report on results of large-scale MD and (mesoscopic) DD simulations intended to probe the ultimate limits of single crystal plasticity.



Title: First-Principles Calculations of Interaction between Carbon Atoms and Edge Dislocations in alpha-Iron

Authors: Mitsuhiro Itakura1, Hideo Kaburaki2, Masatake Yamaguchi2, Tomohito Tsuru2,

Affiliations: 1Center for Computational Science & e-System, Japan Atomic Energy Agency, 178-4-4 Wakashiba, Kashiwa, Chiba 277-0871 Japan; 2 Center for

Computational Science & e-System, Japan Atomic Energy Agency, 2-4 Shirakata-Shirane, Tokai, Ibaraki, 319-1195, Japan

ABSTRACT

The interaction between interstitial impurity elements and edge dislocation is directly related to the hardness of steels. The fundamental theory was established more than 60 years ago, but several key figures, such as the strongest interaction energy at the core and the saturation density, remain unclear. In the present work, interaction between a pure edge dislocation <111>/2 {1-10} aligned in the <2-1-1>direction in alpha-iron and carbon atoms is evaluated by first-principles calculations, using the flexible boundary method. In the dilute carbon limit, the strongest binding energy is about 0.7 eV. In the dense carbon limit, up to seven carbon atoms per <211> unit length can be segregated on the slip plane with binding energy about 0.5 eV. After the binding sites on the slip plane are occupied, the binding energy of further segregation becomes very small owing to the carbon-carbon repulsion.

[1] A.H.Cottrel, Dislocation Theory of Yielding and Strain Ageing of Iron, Proceedings of the Physical Society, 62, 49-62 (1949)

Dislocation Dynamics Study on Dislocation-Preicpitate InteractionMechanism Transition from Cutting to Orowan Looping

Akiyuki Takahashi, Masaki Miyagi

Department of Mechanical Engineering, Faculty of Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda-shi, Chiba, 278-8510, Japan

[email protected]

ABSTRACT

This paper presents the dislocation dynamics study on the dislocation-precipitate interaction mechanism transition from cutting to Orowan looping. In this study, it is assumed that the precipitate has only a coherency strain, and the coherency strain generates a stress, which causes an elastic interaction between the precipitate and a dislocation. By increasing the diameter of the precipitate, the interaction mechanism is changed from the cutting type to Orowan looping. Using the dislocation dynamics method, the critical resolved shear stress (CRSS) for the interactions is calculated. Then, it could be found that the CRSS is smoothly connected at the interaction mechanism transition. The CRSS is then compared to the theoretical solutions of the coherency strengthening[1] and Orowan looping[2]. For the cutting mechanism, the theoretical solution gives a substantially larger CRSS compared to the numerical results, which is attributed to the dislocation line flexibility. On the other hand, for the Orowan looping mechanism, the theoretical solution gives qualitatively good prediction of the CRSS, and in addition, is a good description of the CRSS for the cutting mechanism as well. Then, we derive an equation giving an accurate prediction of CRSS of the interaction with both the cutting and Orowan looping mechanism by giving a slight modification to the theoretical solution of Orowan looping mechanism. In the derivation, the apparent looping diameter and the influence of coherency strain at the closing of dislocation loop is taken into account. The CRSS calculated with the proposed equation is in good agreement with the dislocation dynamics numerical results.

[1] V. Gerold, H. Haberkorn, On the critical resolved shear stresss of solid solutions containing coherent precipitates, Physical Status Solidi, 16, 675-684 (1966)

[2] D.J. Bacon, U.F. Kocks, R.O. Scattergood, The effect of dislocation self-interaction on the Orowan stress, Philosophical Magazine, 28, 1241-1263 (1973)


The role of elastic anisotropy and the 𝜸𝜸𝜸𝜸 surface in mesoscale dislocation simulations.

Authors: Ben A. Szajewski1, Abigail Hunter2, Irene J. Beyerlein1

Affiliations: 1Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545;

2X-Computational Division, Los Alamos National Laboratory, Los Alamos, NM 87545;Correspondence: [email protected]

ABSTRACT

Over the last decade simulations of the motion of discrete dislocations have emerged as a powerful investigative tool for understanding material behavior. Various simulation methodologies have offered considerable insight into the detailed mechanistic processes governing plasticity in strained crystals. Despite appreciable progress, incorporating detailed physics on the atomic scale into temporal and spatial scales relevant towards engineering applications has proven formidable. We present several results from mesoscale phase field (PF) simulations of dislocations incorporating both full elastic anisotropy and the inelastic inter-planar potential (i.e., the 𝜸𝜸𝜸𝜸 surface). First, we quantitatively compare straight, relaxed dislocation cores obtained from our anisotropic PF formulation to those predicted by both discrete elasticity and other more computationally demanding approaches, demonstrating excellent agreement with numerically more intensive methods. Next, we turn our attention to a canonical problem in the physics of dislocations: the small bow-out. By inclusion of both partial dislocations (via the 𝜸𝜸𝜸𝜸 surface) and elastic anisotropy the physics of a dislocation bowing between pinning points is investigated. We compare our simulation results to those predicted by the classical, isotropic and anisotropic singular elastic theories. We validate anisotropic theory that for certain FCC materials, inclusion of anisotropy has a marked influence on the dislocation line tension, and cannot be neglected in quantitative materials science applications. Our results as a whole indicate that conventional, isotropic, singular discrete dislocation models that rely on a phenomenological cut-off parameter cannot reproduce flow processes as predicted by higher fidelity models. This work highlights the necessity of both anisotropic elasticity and realistic, non-discrete dislocation cores in quantitative simulations of dislocations.

The authors are grateful for the support by the Los Alamos National Laboratory (LANL) Laboratory Directed Research and Development (LDRD) office, project 20160619ER.

Investigation of Nonmetallic Inclusion-Driven Failures

Authors: Diwakar P. Naragani1, Michael D. Sangid1, Paul A. Shade2, Jay Schuren2,Hemant Sharma3, Jun-Sang Park3, Peter Kenesei3, Joel V. Bernier4, Todd J. Turner2

Affiliations: 1School of Aeronautics and Astronautics, Purdue University, 701 W. Stadium Avenue, W. Lafayette, IN 47906, [email protected]; 2Air Force Research Laboratory,

Materials and Manufacturing Directorate 2230 10th Street, Wright-Patterson AFB, OH 45433; 3Argonne National Laboratory, Materials Physics and Engineering X-ray Science

Division, 9700 S. Cass Ave., Building 431-A004, Lemont, IL 60439; 4Computational Engineering Division, Science & Technology Principle Directorate, Lawrence Livermore

National Laboratory, 7000 East Avenue, L-129, Livermore, CA 94550.

ABSTRACT

Crack initiation at inclusions is a dominant and unavoidable failure mechanism as fatigue progresses to find the ‘weakest link’ in the material to nucleate a crack. In this study, a Ni-based superalloy sample is seeded with an alumina inclusion and cyclically loaded. The test was sequentially interrupted to conduct absorption contrast tomography to determine spatial and morphological information about the inclusion. High energy x-ray diffraction microscopy (HEDM) was carried out to simultaneously characterize the microstructure (position and orientation) with information about the stress state of the grains. The results of the reconstruction elucidating temporal and spatial strain evolution of the grains around the inclusion are presented. Strain heterogeneity and the associated stress localization are indicative of damage evolution; particular cases illustrating this are shared.


1

Microscopic investigation of strain gradient plasticity under non-

proportional loading

Authors: Ill Ryu1, John W. Hutchinson2, and Huajian Gao1

Affiliations: 1 School of Engineering, Brown University, Providence RI, 02912,

[email protected]; 2 School of Engineering and Applied Sciences, Harvard

University, Cambridge MA, 02138

Abstract

Three dimensional dislocation dynamics (DD) simulations are performed to make a critical assessment of two classes of strain gradient plasticity theories currently available for studying size dependent plasticity at the micrometer-scale. Non-incremental version of strain gradient plasticity theories is characterized by certain stress quantities expressed in terms of increments of strains and their gradients, whereas incremental version of theories employ incremental relationships between all stress quantities and the increments of strains and their gradients. From the previous work, two classes of theories showed marked difference in the prediction of the onset of plasticity under non-proportional loading. In this work, our DD results show that plastic flow could continuously occur even with passivation, which lead to severe hardening, without showing the elastic loading gap.

Dislocation Dynamics Modeling of Material Strength Changein Spinodally Decomposed Ferritic Fe-Cr Alloys

Takuya Suzuki1, Akiyuki Takahashi2, and Akiyoshi Nomoto3

1,2Department of Mechanical Engineering, Tokyo University of Science,2641 Yamazaki, Noda-shi, Chiba, 278-8510, Japan

3Central Research Institute of Electric Power Industry2-11-1 Iwado-kita, Komae-shi, Tokyo, 201-8511, Japan

[email protected], [email protected], [email protected]

ABSTRACT

When Fe-Cr alloys are aged at high temperatures, the phenomenon called “Spinodal decomposition” occurs in the ferrite phases, which causes an ultrafine phase separation mixing Fe-rich and Cr-rich phases. It is known that the material embrittlement and the strength change occur because of the modulated structure. Cahn derived the equation which expresses the internal stress distribution in the material caused by mismatch strain [1]. And Kato devised the theoretical calculation method of incremental Critical Resolved Shear Stress(CRSS) using Cahn model [2,3]. However, the some details were not discussed. So, the goal of this study is to reveal the detail of the strength changing mechanism using the Dislocation Dynamics (DD) computer simulation. In this study, based on the Cahn equation, we created the spinodally decomposed Fe-Cr alloy model. Then we observed the dislocation behavior in the model and evaluated the incremental CRSS due to spinodal decomposition using DD method. In the simulation results, it could be found that Kato method can’t give us a good evaluation of the incremental CRSS, because the dislocation shape is assumed to be straight in the method. So, in order to make an accurate evaluation of it, it must be accounted for the curvature of dislocation. In this study, it could be found that it is able to estimate the incremental CRSS when part of the dislocation shape is approximated by an arbitrary simple function.

[1] J.W. Cahn, Hardening by Spinodal Decomposition, Acta Metall., 11, 1275 (1963)[2] M. Kato, Hardening by Spinodally Modulated Structure in b.c.c. Alloys, Acta Metall., 29,

79 (1981)[3] M. Kato, S. Horie, and T.C. Lee, Evaluation of Critical Resolved Shear Stress for Systems

with General Periodic Stress Fields, Phys. Stat. Sol. (a), 98, 209 (1986)


Investigating Microstructural Features In Ti-6Al-4V Using Crystal Plasticity Finite Element Modeling

Authors: Kartik Kapoor1, Michael D. Sangid1

Affiliations: 1 School of Aeronautics and Astronautics, Purdue University, 701 W. Stadium Ave, West Lafayette, IN 47907-2045, email: [email protected]

ABSTRACT

There is a growing need to understand the damage mechanisms in two-phase titanium alloys due to their widespread use in the aerospace industry (especially within gas turbine engines),variation in their properties and performance based on their microstructure, and their tendency to undergo premature failure due to dwell and high cycle fatigue well below their yield strength. Two-phase titanium alloys occur in a number of microstructural forms depending on the nature of processing and heat treatment they have undergone. This work focuses on Ti-6Al-4V with a duplex microstructure, consisting of α (HCP) and β (BCC) phases arranged in a lamellar arrangement via a continuum description of dislocation motion. A crystal plasticity finite element (CPFE) model for a polycrystal that incorporates the microstructural features such as α-β colonies is presented in this work. Behavior of the slip systems at the single crystal level, influenced by the dynamics of dislocations such as dislocation motion and hardening due to pile-up, is taken into account at the continuum scale within the model formulation. Also, geometrically necessary dislocations arising due to strain gradient effects are explicitly included in the model as these contribute to additional hardening at the slip system level and make the model size dependent. Most crystal plasticity models in literature for Ti-6Al-4V homogenize the α and β phases or neglect the β phase due to its low volume fraction. In the CPFE model presented in this research, the α and β phases are modeled explicitly in order to capture the anisotropy between them, which is very important to understand fatigue and damage. The implications of this work look at linking microstructural features to damage in two-phase titanium alloys.

An anisotropic non-singular theory of dislocations with atomic resolution

Giacomo Po1, Markus Lazar2,Nikhil Admal3, Jaime Marian3, Nasr Ghoniem1

1Mechanical and Aerospace Engineering Department, University of California, Los Angeles, Los Angeles, CA 90095, USA, [email protected]; 2Department of Physics, Darmstadt University of Technology, Hochschulstraße 6, D-64289 Darmstadt,

Germany; 3Materials Science and Engineering Department, University of California Los Angeles, Los Angeles, CA 90095, USA

ABSTRACT

The singular nature of the elastic fields produced by dislocations presents conceptual challenges and computational difficulties in the implementation of discrete dislocation-based models of plasticity. In this work we consider theoretical and numerical aspects of the non-singular theory of discrete dislocation loops in a particular version of Mindlin’s anisotropic gradient elasticity with up to six independent gradient parameters. The framework models anisotropic materials where there are two sources of anisotropy, namely the bulk material anisotropy and a weak non-local anisotropy relevant at the nano-scale. The Green tensor of this framework, which we derive as part of the work, is non-singular and it rapidly converges to its classical counterpart a few characteristic lengths away from the origin. Therefore, the new Green tensor can be used as a physical regularization of the classical Green tensor. The Green tensor is the basis for deriving a non-singular eigenstrain theory of defects in anisotropic materials, where the non-singular theory of dislocations is obtained as a special case. The fundamental equations of curved dislocation loops in three dimensions are given as non-singular line integrals suitable for numerical implementation using fast one-dimensional quadrature. These include expressions for the interaction energy between two dislocation loops and the line integral form of the generalized solid angle associated with dislocations having a spread core. The six characteristic length scale parameters of the framework are obtained from the components of the rank-six tensor of strain gradient coefficients of Mindlin’s theory. In turn, the components of such tensor are obtained from atomistic calculations. In particular, we show that the rank-six tensor of strain gradient coefficients has an explicit local representation in terms of the derivatives of atomistic potentials. By virtue of this explicit representation, the link between atomistic and the simplified theory of gradient elasticity is established, and a non-singular and parameter-free theory of dislocations in anisotropic materials is obtained. Several applications of the theory are presented.


Investigating Microstructural Features In Ti-6Al-4V Using Crystal Plasticity Finite Element Modeling

Authors: Kartik Kapoor1, Michael D. Sangid1


ABSTRACT

There is a growing need to understand the damage mechanisms in two-phase titanium alloys due to their widespread use in the aerospace industry (especially within gas turbine engines),variation in their properties and performance based on their microstructure, and their tendency to undergo premature failure due to dwell and high cycle fatigue well below their yield strength. Two-phase titanium alloys occur in a number of microstructural forms depending on the nature of processing and heat treatment they have undergone. This work focuses on Ti-6Al-4V with a duplex microstructure, consisting of α (HCP) and β (BCC) phases arranged in a lamellar arrangement via a continuum description of dislocation motion. A crystal plasticity finite element (CPFE) model for a polycrystal that incorporates the microstructural features such as α-β colonies is presented in this work. Behavior of the slip systems at the single crystal level, influenced by the dynamics of dislocations such as dislocation motion and hardening due to pile-up, is taken into account at the continuum scale within the model formulation. Also, geometrically necessary dislocations arising due to strain gradient effects are explicitly included in the model as these contribute to additional hardening at the slip system level and make the model size dependent. Most crystal plasticity models in literature for Ti-6Al-4V homogenize the α and β phases or neglect the β phase due to its low volume fraction. In the CPFE model presented in this research, the α and β phases are modeled explicitly in order to capture the anisotropy between them, which is very important to understand fatigue and damage. The implications of this work look at linking microstructural features to damage in two-phase titanium alloys.

An anisotropic non-singular theory of dislocations with atomic resolution

Giacomo Po1, Markus Lazar2,Nikhil Admal3, Jaime Marian3, Nasr Ghoniem1

1Mechanical and Aerospace Engineering Department, University of California, Los Angeles, Los Angeles, CA 90095, USA, [email protected]; 2Department of Physics, Darmstadt University of Technology, Hochschulstraße 6, D-64289 Darmstadt,

Germany; 3Materials Science and Engineering Department, University of California Los Angeles, Los Angeles, CA 90095, USA

ABSTRACT

The singular nature of the elastic fields produced by dislocations presents conceptual challenges and computational difficulties in the implementation of discrete dislocation-based models of plasticity. In this work we consider theoretical and numerical aspects of the non-singular theory of discrete dislocation loops in a particular version of Mindlin’s anisotropic gradient elasticity with up to six independent gradient parameters. The framework models anisotropic materials where there are two sources of anisotropy, namely the bulk material anisotropy and a weak non-local anisotropy relevant at the nano-scale. The Green tensor of this framework, which we derive as part of the work, is non-singular and it rapidly converges to its classical counterpart a few characteristic lengths away from the origin. Therefore, the new Green tensor can be used as a physical regularization of the classical Green tensor. The Green tensor is the basis for deriving a non-singular eigenstrain theory of defects in anisotropic materials, where the non-singular theory of dislocations is obtained as a special case. The fundamental equations of curved dislocation loops in three dimensions are given as non-singular line integrals suitable for numerical implementation using fast one-dimensional quadrature. These include expressions for the interaction energy between two dislocation loops and the line integral form of the generalized solid angle associated with dislocations having a spread core. The six characteristic length scale parameters of the framework are obtained from the components of the rank-six tensor of strain gradient coefficients of Mindlin’s theory. In turn, the components of such tensor are obtained from atomistic calculations. In particular, we show that the rank-six tensor of strain gradient coefficients has an explicit local representation in terms of the derivatives of atomistic potentials. By virtue of this explicit representation, the link between atomistic and the simplified theory of gradient elasticity is established, and a non-singular and parameter-free theory of dislocations in anisotropic materials is obtained. Several applications of the theory are presented.


Title: Microstructurally-Short Crack Growth Driving Force Identification:Combining DCT, PCT, Crystal Plasticity Simulation and Machine Learning

Technique

Authors: Andrea Rovinelli1,*, Michael D. Sangid1, Ricardo A. Lebensohn2, WolfgangLudwig3, Yoann Guilhem4, Henry Proudhon5

Affiliations: 1Purdue University, School of Aeronautics and Astronautics, 701 W. StadiumAve, West Lafayette, IN 47907-0307, email: *[email protected]; 2Los Alamos National

Lab; 3European Synchrotron Radiation Facility; 4ENS de Cachan; 5MINES ParisTech

ABSTRACT

Identifying the Microstructurally-Short Crack (MSC) growth driving force of polycrystallineengineering alloys is a critical need in assessing performances of materials subject to fatigue loadand to improve both material design and component life prediction. However, due to (i) the lackof “cycle-by-cycle” experimental data, (ii) the complexity of MSC growth phenomenon, and (iii)the incomplete physics of constitutive relationships, only simple driving force metrics,inadequate to predict MSC growth, have been postulated. Based on experimental results byLudwig, Guilhem, et al., “cycle-by-cycle” data of a MSC propagating through a beta-metastabletitanium alloy are available via phase and diffraction contrast tomography. To identify the crackdriving force, we developed a framework utilizing the aforementioned experimental results andFFT-based crystal plasticity simulations (to compute micromechanical fields not available fromthe experiment). These results are combined and converted into probability distributions for usein a Bayesian Network.

A. Rovinelli and M. D. Sangid acknowledge support from the Air Force Office of Scientific Researchunder Contract No. FA9550-14-1-0284

(Nano-)Mechanical properties and deformation mechanisms of the topologically closed packed µ-phase in the Fe-Mo system

Sebastian Schröders1, Christoffer Zehnder1, James Gibson1, Stefanie Sandlöbes1,Sandra Korte-Kerzel1


ABSTRACT

Topologically close-packed (TCP) intermetallic phase precipitates in nickel-base superalloys are assumed to cause a deterioration of the mechanical properties of the γ - γ‘matrix. Although these intermetallic phases are well studied in terms of their structure, their mechanical properties have not yet been investigated in detail due to their large and complex crystal structures and pronounced brittleness. In this study we have chosen the Fe-Mo system as a model system in order to investigate the plastic deformation behavior of these phases. A special focus is placed on the hexagonal μ-phase. To this aim we apply nano-mechanical testing methods: nano-indentation and micropillar-compression to enable plastic deformation of these brittle phases. This is due to the confining pressure in nano-indentation and the reduction in specimen size in micro-compression experiments [1]. Indentation experiments at room temperature show a hardness of ~11 GPa and a Young’s modulus of ~270 GPa. Strain rate sensitivity and the respective activation volumes have been determined by nano-indentation strain rate jump tests. Electron backscatter diffraction (EBSD) assisted slip trace analysis reveals dominant dislocation activity on basal planes at room temperature. Micro-compression experiments on well-oriented single-crystalline micro-pillars reveal the structure related anisotropy of the critical shear stresses (CRSS) of different slip systems. Finally, transmissionelectron microscopy (TEM) and high-resolution transmission electron microscopy (HR-TEM)investigations of specimens target-prepared from nano-indents and deformed micro-pillars reveal the dislocation and defect structures of the µ-phase.



Multi-scale modeling of plasticity under pressure:from dislocation core to texture evolution

Jonathan Amodeo1,2, Sylvain Dancette1, Philippe Carrez2, Patrick Cordier2

and Laurent Delannay3

1Laboratoire MATEIS, INSA-Lyon Université de Lyon, F-69621 Villeurbanne, France2Unité Matériaux Et Transformations (UMET), Université de Lille 1, F- 59655

Villeneuve-d’Ascq, France3Department of Mechanical Engineering (MEMA), Université Catholique de Louvain

(UCL), 1348 Louvain-la-Neuve, Belgium

[email protected]

ABSTRACT

High-pressures (HPs) are responsible for significant changes in the mechanical properties of materials. Besides Earth’s sciences, where solid rocks deform under hundreds GPa hydrostatic pressure, HPs influence elasticity and plasticity in various fields of materials science, such as nanoindentation, materials confinement, processing or sintering methods as well as small-scale engineering. By investigating the role of HPs based on a multi-scale modeling approach, the present study provides an alternative to current experimental techniques and aims to contribute bridging the gap between several scientific communities.

In this study, we consider MgO, which is one of the main constituent of the Earth’s lower mantle, but the method and the main results can easily be extended to other anisotropic materials (e.g. hcp metals).

From a bottom-up approach, the role of hydrostatic pressure on dislocation glide may be investigated at the finest scales using first principles and atomistic simulations. HPs are known to constrain the long-range elastic strain field around the dislocation as well as the dislocation core structure, which influence both the Peierls stress and the dislocation mobility.Here we will show that both a generalized Peierls-Nabarro approach and atomistic simulations allow identifying the premises of a pressure-dependent plasticity in MgO. This will further be confirmed by the modeling of the dislocations mobility and its implementation into dislocation dynamics (DD) simulations of single crystal compression tests. On the other hand, the mechanical response can hence be investigated at the macroscopic scale usingpolycrystalline simulations. Based on atomistically-informed crystal plasticity simulations(Taylor and full-field finite element models), we will demonstrate how the hydrostatic pressure constrains both the strength and the texturing process in MgO polycrystals.Simulation results will be discussed in the light of recent HPs experiments.

A crystal defect field theory for coupled plasticity and fracture

Vincent Taupin, Claude Fressengeas

Laboratoire d’Etude des Microstructures et de Mécanique des Matériaux Université de Lorraine/CNRS, Ile du Saulcy, 57045 Metz Cedex, France

[email protected]

ABSTRACT

We propose a unified field theory for plasticity and fracture where the displacement and rotation discontinuities arising between crack surfaces are assigned to smooth tensorial densities of line crystal defects referred to as disconnections and rotational disconnections (r-disconnections), via the incompatibility of the strain and curvature tensors. Conservation arguments for the defect’s strength (the crack opening displacement and opening rotation) provide a natural dynamic framework for crack propagation in terms of transport laws for the defect densities. Similar methodology applies to discontinuities of the plastic displacement and rotation arising from the presence of dislocations and disclinations in the body, which results in the concurrent involvement of the dislocation/disclination density tensors in the analysis.

The theory can be viewed as an extension of the mechanics of dislocation and disclination fields to the case where continuity of the body is disrupted by cracks. From the continuity of the elastic strain and curvature tensors, it is expected that the stress/couple stress fields remain bounded everywhere in the body, including at the crack tips and dislocation cores. Thermodynamic arguments provide the driving forces for crack growth through disconnection motion, and guidance for the formulation of constitutive relationships insuring non-negative dissipation. Peach-Koehler-type forces are defined for disconnections and r-disconnections. A threshold in the (r-) disconnection driving force vs. velocity relationship translates into a Griffith-type fracture criterion. The finite element simulations operate on regular meshes, and no mesh disruption is needed to update crack growth.

Phenomena such as grain boundary migration, grain rotation/dislocation emission in the crack tip area, crack shielding/anti-shielding by dislocations and grain boundaries, inter-granular crack growth, which have been observed in ultrafine-grained materials, are interpreted in terms of static and dynamic interactions between dislocation / disclination / disconnection fields. Sample/grain size effects on crack growth are a natural outcome of the theory.


Dislocation induced stress drop in cubic metals

Soon Kim1, Keonwook Kang2 and Sung Youb Kim1*

1Department of Mechanical and Nuclear Engineering, Ulsan National Institute ofScience and Technology, Ulsan, 689-798, South Korea.

2Department of Mechanical Engineering, Yonsei University, Seoul, 120-749, South Korea.

*E-mail address : [email protected]

ABSTRACT

Dislocation core has nonlinear properties which cannot be explained with linear elasticity theory [1]. In respect that dislocation core is responsible for determining dislocation mobility, there have been many efforts to understand the core structures of dislocations. In this work, we firstly report that stress applied on free surfaces of nanoplate is dropped to certain value inside the plate when dislocation starts to move. We insist that phonon scattering induced byanharmonic strain field near the dislocation core reduces the applied stress during dislocation motion and derived relation between the applied stress and the amount of stress drop based on the model. We simulated edge dislocation in iron and aluminum by using molecular dynamics simulation and measured the amount of stress drop. Also, we observed that screw dislocation induces stress drop whose amount is much smaller than the edge dislocation. There was a good agreement between the model and simulation results when kink is not formed on dislocation line for both cases. Furthermore, our model predicts that the amount of stress drop decreases as temperature increases, which coincides with simulation result.

[1] J. P. Hirth, Some current topics in dislocation theory, Acta Materialia, 48, 93 (2000)

Atomistic Simulations for the Interaction between Grain Boundaries and Avalanche Motion of Dislocations

Authors: Tomoaki Niiyama, Tomotsugu Shimokawa

Affiliations: College of Science and Engineering, Kanazawa University, Kakuma-machi, Kanazawa, Ishikawa 920-1192, Japan

[email protected]

ABSTRACT

A new insight into the crystalline plasticity is provided from non-equilibrium physics; avalanche-like discontinuous deformation, called intermittent plasticity or dislocation avalanches, characterized by power-law distribution is just beginning to be known as an intrinsic nature of the plasticity [1]. From the same perspective, the role of grain boundaries (GBs) as obstacles to the avalanche propagation has been demonstrated [2]. The role might be closely related to mechanical properties of polycrystalline materials. However, theoretical approaches are still quite preliminary, because the role is fully atomistic scale behaviors.

In our previous numerical study, avalanche behaviors of dislocations in single crystals have been successfully reproduced by molecular dynamics simulations of constant strain rate uniaxial tensile deformation [3]. We applied the numerical method to polycrystal models simplified by symmetric tilt GBs. The result shows that the stress drops by plastic deformation follow power-law distributions even in polycrystals, but the cut-off of the distribution is dependent upon grain thickness of the models. Some avalanches are blocked by the GBs, but others transmit across those. Some of the latter percolate the system entirely. The impedance of avalanches by one GB is evaluated from the probability of the system-spanning events. The estimated values of the impedance are in good agreement with our theoretical description. This quantification will contribute to the construction of mesoscopic models, e.g., discrete dislocation dynamics or the phase field method for polycrystals.

[1] M. C. Miguel, A. Vespignani, S. Zapperi, J. Weiss, and J.-R. Grasso. Intermittent dislocation flow in viscoplastic deformation, Nature, 410, 667, (2001).

[2] T. Richeton, J. Weiss, and F. Louchet. Breakdown of avalanche critical behaviour in polycrystalline plasticity. Nature Mater, 4, 465 (2005).

[3] T. Niiyama and T. Shimokawa. Atomistic mechanisms of intermittent plasticity in metals: Dislocation avalanches and defect cluster pinning. Phys. Rev. E, 91, 022401, (2015).


Dislocation Processes in Deformation of Semiconductors

Ichiro Yonenaga 1

1 Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan

ABSTRACT

Semiconductors are typically ductile at high temperature regime higher than ~2/3TM (TM:melting temperature). Knowledge on dislocation characters and dynamical properties is essential as a basis for the control of dislocation generation and deformation during crystal growth and processing. Recently, the present author overviewed dislocation processes of Si experimentally observed and theoretically estimated in the wide temperature range from RT to TM [1]. At elevated temperatures higher than ~600˚C Si shows clear ductile character governed by collective motion of glide-set dislocations. The process is well reproduced by the constitutive model with mutual interaction and self-multiplication of dislocations. Contrarily, at low temperature as RT to 400~600˚C Si is brittle and encounters fracture due to low velocities of dislocations. At such low temperatures generation of shuffle-set dislocations is favorable under the application of high stress.In contrast to Si, understanding of deformation and dynamic behavior of dislocations in sphalerite and wurtzite compound semiconductors is far limited. Here, we summarize current knowledge on dislocation velocities and mechanical strengths as hardness and yield stresses for various kinds of semiconductor crystals, including recently developed so-called wide bandgap compounds of SiC, GaN, ZnO, ZnSe, etc., in order to understand a universal rule for the basic dislocation mechanisms in semiconductors.Hardness homology scaled by using shear modulus G and magnitude of dislocation Burgers vector b was found for hcp-based semiconductors, different from that for cubic-based semiconductors. The activation energy for dislocation motion in various semiconductors shows a unique dependence on the dislocation energy with the minimum length, given by the product of G and b. These findings are discussed with recent ab initio estimations for kink formation and migration as a basic mechanism of dislocation processes.

[1] I. Yonenaga, An overview of plasticity of Si crystals governed by dislocation motion, Eng. Fracture Mech. 147, 468 (2015)


Ainara Irastorza-Landa1,2, Helena Van Swygenhoven1,2, Steven Van Petegem1, Alex Bollhalder3, Stefan Brandstetter4, Daniel Grolimund1

1Swiss Light Source (SLS), Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland; 2NXMM laboratory, IMX, École Polytechnique Fédéral Lausanne (EPFL), CH-1015Lausanne, Switzerland; 3Laboratory for Developments and Methods (LDM), NUM,

Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland; 4DECTRIS Ltd., Täfernweg 1, CH-5405 Baden-Dättwil, Switzerland

ABSTRACT

Metals catastrophically fail under a repeated load that would not be sufficient to cause failure when applied once. The origin lies in the dislocation organization at the mesoscale that isresponsible for long-range internal stresses and lattice rotation. Efforts to develop computational schemes that can predict dislocation patterning such as for instance [1] missquantitative experimental information to validate the transition from uniform to non-uniform dislocation structures. Here we present a new experimental approach to follow dislocation patterning during accumulation of fatigue cycles. The method is based on x-ray Laue diffraction scanning and provides a sub-micron spatial resolution in 2D and statistical information on orientation spread in the third dimension. A miniaturized shear device is installed at the MicroXAS beamline of the Swiss Light Source. Single crystal Cu samples oriented for single and double slip are shaped in Miyauchi’s geometry using picosecond laser ablation [2]. At various stages of cyclic shear deformation with different strain amplitudes,spatial resolved Laue diffraction patterns are recorded in transmission mode. The evolving dislocation microstructures are analyzed in terms of lattice rotation, geometrically necessary dislocation density and their spatial distribution [3]. The developed approach allows increasing the synergism with dislocation density based computational schemes.

[1] N. Grilli, K.G.F. Janssens, H. Van Swygenhoven, Crystal plasticity finite element modelling of low cycle fatigue in fcc metals, J. Mech. Phys. Solids 84, 424 (2015)

[2] A. Guitton, A. Irastorza-Landa, R. Broennimann, D. Grolimund, S. Van Petegem, H. Van Swygenhoven, Picosecond pulsed laser for microscale sample preparation, Mater. Lett. 160, 589 (2015)

[3] A. Irastorza-Landa, H. Van Swygenhoven, S. Van Petegem, A. Bollhalder, S. Brandstetter, D. Grolimund, Following dislocation patterning during fatigue (submitted)

Acknowledgement: The authors thank the Swiss National Science Foundation and HVS thanks the European Research Council for the advanced grant MULTIAX.


Discontinuous Yielding in Ultrafine Grained Metals

Nobuhiro Tsuji1,2, Si Gao1, Daisuke Terada2,3, Xiaoxu Huang 4, Niels Hansen4

1 Dept. Materials Science and Engineering, Kyoto University, 606-8501, Kyoto, Japan;

2 Elements Strategy Initiative for Structural Materials (ESISM), Kyoto University,606-8501, Japan;

3 Dept. Mechanical Science, Chiba Institute of Technology, 275-0016, Japan;4 Dept. Wind Energy, Technical University of Denmark, 4000, Denmark;

It was reported that pure aluminum and ultra low-carbon interstitial free (IF) steel having ultrafine grain sizes smaller than 1-2 micro-meters showed discontinuous yielding on their stress-strain curves, although the same materials with conventionally coarse-grained microstructures showed typical continuous yielding [1]. In the present study, various kinds of materials, i.e., high purity aluminum, commercial purity aluminum, Cu-Al alloy, IF steel, high-Mn steel and pure titanium, were conventionally deformed by cold-rolling or highly deformed by accumulative roll bonding (ARB) process and then annealed to obtain fully recrystallized microstructures with various grain sizes. All ultrafine grained specimens with mean grain sizes smaller than 1-2 micro-meters showed discontinuous yielding accompanied with clear yield-drop phenomena universally regardless of the kind of materials. We will propose a new model for explaining the universal discontinuous yielding, based on the detailed experimental data including dislocation densities and deformation inhomogeneity measured by digital image correlation (DIC) technique.

[1] N.Tsuji et al, Scripta Materialia, 47 (2002), 893-899.

Molecular Dynamics Simulations of Dislocation Kinematics and Dynamics in Copper

Eyal Oren, Guy Makov

Materials Engineering Department, Ben-Gurion University of the Negev, Beer-Sheva 8410501, Israel, [email protected]

ABSTRACT

The kinematics of dislocation motion and cross-slip in copper are studied by molecular dynamics simulations, applying full periodic boundary conditions on an ideal crystal andincorporating a dislocation dipole with zero net Burgers vector. Particular emphasis was placed on minimizing image interactions due to periodic boundary conditions. Kinematics were studied by accelerating dislocations at constant stress and temperature (Nose-Hoover thermostat, NPT ensemble) until achieving a terminal velocity. The relation between stressand terminal velocity at cryogenic and room temperatures for both screw and edge dislocations was obtained. While applying high stresses, a breakdown of the viscous behavior is observed such that terminal velocity shifts from linearity with the increasing applied stress to an asymptote, approaching the first sound velocity of the crystal. At even higher stress we observe a shift into the transonic regimes, which appears to constitute a transition from subsonic state to transonic state. For screw dislocation dipoles we have simulated cross-slip followed by annihilation as a function of temperature and stress. Dislocation length was extended to ensure independence of nucleation sites along the dislocation line. Cross-slip at each temperature-stress point was simulated multiple times, creating statistical data from which the kinetics and activation parameters are obtained.


Green’s function molecular dynamics meets

discrete dislocation plasticity

S. Venugopalan1, Lucia Nicola1

Affiliations: 1Department of Materials Science and Engineering, Delft University of Technology, Delft, the Netherlands, [email protected]

ABSTRACT

Contact between metal surfaces results already at small loads in plastic deformation of the surface asperities. Such asperities span various length scales, and at the micron-scale their plastic response is size dependent. Size dependent plasticity can be captured by discrete dislocation plasticity simulations [1]. However, so far, only simulations for very simple surface geometries have been carried out using dislocation dynamics, e.g. two-dimensional surfaces with sinusoidal profile. The study of more complex three-dimensional surface geometries requires prohibitive computational time.Our aim is to be able to address realistic three dimensional surfaces. To this end we here present a modified version of the discrete dislocation plasticity method [2] to solve contact problems. This method relies on Green’s functions molecular dynamics [3] to track the change in true contact area during contact loading. Preliminary results show that the results obtained by discrete dislocation plasticity simulations for simple surfaces can be reproduced with this method at significantly lower computational costs.

[1] V.S. Deshpande, D.S. Balint, A. Needleman and E. Van der Giessen, Size effects in single asperity frictional contacts, Model Simul Mater Sci Eng, 15, S97 (2007)

[2] E. Van der Giessen, A. Needleman, Discrete dislocation plasticity: a simple planar model, Model Simul Mater Sci Eng, 5, 689 (1995)

[3] C. Campana, M.H. Mueser, Prcatical Green’s function approach to the simulation of elastic semi-infinite solids, Phys Rev B, 74, 075420 (2006)

Dislocation-precipitate interaction in aluminum alloys

Authors: Inga G. Ringdalen1, Sigurd Wenner2, Jesper Friis1, Odd Sture Hopperstad3,Jaime Marian4

Affiliations: 1SINTEF Material and Chemistry, Department of Materials and Nanotechnology; 2 NTNU, Department of Physics; 3NTNU, Department of Structural

Engineering; 4UCLA, Department of Material Science and Engineering

ABSTRACT

Partial ageing of AA6060 aluminum alloys is known to develop a microstructure characterized by needle-shaped Si/Mg-rich precipitates. These precipitates belong to the non-equilibrium β'' phase and are coherent with the fcc Al lattice, despite of which they can cause considerable hardening. We have investigated the interaction between these β'' precipitatesand dislocations using a unique combination of modeling and experimental feedback. Dislocation-precipitate interactions are simulated using dislocation dynamics (DD)parameterized with atomistic simulations. The elastic fields due to the precipitates are described by a phenomenological law guided by high-resolution TEM observations, which point to a fast-decaying displacement field along the radial direction of the precipitates. The stress fields are derived from the displacements assuming isotropic elasticity, and used to study the strength of individual precipitates as a function of size and orientation. Our results are used to parameterize a probabilistic analysis model to calculate the stochastic strengthening of AA6060 at the macroscopic level.

This work is performed with support from the Norwegian Research Council project number 231762.


Simulation of the Creep Behavior of Directionally Solidified NiAl-9Mo with a Large Strain Gradient Plasticity Model

Hannes Erdle, Jürgen Albiez, Eric Bayerschen, Thomas Böhlke

Chair for Continuum Mechanics, Institute of Engineering Mechanics,Karlsruhe Institute of Technology (KIT), Kaiserstr. 10, 76131 Karlsruhe, Germany

E-Mail: [email protected]

ABSTRACT

For high temperature structural applications, directionally solidified NiAl-9Mo (at.%) eutectic has promising material properties, such as high melting temperature and good creep resistance [1]. The presence of well-aligned single-crystal molybdenum-rich fibers embedded in a NiAl matrix results in strong interactions of dislocations across phase boundaries [2]. To model these interactions, balance equations for additional degrees of freedom are evaluated at sharp interfaces with finite elements based on discontinuous trial functions. An equivalent gradient plasticity model, including an energetic grain boundary yield criterion [3], is extended to a micromorphic finite strain theory to account for finite deformations occuring during creep. Furthermore, the framework is extended by taking into account discontinuous dislocation density fields. As a result, experimentally observed work-hardened zones, formed by NiAl dislocations around Mo fibers [2], are reproduced. Discussion of different lamellar microstructures and an outline of further possible applications conclude the talk.

[1] D. R. Johnson, X. F. Chen, B. F. Oliver, Processing and mechanical properties of in-situ composites from the NiAl-Cr and the NiAl-(Cr,Mo) eutectic systems, Intermetallics 3(1995), 99–113

[2] M. Dudová, K. Kuchařová, T. Barták, H. Bei, E. P. George, Ch. Somsen, A. Dlouhý, Creep in directionally solidified NiAl-Mo eutectics, Scripta Mater. 65 (2011), 699–702

[3] S. Wulfinghoff, E. Bayerschen, T. Böhlke, A gradient plasticity grain boundary yield theory, Int. J. Plasticity 51 (2013), 33–46

The support of the German Research Foundation (DFG) in the projects “Process chains in sheet metal manufacturing” of the DFG Research Group 1483, “Dislocation based GradientPlasticity Theory” of the DFG Research Group 1650, and the support of the the Initiative and

Dislocation Grain Boundary Interaction In Aluminum Nano Poly Crystals Analyzed Using Molecular Dynamics

M. Hummel1, P. Binkele1, S. Schmauder1

1Institute for Materials Testing, Materials Science and Strength of Materials (IMWF), University of Stuttgart, Stuttgart, Germany, [email protected]

ABSTRACT

In the context of Molecular Dynamics simulations with the limitation to nanometer sized grain diameters of nano poly crystals the grain boundary holds a dominant position for the nucleation and the extinction of dislocations. Therefore a detailed investigation of dislocation nucleation from grain boundaries under uni- and multidirectional simulated tensile tests is carried out. Further the movement of the dislocation through the grain with the connected plastic deformation until the vanishing at the grain boundaries is observed and evaluated. The blocking and detachment of pairs of dislocation is as well in the focus of the research. The widely used and open source code LAMMPS is used as simulation package. The interaction of the atoms is described by two different types of potentials for different simulations, anangular dependent potential (ADP) by Apostol and Mishin [2] and an embedded atom method (EAM) type potential as well by Mishin [3].

[1] S. Plimpton, Fast Parallel Algorithms for Short-Range Molecular Dynamics, J Comp Phys, 117, 1-19 (1995), http://lammps.sandia.gov

[2] F. Apostol, Y. Mishin, Interatomic potential for the Al-Cu system, Physical Review B, 83(5), 54116, 1-8, (2011)

[3] Y. Mishin, Atomistic modeling of the γ and γ′-phases of the Ni–Al system, Acta Materialia, 52(6), 1451-1467, (2004)

Financial support of the German Research Foundation (DFG) is acknowledged as well as the HLRS High Performance Computing Center Stuttgart, where the simulations are carried out.


From glissile to sessile:

the fate of <110> dislocations in perovskites deformed at high temperature

Authors: Pierre Hirel1, Philippe Carrez1, Patrick Cordier1

Affiliations: 1Unité Matériaux et Transformations, Université Lille, 59655 Villeneuve d'Ascq, France

ABSTRACT

Compounds with the perovskite structure can exhibit very different mechanical properties. The archetypal perovskite material strontium titanate (SrTiO

3) presents a very atypical

mechanical behavior, characterized by a double ductile-brittle-ductile transition [1]. The plastic deformation at low temperature is accommodated by the motion of dislocations of <110> Burgers vector, however these dislocations suddenly loose their mobility around 1050 K, leading to brittle failure. The mechanisms responsible for the loss of this slip system are still unknown, and also raise the question of the existence of similar mechanisms in other related compounds.

The effects of temperature on the core structure of <110> dislocations are investigated by means of atomic-scale simulations in two perovskites: SrTiO

3because of its important

technological applications, and MgSiO3

because of its geophysical applications, as it is the

most abundant mineral in the Earth's lower mantle. We demonstrate that in both phases,<110> dislocations transform from a glissile core spread in their slip plane, into a sessile, climb-dissociated core at high temperature. The results indicate that the mechanisms for this transformation may be general to all perovskites, with an activation energy that strongly depends on the chemical composition. This leads to a competition between this temperature-induced transformation and the stress-driven motion of dislocations. As a result the mechanisms for the deformation are extremely different depending on the conditions of deformation: at low temperature and high stress the glide of <110> dislocations dominates, while at high temperature and low stress <110> dislocations become sessile, and deformation has to occur by different mechanisms.

[1] P. Gumbsch et al., Phys. Rev. Lett. 87, 085505 (2001)

This work is supported by funding from the European Research Council under the

GENERIC-based coarse-graining of the dynamics of discrete dislocation line ensembles with variable orientation

Authors: Bob Svendsen1,2, Markus Hütter3

1RWTH Aachen University, Aachen, Germany;2Max-Planck-Institut für Eisenforschung GmbH, Düsseldorf, Germany;

3Eindhoven University of Technology, Eindhoven, The Netherlands;email: [email protected]

ABSTRACT

Collective dislocation behavior in metallic systems is highly dissipative in nature and results in the formation and evolution of a wide variety of microstructures such as tangles, networks, cell-wall systems, or sub-grains. Discrete modeling approaches to such dislocation systems at the mesoscopic level include for example kinetic Monte Carlo or line dislocation dynamics (LDD) [1,2]. Related continuum modeling approaches are often statistical and diffusive in nature [3,4]. In the current work, the LDD-based model of a dislocation network as a discrete system of interacting dislocation line segments with variable orientation is used as a basis for the formulation of a coarse-grained continuum model for collective dislocation thermodynamics. Following previous work [5], coarse-graining of LDD is carried out in the context of non-equilibrium statistical thermodynamics with the help of projection-operator methods [5] and the General Equation for Non-Equilibrium Reversible Irreversible Coupling [6]. In particular, this formulation results in continuum balance, transport, and non-local thermodynamic flux-force, relations for dislocation line segment density and orientation depending on the details of the underlying discrete system energetics and kinetics. Examples will be given.

[1] V.V. Bulatov, W. Cai, Computer Simulation of Dislocations, Oxford University Press, (2006).

[2] W. Cai, A. Arsenlis, C.R. Weinberger, V.V. Bulatov, A non-singular continuum theory of dislocations, Journal of the Mechanics and Physics of Solids 54, 561 (2006).

[3] Y.S. Chen, W. Choi, S. Papanikolaou, M. Bierbaum, J.P. Sethna, Scaling theory of continuum dislocation dynamics in three dimensions: Self-organized fractal patternformation, International Journal of Plasticity 46, 94 (2013).

[4] J. Deng, A. El-Azab, Temporal statistics and coarse graining of dislocation ensembles,Philosophical Magazine 90, 3651 (2010).

[5] M. Kooiman, M. Hütter, M.G.D. Geers, Effective mobility of dislocations from systematic coarse-graining, Journal of Statistical Physics PO6005 (2015).

[6] H. Grabert, Projection Operator Techniques in Non-Equilibrium Statistical Mechanics,Springer (1982).

[7] H.C. Öttinger, Beyond Equilibrium Thermodynamics, Wiley Interscience (2005).

Abstracts will only be accepted in MS Word Format for ease of compilation.


Dislocation mobility: an atomistic perspective

Authors: Jonas Verschueren*1, Beñat Gurrutxaga-Lerma1, Daniele Dini1, Daniel S. Balint1, Adrian P. Sutton2

Affiliations: 1Department of Mechanical Engineering, Imperial College London, SW7 2AZ; 2 Department of Physics, Imperial College London, SW7 2AZ;

*[email protected]

ABSTRACT

Our understanding of dislocation mobility - quantifying the relationship between the force on a dislocation and its resulting velocity - is largely based on experiment [1]. However, the validity of mobility laws extracted from this work breaks down for fast travelling dislocationsmoving with speeds comparable to the speed of sound in the medium. A physically motivated understanding of dislocation mobility - in which lattice-dislocation interactions are widely hypothesised to play an important role – could shed light on the phenomenology associated with these fast travelling dislocations. Debate on this topic has been ongoing for over half a century and is problematic given that in this regime, the usual approximations by which elasticity theory is linearised are violated and the quasi-static approximation no longer holds. Recently, Gurrutxaga-Lerma et al. derived the elastodynamic fields associated with the injection of dislocations in discrete dislocation dynamics simulations using the Caignard-de Hoop solution technique [2,3]. Atomistic molecular dynamics simulations of this injection process in crystalline tungsten for both edge and screw dislocations revealed an emission of elastic waves along the entirety of the cut plane not predicted by continuum theory. These were found to be a direct consequence of the explicit treatment of the lattice structure and were subsequently reproduced analytically. The implications of further investigations into dislocation-lattice interactions on dislocation mobility will be discussed.

[1] W.G. Johnston, J.J. Gilman, Dislocation velocities, dislocation densities, and plastic flow in lithium fluoride crystals, Journal of Applied Physics, 30, 129 (1959)[2] B. Gurrutxaga-Lerma, D.S. Balint, D. Dini, D.E. Eakins, A.P. Sutton, A dynamic discrete dislocation plasticity method for the simulation of plastic relaxation under shock loading,Proceedings of the Royal Society A, 469, 2156 (2013)[3] B. Gurrutxaga-Lerma, D.S. Balint, D. Dini, A.P. Sutton, Elastodynamic image forces on dislocations, Proceedings of the Royal Society A, 471, 2181 (2015)

Transient Mechanical Behavior of Body-Centered Cubic Chromium Studied by High-Temperature Nanoindentation

Authors: In-Chul Choi, Christian Brandl, Ruth Schwaiger

Affiliations: Karlsruhe Institute of Technology, Institute for Applied Materials, Eggenstein-Leopoldshafen, Germany

[email protected]

ABSTRACT

Body-centered cubic (bcc) metals show a ductile-brittle transition at a certain temperature, which is related to the mobility of screw dislocations. And the deformation behavior of bcc metals, in general, shows the non-trivial effects of the non-planar dislocations core structure of the screw dislocation due to their less dense atomic structure. We study the behavior of Chromium (Cr) as a model material with the goal to understand and quantify the thermally-activated dislocation plasticity and the transition to the athermal regime in bcc materials. We utilize high-temperature nanoindentation experiments to characterize the deformation behavior of bcc Cr. To validate the indentation method itself for elevated temperatures, we systematically studied the temperature-dependent indentation modulus, which clearly shows adiscontinuity at the magnetic phase transition at 35 °C on top of the thermal softening, which is quantitatively consistent with literature data. We characterized the kinetics of dislocation plasticity by strain-rate sensitivity of the hardness at various temperatures. The observed signatures of the plastic relaxation mechanisms (i.e. hardness and strain rate sensitivity) are discussed in context of screw dislocation mobility governed by thermally-activated kink-pair nucleation, kink-drift and dislocation-impurity interaction. Moreover, the indentation pile-up/sink-in morphology and its temperature-dependence indicates a change of strain hardening behavior with temperature. This mesoscale aspect of deformation behavior implies a change of dislocation-dislocation interactions in the plastic zone with temperature. Finally, we will conclude with the implications of the dislocation-dislocation interaction and dislocation mobility on the brittle-ductile transitions in bcc Cr.


Grain Boundary Resistance in Alpha-titanium Quantified byNanoindentation and Boundary-aware Crystal Plasticity Modeling

Authors: Y. Su1, C. Zambaldi2, D. Mercier2, P. Eisenlohr1,T. R. Bieler1, M.A. Crimp1

Affiliations: 1Department of Chemical Engineering and Materials Science, Michigan State University, East Lansing, MI 48824-1226, USA

2 Max-Planck-Institut für Eisenforschung GmbH, D-40237 Düsseldorf, Germany

ABSTRACT

To understand how grain boundaries modulate plastic deformation of commercially pure titanium, sphero-conical nanoindentations were placed near preselected grain boundaries where corresponding grain orientations had been mapped by electron backscatter diffraction (EBSD). The resistance of grain boundaries to dislocation slip wascharacterized by comparing bi-crystal and single crystal nanoindentation surface topographies. The effects of grain boundary misorientation and subsurface inclination (determined by focused ion beam sectioning) on the topography were categorized by anumber of slip transmission criteria. A crystal plasticity finite element (CPFE) model was built for simulating bi-crystal indentations using STABiX [1], a Matlab toolbox developed for converting orientation data into a variety of outputs, and used as input for simulations performed with MSC.Marc/Mentat. The accuracy of the simulations wasquantified by comparing with experimental indentation topographies at multiple grain boundaries. Two layers of elements with the same orientation of the grain on each side but with different slip parameters were built into the computational model by assigning new slip parameters (different from those in the grain interiors) to each layer. The boundary layer slip parameters were optimized by minimizing the difference in the topography between experimental and simulated indents. In general, the accuracy of indent simulations was improved with the implementation of the explicit grain boundary layers. Nevertheless, the boundary parameters necessary to achieve good matches vary for different boundary misorientation and grain orientations.

[1] D. Mercier, C. Zambaldi, T.R. Bieler, A Matlab toolbox to analyze slip transfer through grain boundaries, IOP Conference Series-Materials Science and Engineering, 82, 012090 (2015).

This work was supported by National Science Foundation (NSF) through the Materials World Network Grant DMR-1108211 and corresponding Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) grant ZA523/3-1, as well as NSF grant DMR-1411102.


Authors: Veerappan Prithivirajan1, Michael D. Sangid1


ABSTRACT

Direct metal laser sintering (DMLS) manufacturing method can be deployed for aerospace applications to realize advantages that are well documented. However, prior to their use in safety critical components, the failure mechanisms have to be well understood, especially for the unique defects in DMLS materials, such as porosity and large residual stress gradients. In our work, fatigue crack initiation of a Ni-based superalloy, IN 718, produced by DMLS is studied via crystal plasticity-finite element (CP-FE) simulations. Microstructural features, such as grain size distribution, orientation distribution, presence of twins, and voids, lead to heterogeneous deformation causing strain localization at certain locations where a fatigue crack is likely to initiate. Multitude of factors contribute to the initiation site, namely large grains, grain neighborinteractions, twin boundaries, volume fraction of voids, void size, and void interactions. 3D virtual microstructures are developed based on microstructure attributes obtained from theEBSD. Cyclic simulations are carried out based on a continuum description of dislocation mechanisms, namely a CP-FE framework. Slip level metrics such as the plastic strain accumulation, dislocation density, resolved shear stress and mesoscale metrics like triaxiality, hydrostatic stresses obtained from the simulations are used to identify the possible location of the crack initiation. Also, these results are used to understand the role of pores and residual stresses on the fatigue crack initiation.


Atomic Scale Strengthening Mechanisms due to Localized Obstaclesin Fe

Yury Osetskiy and Roger Stoller

Materials Science and Technology Division, ORNL, Oak Ridge, TN 37831- 6138, USA

ABSTRACT

Localized microstructural components such as vacancy voids, gas filled bubbles, secondary phase precipitates and rigid oxides, nitrides and carbides are usual obstacles for dislocation motion in irradiated metals and alloys. In this report we describe interactions between gliding ½<111>{110} edge dislocation in bcc-Fe with such obstacles modeled over a wide range of environmental and microstructural parameters. Conventional range of parameters such asobstacle size, temperature range and dislocation speed effects was considered together with the specific output from “computer modeling experiment”. This includes stress-strain behavior, critical resolved shear stress (CRSS) temperature dependence and a complete analysis of the interaction mechanisms and their temperature behavior. For the mechanism analysis we used arecently developed new dislocation characterization and visualization technique when the dislocation line direction and Burgers vector can be identified locally. This new technique allows us to have a direct comparison with in situ deformation TEM experiments and especially with the recently developed 3D TEM tomography.

This work was supported by the US Department of Energy Office of Fusion Energy Sciences.

Atomic Scale Dynamics of Screw Dislocation in concentrated Ni-Fe alloys

Yuri Osetsky and James Morris


ABSTRACT

In this research we have studied screw dislocation glide over pure Ni and fcc random alloys of Ni and Fe with concentration up to 50 at.%. ½<110>{111} dislocation glides smoothly in pure Ni and stress-velocity dependences produce a reasonably accurate friction coefficient over a wide temperature range from 300 to 900K. However the glide mechanism is very different in concentrated alloys where Ni-Fe interfaces play the role of rather strong obstacles, which strength depends very much on the local configuration. The random character of Ni-Fe distribution demands modeling of a long dislocation line gliding over long distance to consider maximum possible spectrum of configurational fluctuations. We present results for stress and strain controlled dislocation glide and describe correlations between some observed microstructures and flow stress at different temperatures. The results obtained are discussed in application to deformation experiments in single phase high entropy alloys.

This work was supported by the US Department of Energy Office of Science, Basic Energy Sciences, Materials Science and Engineering Division.


Atomic Scale Strengthening Mechanisms due to Localized Obstaclesin Fe

Yury Osetskiy and Roger Stoller


ABSTRACT

Localized microstructural components such as vacancy voids, gas filled bubbles, secondary phase precipitates and rigid oxides, nitrides and carbides are usual obstacles for dislocation motion in irradiated metals and alloys. In this report we describe interactions between gliding ½<111>{110} edge dislocation in bcc-Fe with such obstacles modeled over a wide range of environmental and microstructural parameters. Conventional range of parameters such asobstacle size, temperature range and dislocation speed effects was considered together with the specific output from “computer modeling experiment”. This includes stress-strain behavior, critical resolved shear stress (CRSS) temperature dependence and a complete analysis of the interaction mechanisms and their temperature behavior. For the mechanism analysis we used arecently developed new dislocation characterization and visualization technique when the dislocation line direction and Burgers vector can be identified locally. This new technique allows us to have a direct comparison with in situ deformation TEM experiments and especially with the recently developed 3D TEM tomography.

This work was supported by the US Department of Energy Office of Fusion Energy Sciences.

Atomic Scale Dynamics of Screw Dislocation in concentrated Ni-Fe alloys

Yuri Osetsky and James Morris


ABSTRACT

In this research we have studied screw dislocation glide over pure Ni and fcc random alloys of Ni and Fe with concentration up to 50 at.%. ½<110>{111} dislocation glides smoothly in pure Ni and stress-velocity dependences produce a reasonably accurate friction coefficient over a wide temperature range from 300 to 900K. However the glide mechanism is very different in concentrated alloys where Ni-Fe interfaces play the role of rather strong obstacles, which strength depends very much on the local configuration. The random character of Ni-Fe distribution demands modeling of a long dislocation line gliding over long distance to consider maximum possible spectrum of configurational fluctuations. We present results for stress and strain controlled dislocation glide and describe correlations between some observed microstructures and flow stress at different temperatures. The results obtained are discussed in application to deformation experiments in single phase high entropy alloys.

This work was supported by the US Department of Energy Office of Science, Basic Energy Sciences, Materials Science and Engineering Division.



Authors: Amuthan A. Ramabathiran, Michael Ortiz

EAS Division, California Institute of Technology, Pasadena, CA 91125, USACorresponding author email: [email protected]

ABSTRACT

Understanding the atomistic basis of plasticity in hexagonal close packed (hcp) crystals is crucial for many applications involving hcp metals like Mg and its alloys. The absence of sufficient slip systems to accommodate homogeneous plastic deformation further implies twinning as an important deformation mechanism for hcp metals. In this work, we present a multi-scale analysis of dislocations in single crystal Mg using the non-equilibrium finite temperature quasicontinuum method, a unique multiscale framework for coarse-graining in both space and time while retaining full atomistic resolution near defect cores [1]. In particular, we focus on nano-void growth and present dynamic simulations that highlight the role of (c+a) dislocations on the pyramidal planes to accommodate deformation along the c-axis. We also present new results on the effect of temperature and strain rate on the dislocation mechanisms and discuss the implications of these studies on nano-void growth for spallation in Mg.

[1] Venturini G, Wang K, Romero I, Ariza MP and Ortiz M “Atomistic long-term simulation of heat and mass transport” J. Mech. Phys. Solids 73: 242-268 (2014)

The authors gratefully acknowledge support from the U.S. Army Research Laboratory (ARL) through the Materials in Extreme Dynamic Environments (MEDE) Collaborative Research Alliance (CRA) under award No. W911NF-11-R-0001.

Influence of Cottrell atmospheres on dislocation mobility in ferritic iron

H.Ganesan1, C.Begau1, G.Sutmann2, A.Hartmaier1

1Interdisciplinary Centre for Advanced Material Simulation (ICAMS), Ruhr Universität Bochum, 44801 Bochum, Germany. ([email protected])2Jülich Supercomputing Centre, Forschungszentrum Jülich, 52425 Jülich, Germany.

ABSTRACT

The yield strength of low carbon steels can be increased by the strain aging mechanism. During heat treatment, light elements such as carbon, which have a low solubility in ferritic iron, segregate towards dislocations and form cloud like pattern known as Cottrell atmospheres. These locally high carbon concentrations retard the dislocation mobility, thus higher stresses are required to unpin the dislocation and cause plastic deformation. Although this strengthening mechanism is widely applied, it is not well understood at the atomic length scale. Therefore, atomistic methods namely Molecular Dynamics (MD) and Metropolis Monte Carlo (MC) were coupled in a unified framework to investigate this problem. Using this framework, the segregation of carbon atoms towards dislocations was simulated using MC, mimicking the heat treatment step. The distribution of carbon in ferrite was studied using different dislocation configurations, carbon concentrations and temperatures. Different concentration profiles are observed, where for example, three fold symmetric pattern of carbon atoms are found around the dislocation core of screw dislocations. The influence of carbon on the dislocation mobility is then studied using MD, by applying shear stresses on the samples. Here, an increase in the Peierls stress is measured in comparison to carbon free or untreated samples. Such atomic level study of dislocations-carbon interaction provide further insights on the strain aging mechanism.


Analysis of Plastic Anisotropy in Nanotwinned Copper by a Statistical Grain Boundary Dislocation Model

Authors: Rui Yuan1, Irene J. Beyerlein2, Caizhi Zhou1,

Affiliations: 1Department of Materials Science and Engineering, Missouri University of Science and Technology, Rolla, MO 65409, USA; 2Theoretical Division, Los Alamos

National Laboratory, Los Alamos, NM 87545, USA.

ABSTRACT

Metals with nanoscale twins (NT) have been under the spotlight in the materials community for many years because of their unique properties and great potential in nanoscale devices. Among the NT metals, copper (Cu) has been one of the most intensely researched. Equiaxial-grained NT Cu exhibits near plastic isotropy because of the randomly oriented twin layers. In contrast, due to the preferential crystallographic orientation, columnar-grained NT Cu exhibitsstrong plastic anisotropy when subsequently deformed. In this work, we explore the microstructural properties that give rise to the plastic anisotropy observed in columnar-grained NT Cu. A statistical model for random dislocation source lengths is developed to calculate the corresponding critical resolved shear stresses for propagating a dislocation within a twin lamella. By incorporating this model into a 3D crystal plasticity finite element model, we demonstrate that the twin thickness dependent strength of NT Cu arises from statistical variability in dislocation source length and the predicted yield strengths agree with reported values in the literature for NT Cu with the same average twin thickness. Distinct from conventional crystal plasticity models, in this model, slip occurs within each twin lamella by discrete slip events whose range is restricted by the grain size and twin thickness. We also use this model to explore the relative effects of twin thickness, grain size, and initial texture on the plastic anisotropy in yield strength, flow stress, and strain hardening of NT Cu. We aim to gain insight into how the fine NT structure can alter the slip systems on which dislocations prefer to glide.

Atomistic Modeling of Plastic Deformation of Polycrystalline Metallic Nanolayered Composites

Authors: Sixie Huang, Caizhi Zhou

Affiliations: Department of Materials Science and Engineering, Missouri University of Science and Technology, Rolla, MO 65409, USA.

ABSTRACT

Metallic nanolayered composites (MNCs) exhibit order-of-magnitude increases in strength compared to bulk constituents showing great potential for applications in a variety of fields. Previous studies on MNCs focused on the effect of phase interface properties on the mechanical behaviors of MNCs and ignored the influence of grain boundaries (GBs) in eachmetallic phase. Since most MNCs are comprised of polycrystalline metallic phases, in this work we explore how the grain boundaries and grain sizes influence the deformation behavior of Cu/Nb MNCs by molecular dynamics (MD) simulations. The results indicate that grain boundaries facilitate the dislocation source nucleation and lower the strength of MNCs; in contrast, dislocations nucleate from the interface in MNCs without GBs. In addition, the strength of MNCs increases with decreasing the layer thickness, when layer thicknesses are larger than a critical size. With the interaction between gilding dislocations and GBs/phase interfaces, there are several possible deformation mechanisms that can govern the strength of MNCs, including the confined layer slip of partial/full dislocations, grain boundary slidingand interface shearing. Both dislocation nucleation and gliding play important roles on the plastic deformation of polycrystalline MNCs. We also explore the relative effects of layer thicknesses and interface structures on yield strength, flow stress, and strain hardening of MNCs. We aim to reveal the controlling factor of mechanism transition and its influence on the strength.


A strain gradient plasticity theory accounting for multi-slip

Andreas Prahs, Eric Bayerschen, Hannes Erdle, Thomas Böhlke

Chair for Continuum Mechanics, Institute of Engineering Mechanics, Karlsruhe Institute of Technology (KIT), Kaiserstrasse 10, 76131 Karlsruhe, Germany,

[email protected]

ABSTRACT

Microstructured materials exhibit a non-local mechanical behavior. In oligo- or polycrystals, the behavior is influenced by the presence of grain boundaries (GB) and their resistance against the movement of dislocations. The introduction of an internal length scale, e.g., [1], into the classical theories of plasticity is one possibility to investigate the occurring size effects in such materials. Thus, e.g., the Hall-Petch effect, that has been experimentally investigated for several metals, e.g., [2], can be reproduced by simulations. For this purpose, strain gradient plasticity theories, e.g., [3], can be used. Based on an energetical formulation for the bulk material and the GBs, the derivation of a strain gradient plasticity theory is presented that accounts for multi-slip phenomena in a face-centered cubic (FCC) crystal aggregate within a large strain context. Considering the GBs, a boundary condition is formulated in terms of the free energy on the GB. Finite-Element simulations are performed under different loading conditions. Furthermore, for the special case of single-slip, an analytical solution is compared to the simulations and discussed.

[1] X. Zhang, K.E. Aifantis, J. Senger, D. Weygand, M. Zaiser, Internal length scale and grain boundary yield strength in gradient models of polycrystal plasticity: How do they relate to the dislocation microstructure?, J. Mater. Res. 18, 2116–2128 (2014)

[2] R. Armstrong, I. Codd, R. Douthwaite, N. Petch, The plastic deformation of polycrystalline aggregates, Philosoph. Mag. 73, 45–58 (1962)

[3] E. Bayerschen, M. Stricker, S. Wulfinghoff, D. Weygand, T. Böhlke, Equivalent plastic strain gradient plasticity with grain boundary hardening and comparison to discrete dislocation dynamics, Proc. R. Soc. A 20150388, http://dx.doi.org/10.1098/rspa.2015.0388 (2015)

The support of the German Research Foundation (DFG) in the project 'Dislocation based Gradient Plasticity Theory' of the DFG Research Group 1650 'Dislocation based Plasticity' under Grant BO 1466/5-1 is gratefully acknowledged.

Interaction of Prismatic Dislocation Loops with Free Surfaces by Atomistic Simulations and Experiments

Authors: Jan Fikar1, Ivo Kuběna1, Roman Gröger1

Affiliations: 1 Central European Institute of Technology & Institute of Physics of Materials (CEITEC IPM), Academy of Sciences of the Czech Republic, Žižkova 22,

61662 Brno, Czech [email protected]

ABSTRACT

The prismatic loops appear in metals as a result of high-energy irradiation or plastic deformation. Understanding of the prismatic loop formation and interaction is important for quantification of irradiation-induced deterioration in mechanical properties. Transmission electron microscopy (TEM) observation of dislocation loops in thin foils is commonly used, however, the results are inevitably influenced by the proximity of the free surfaces. The prismatic loops are attracted to the free surfaces by the image forces and, depending on their type, size and depth in the foil, can escape via the free surfaces invalidating the TEM observations and conclusions. That is why it is necessary to quantify the effects induced by the free surfaces. There exist two theoretical elastic solutions for isotropic material and Burgers vector exactly perpendicular to the free surface [1,2]. The first atomistic simulations in BCC iron for circular and hexagonal 1/2<111> loops and perpendicular surfaces show good agreement with surprisingly both elastic solutions, but the critical stress needed to move the loop is very shape and potential dependent. This critical stress should be determined by experiment. We intend to generalize and verify these findings using both atomistic simulations and TEM experiments.

[1] J. Bastecka, Czech J. Phys. B 14 (1964) 430.

[2] P.P. Groves, D.J. Bacon, Philos. Mag. 22 (1970) 83.


Systematic identification of crystal plasticity constitutive parameters in ß-Sn

Aritra Chakraborty1, Zhuowen Zhao, Philip EisenlohrDepartment of Chemical Engineering and Materials Science, Michigan State University.

[email protected]

ABSTRACT

The highly anisotropic nature in ß-Sn has restricted formulation of reliable material models describing their deformation behavior. ß-Sn forms an integral part of lead-free solder interconnects and, hence, are quintessential to the reliability of the device. Since these interconnects mostly form single or oligo-crystals of ß-Sn, the crystal anisotropy has a pronounced effect on their overall response under external load [1]. Simulating their deformation behavior necessitates a suitable technique to identify the material parameters that govern the single crystal constitutive response. A suggested methodology, been used to quantify slip behavior in cubic and hexagonal crystal systems [2,3], estimates these constitutive parameters by fitting crystal plasticity simulations of single-crystal indentation to their corresponding experiments using an axisymmetric indenter for multiple grain orientations. An integral part of the method is a robust optimization algorithm to cope with the high-dimensional parameter spacein connection with the extensive computational cost of evaluating the fitness function due to low crystal symmetry. Therefore, gradient-free algorithms are favored. We investigate the sensitivities and cost associated with these algorithms as well as the required experimental reference in terms of load–displacement data and indentation topography. The immediate goal of this activity is to enhance our understanding of slip activity in ß-Sn. Moreover, the methodology could turn into a useful toolkit to investigate other materials with higher anisotropy. Support through NSF grant DMR-1411102 is gratefully acknowledged.

[1] Lee, T.-K., Bieler, T.R., Kim, C.-U., Ma, H., “Fundamentals of Lead-Free Solder Interconnect Technology,” Springer US (2015)

[2] Zambaldi, C., Raabe, D., Plastic anisotropy of γ-TiAl revealed by axisymmetric indentation, Acta Mater., 58, 3516–3530 (2010)

[3] Zambaldi, C., Yang, Y., Bieler, T.R., Raabe, D., Orientation informed nanoindentation of α-titanium: Indentation pileup in hexagonal metals deforming by prismatic slip, J. Mater. Res.,27, 356–367 (2012)

On the Representation of Internal Length Scales at the Discrete-Continuum Transition

Severin Schmitt1, Katrin Schulz1, Peter Gumbsch1,2

1Karlsruhe Institute of Technology, Institute of Applied Materials (IAM-CMS), Kaiserstr. 12, 76131 Karlsruhe, [email protected]

2Fraunhofer Institute for Mechanics of Materials IWM, Wöhlerstr. 11, 79108 Freiburg

ABSTRACT

Many efforts have been made to incorporate internal length scales into dislocation density based continuum theories. One way to obtain an internal length scale implicitly from dislocation dynamics is the analysis of dislocation-dislocation correlation functions computed from discrete dislocation dynamics simulations [1,2].Similitude solutions can be defined by the investigation of the evolution equations of dislocation dynamics and yield classes of solutions which are invariant under specific transformations, naturally characterized by the total dislocation density ρ (all lengths scale with ρ-1/2) [1]. However, it was pointed out that the scale of the similitude solutions should be identified with the number of dislocations [3].This raises questions concerning the scaling and the influence of the number of dislocations in an averaging volume regarding the dislocation-dislocation correlation functions. In order to address this issue, we present 2d discrete dislocation dynamics simulations to analyze the convergence of the ensemble averages with respect to the number of simulations and compare the dislocation-dislocation correlation functions obtained for specific initial conditions for different number of dislocations with the screened dislocation-dislocation correlation functions from [1,2]. We discuss the results and identify a limit, i.e. the “continuum limit”, where the considered system can be modeled using continuum theory versus the “discrete” case in which the effects of individual dislocations remain important.

[1] M. Zaiser, M.-C. Miguel, I. Groma, Statistical dynamics of dislocation systems: The influence of dislocation-dislocation correlations, Phys. Rev. B, 64, 224102 (2001)

[2] I. Groma, F. Csikor, M. Zaiser, Spatial correlations and higher-order gradient terms in a continuum description of dislocation dynamics, Acta Mater.,51, 1271 (2003)

[3] M. Zaiser, S. Sandfeld, Scaling properties of dislocation simulations in the similitude regime, Model. Simul. Mater. Sci. Eng., 22, 065012 (2014)


Title: In situ TEM analysis of dislocation interactions with grain boundaries in BCC Metals

Kaila M. Bertsch1, I. M. Robertson2

1University of Illinois at Urbana-Champaign Materials Science and Engineering Department, 201 Materials Science and Engineering Building, 1304 W. Green St.,

Urbana, IL, 61801, [email protected]. 2University of Wisconsin-Madison Engineering Physics Department, 2610 Engineering Hall, 1415 Engineering Drive,

Madison, WI, 53706, [email protected].

ABSTRACT

Grain boundaries play a key role in the strengthening and deformation of metals. It is well established for FCC metals and alloys that during slip transmission across grain boundaries, the magnitude of the Burgers vector of the incoming dislocation system determines the slip system of outgoing dislocations activated by the boundary. Conversely, for BCC metals and alloys, macroscale tests may indicate that the activated system is determined by the magnitude of the global Schmidt factor. To verify this, straining experiments have been performed in situ in the TEM to directly observe how dislocations interact with grain boundaries in various BCC metals and alloys. This dynamic technique has been coupled with electron tomography to enhance the visualization and interpretation of the interactions in 3D. The observed interactions include slip transmission, several accommodation mechanisms, and generation of dislocations along the length of the grain boundary. This latter observation provides insight to the dislocation sources in the grain boundary and will be compared and contrasted with molecular dynamics computer simulation results. The slip transmission results will be assessed in terms of the criteria that have been observed for FCC metals, primarily with respect to the importance of Burgers vector in determining the outgoing slip system.

Coupled 3D dislocation dynamics at nano- and micro-scales

Jaehyun Cho, Guillaume Anciaux, Jean-François Molinari

Civil Engineering Institute, Materials Science and Engineering Institute, École Polytechnique Fédérale de Lausanne (EPFL), Station 18, CH-1015, Lausanne,

Switzerland

ABSTRACT

Dislocation dynamics are important to understand material plasticity in small-sized materials. In case of face-centered cubic crystalline systems, densities of initial dislocations, dislocation nucleations and starvations processes influence material strengths at micro- and nano-scales [1]. To model these multi-scale physics in concurrent manners, 2D Coupled Atomistic and Discrete Dislocation dynamics (CADD) [2] is the only available computational tool. However, in CADD, the described dislocation dynamics are limited to 2 dimensional systems. In this presentation, we propose a new method for coupling MD and DD simulations in 3D (CADD3D) to resolve the limitations of CADD. We introduce its required building blocks (core templates [3] and mobility law) and the coupling-communication scheme. The dynamics of a hybrid dislocation, which is a dislocation structure composed of atomic and discrete dislocations, will be shown to demonstrate the workability of the proposed communication scheme. Furthermore, several applications will be presented using CADD3D such as an expanding dislocation loop nucleated from a Frank-Read source.

[1] Greer JR, De Hosson JTM. Plasticity in small-sized metallic systems: Intrinsic versus extrinsic size effect. Prog Mater Sci (2011), doi:10.1016/j.pmatsci.2011.01.005

[2] Shilkrot et. al. Journal of the Mechanics and Physics of Solids, 52(4):755-787, 2004[3] Cho et. al. Advanced Modeling and Simulation in Engineering Sciences, 2(1):1-17, 2015

This work is supported by the Swiss National Science Foundation (grant no. 200021-

140506/1).


Predicting fatigue crack initiation in metals using dislocation dynamics simulations

Christian Heinrich1, Veera Sundararaghavan1

1Department of Aerospace Engineering, University of Michigan, 1320 Beal Avenue, Ann Arbor, MI, 48105, [email protected]

ABSTRACT

The presented work aims at deepening the understanding of the initiation of fatigue cracks in metals. The work is inspired by an argument of Mura and Nakasone [1] where an energy criterion is used to predict the initiation of a fatigue crack from a slip band. The discussion is based on the evolution of dislocation networks, as these are the prime cause for permanent deformation in metals. Using high performance computing, 3D dislocation dynamics simulations are performed over several cycles to study the growth of the dislocationarrangement. Then the evolution of energy in the system is determined, including all relevant terms such as: energy of the elastic field of the dislocations and their interaction, core energies, dissipation, energy stored in the continuum and external work. A hypothetical crack is placed in the region of the largest dislocation density and it is checked, if the energies stored in part of the dislocation network should be exchanged with the surface energy of a crack to lower the overall energy state of the system. The size of the crack is based on the number of dislocations that were previously formed in the network, as the motion of these dislocations towards the hypothetically formed free surface would form the actual crack. The presented work requires only minimal input in form of elastic constants and dislocation mobilities (for example from molecular dynamics). Results are presented for different materials (Cu and Mg), grain sizes and loading rates.

[1] T. Mura, Y. Nakasone, A Theory of fatigue crack initiation in solids, Journal of Applied Mechanics, 57 (1990)

This work is supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award #DE-SC0008637 as part of the Center for PRedictive Integrated Structural Materials Science (PRISMS Center) at University of Michigan.

Analysis Of The Deformation Behavior Of Wires Under Torsion: Insights From Simulations And Experiments

Authors: M. Stricker1, M. Ziemann1, M. Walter1,P. Gruber1, S.M. Weygand2, D. Weygand1

Affiliations: 1Karlsruhe Institute of Technology (KIT), Institute for Applied Materials (IAM), 76131 Karlsruhe, Germany ([email protected]); 2University of Applied

Science, Faculty of Mechanical Engineering and Mechatronics (MMT), 76133Karlsruhe, Germany

ABSTRACT

The understanding of the role of imposed strain gradients on the plastic deformation is a key issue for modeling the mechanical behavior of wires under complex loadings such as torsion. Therefore, Discrete Dislocation Dynamics simulations (DDD) [1], crystal plasticity and experiments of torsion of <100> and <111> oriented single crystalline wires are combined, extending the preliminary work [2]. The hardening behavior obtained by DDD is size dependent. The strong hardening observed for the smallest samples is due to pile-up formation. For larger sizes more homogeneously distributed plasticity occurs, leading to a strong decrease in hardening, consistent with a simple model. Another aspect concerns the distribution of the plastic deformation. The analysis is based on local plastic strain measures evaluated for DDD and crystal plasticity results: DDD results clearly show a plastification of the volume around the torsion axis contrary to the crystal plasticity results. This is a strong signature of internal stresses, which push dislocations through the neutral fiber. Furthermore, an analysis of experiments also aims at comparing the local plastic deformation: local crystallographic orientations are obtained by measuring the samples in cross- and longitudinal sections with EBSD. Despite a difference in sample size by a factor of about 5-10 between experiment and DDD, the resulting pattern in the measures used for quantification of the local plastic deformation show similarities. This allows correlating the emerging patterns with an underlying dislocation microstructure.

[1] Weygand D, Friedman LH, Giessen E Van der, Needleman A. Model Simul Mater Sci Eng 2002;10:437.

[2] Senger J, Weygand D, Kraft O, Gumbsch P. Model Simul Mater Sci Eng 2011;19:74004.

The financial support for the research group FOR1650 Dislocation based plasticity funded by the German Research Foundation (DFG) under contract number WE3544/5-1 is gratefully acknowledged.


Full Strain and Stress Tensors Measured from Individual Dislocation Cells in Severely Plastic Deformed Aluminum

Lyle E Levine1, Thien Phan1, Ruqing Xu2, Michael Kassner3

1National Institute of Standards and Technology, Gaithersburg, MD 20899-85532Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439-48003Department of Chemical Engineering & Materials Science, University of Southern

California, Los Angeles, CA, 90089Presenter Email: [email protected]

ABSTRACT

A critical factor in plastic deformation of metals is the drastically inhomogeneous distribution of stresses over micrometer length scales. Over the past decade, experimental measurements using synchrotron X-ray microbeam diffraction have characterized these stresses along asingle crystallographic direction with submicrometer spatial resolution within dislocation microstructures in deformed metal single crystals [1] and polycrystalline alloys [2]. These measurements have generally demonstrated the presence of localized dipolar stress fields that are consistent with Mughrabi composite-model predictions. Now, groundbreaking improvements in the microbeam diffraction technique enable full strain and stress tensors to be extracted from buried, submicrometer sample volumes within complex devices and microstructures [3]. Here, we report such measurements from individual dislocation cells within a commercial Al alloy subjected to various levels of severe plastic deformation. The stress tensors exhibit large directional stresses that align with the deformation geometry and are inconsistent with the two-component composite model. We will explain the measurement method, describe the distribution of stresses within the samples, and discuss the implications for the composite model.

[1] L.E. Levine, P. Geantil, B.C. Larson, J.Z. Tischler, M.E. Kassner, W. Liu, M.R. Stoudt, F. Tavazza, Disordered long range internal stresses in deformed copper and the mechanisms underlying plastic deformation, Acta Mater. 59, 5803 (2011)

[2] I.F. Lee, T. Phan, L.E. Levine, J.Z. Tischler, P. Geantil, Y. Huang, T.G. Langdon, M.E. Kassner, X-Ray microbeam diffraction study of long range internal stresses in equal-channel angular pressed aluminum, Acta Mater., 61, 7741 (2013)

[3] L.E. Levine, C. Okoro, R. Xu, Full elastic strain and stress tensor measurements from individual dislocation cells in copper through Si vias, IUCrJ, 2, 635 (2015)

Microstructural evolution in SAC105 and SAC305 solder joints with different initial cooling rates and thermal cycling conditions

using HE-XRD

Authors: Quan Zhou1, Justin Roe1, Thomas R. Bieler1, Tae-Kyu Lee2

Affiliations: 1 Department of Chemical Engineering and Materials Science, Michigan State University, USA; 2Department of Mechanical & Materials Engineering, Portland

State University.

ABSTRACT

While lead free solders have replaced conventional leaded solders in the electronic packaging industry, there are still unpredictable failures arising from the highly anisotropic properties of Sn-based solder joints. In our previous study, the effects of cooling rates on the microstructure and grain orientation evolution in lead-free solder joints in ball grid array packages was characterized using polarized light microscopy and electron backscattered diffraction (EBSD). A fine pitch chip array ball grid array package design was reflowed with either higher or lower cooling rates than in common use, resulting in refined grains with high cooling rates or mechanical twins in lower cooling rates, which also depended on the joint location, and the original crystal orientation(s). Some joints were removed near the corners to enable periodic in situ assessment of strain evolution in two of the corner joints using high-energy X-Ray diffraction (HE XRD) at beamline 6-ID-D at Argonne National Lab. The microstructure evolution during the cool down following solidification was measured.Samples underwent accelerated thermal cycling for 100 or more cycles prior to in situ measurements and they were stored until the next opportunity for HE XRD measurements.The related mechanical response and orientation changes throughout the thermal cycling history up to 750 cycles were recorded and characterized. Significant changes in crystal orientations were observed after the first 100 thermal cycles, and the changes varied depending upon the initial orientation and composition.

This work is supported by NSF-GOALI Contract 1006656 and Cisco Systems Inc., San Jose, CA. Use of the Advanced Photon Source was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357.


Mesoscale Theory of Dislocations : from the Discrete to the Continuum

A. Finel, P.-L. Valdenaire, Y. Le Bouar, B. Appolaire

Laboratoire d’Etude des Microstructures (ONERA-CNRS)BP 72, 92322 Châtillon, France

.

ABSTRACT

Because of the various length and time scales involved in dislocation dynamics, the modeling of plastic activity at large scale is not straightforward. The major problem is to identify a physically-based continuum dislocation theory that preserves at mesoscale the space and time correlations that discrete dislocations exhibit at lower scale. This communication focuses precisely on this aspect and elaborates on a key issue: the transition between the discrete, where plastic flow is resolved at the scale of individual dislocations, and the continuum, where dislocations are represented by densities. We in particular focus on the underlying coarse-graining procedure and discuss its implication on the resulting correlation-induced local stresses and transport equations that control the plasticflow at the continuum level.

Grain Boundary motion induced by the glide of disconnections: interaction with radiation induced defects in binary Fe alloys

Anna Serra1, Yanicet Ortega2

Affiliations: 1Department of Civil and Environmental Engineering, Universitat Politècnica de Catalunya. BarcelonaTech. Jordi Girona, 1-3 C-2, 08034 Barcelona. [email protected]; 2Faculty of Physics. University Complutense of Madrid, 28040

Madrid, Spain.

ABSTRACT

Both low- and high-angle grain boundaries (GBs) are known to respond to an applied shear stress by simultaneous migration and shear [1]. It has been demonstrated that an applied shear stress produces a well-defined Peach-Koehler force promoting disconnection motion [2].Disconnections are GB line defects with both, dislocation and step character, and their glide along the GB produces its migration. In pure metals the mobility of disconnections depends on GB orientation and, for a given GB, it depends on the dislocation core structure. The presence of alloying elements may act as an obstacle for the glide of disconnections although this should be dependent on the core structure, the solute atom and temperature. Thus, we first study, by MD simulation, the migration of symmetric GBs in binary Fe-Ni and Fe-Cr alloys as a function of solute concentration and temperature. The GB with highest mobility, i.e., more glissile disconnections, is chosen to study the interaction of the GBs with radiation induced defects such as vacancy and interstitial clusters. In this interaction both types, glissile and sessile clusters, are chosen. Glissile clusters suffer either attraction or repulsion from the GB. Sessile clusters suffer a transformation due to the interaction with disconnections. Clusters may be sessile because of their structure or because they are decorated by solute atoms.

[1] A.P. Sutton, R.W. Balluffi, Interfaces in Crystalline Materials, Oxford University Press, Oxford (1995).[2] H.A. Khater, A. Serra, R.C. Pond, J.P. Hirth, The disconnection mechanism of coupledmigration and shear at grain boundaries, Acta Mater. 60, 2007-2020 (2012).

This project has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 661913 (SOTERIA). The computing was partly done in CSUC (www.csuc.cat).


Atomistic mechanisms of dislocation nucleation and interactions with perfect and imperfect twin boundaries

Qiongjiali Fang1 and Frederic Sansoz1,2

1 Mechanical Engineering Program, School of Engineering, The University of Vermont,

Burlington, VT 05405, USA. E-mail: [email protected] Materials Science Program, The University of Vermont, Burlington, VT 05405, USA

ABSTRACT Nanoscale twin boundaries (TBs) have proved to dramatically increase strength and ductility simultaneously in face-centered-cubic (FCC) metals and alloys. At atomic scale, the underlying processes for this unique behavior have been established in terms of dislocation nucleation and interaction mechanisms with perfect coherent TBs. Recent experimental evidence has shown, however, that short segments of incoherent TB forming intrinsic kink-like defects could play a critical role in plastic deformation and ductility of nanotwinned metals [1]; yet our current understanding of the role imperfect TBs on dislocation processes is limited. This talk will present a study using molecular dynamics (MD) simulation and GB-mediated plasticity theory to examine the fundamental mechanisms of dislocation nucleation and interaction with both perfect and defective TBs. First, special attention is placed on screw dislocation – TB interactions using MD simulations to show how kink TB defects oriented at 0 deg. or 60 deg.with respect to the dislocation line, can have a profound impact on interaction mechanisms and strengthening behavior. Second, the emission of partial dislocations from stress concentrationsat grain boundary-TB junctions was investigated, with a particular focus on the dependence of dislocation nucleation stress on kink structure and twin size. The findings of this study are important for designing new nanostructured FCC metals with exceptional mechanicalproperties.

[1] Y.M. Wang, F. Sansoz, T. LaGrange, R.T. Ott, J. Marian, T.W. Barbee, et al., Defective twin boundaries in nanotwinned metals., Nat. Mater. 12, 697–702 (2013)

Displacement-controlled nanoindentation simulations with dislocation dynamics

Joshua C. Crone1, Lynn B. Munday, Jaroslaw Knap

U.S. Army Research LaboratoryComputational and Information Science Directorate

Aberdeen Proving Ground, Aberdeen, MD [email protected]

ABSTRACT

Nanoindention experiments on materials with high dislocation densities show that the onset of plastic deformation occurs over a wide range of indenter loads. Under these conditions, it has been shown that plastic deformation is due to the activation of pre-existing dislocations, rather than homogeneous dislocation nucleation. In the present work, we use discrete dislocation dynamics (DDD) simulations of indentation to identify the underlying dislocation mechanisms that lead to the onset of plastic deformation and pop-in. To include free surface effects and the highly varying stress field induced by the indenter, we couple the bulk DDD simulator, ParaDiS [1], with a parallel finite element solver [2]. We also present a newalgorithm for computing the displacement field of a dislocation to perform simulations ofdisplacement controlled indentation, where the displacement field of the indenter is directly coupled to the plastic deformation due to dislocation motion. Simulations are carried out for multiple randomly seeded dislocation configurations at several dislocation density levels in order to obtain a statistically relevant measure of the indenter’s response. The resulting cumulative distribution function representing the probability of pop-in at a given indenter depth is compared to simpler stochastic models.

[1] A. Arsenlis et al., Model. Simul. Mater. Sci. Eng. 15, 553 (2007)[2] J.C. Crone et al., Model. Simul. Mater. Sci. Eng. 22, 3 (2014)


Title: Dislocation cross-slip mechanism in FCC metals

Authors: Lei Cao, Marisol Koslowski

Affiliations: School of Mechanical Engineering, Purdue University, West Lafayette.

Correspondence: [email protected]

ABSTRACT

Cross slip in face-centered-cubic metals is an important mechanism for dislocation multiplication, strain hardening, dynamic recovery, and dislocation cell formation. The implementation of the cross-slip mechanism in a phase-field dislocation dynamics (PFDD)model is presented, demonstrated with examples of dislocation double cross slip and dislocation bypassing precipitate. Screw dislocations, which glide on adjacent planes, are found to cross-slip and annihilate each other, leading to an effective elimination of screw dislocations in materials. Moreover, the influence of dislocation cross slip on stress-strain behaviors and dislocation microstructures are investigated, in order to establish a relationship between the microstructure and mechanical properties of materials. In addition, strain rate, initial dislocations, stacking fault energy and grain boundary structure are found to have significant influences on the cross-slip process.

Dislocation pattern formation in a 2D continuum theory of dislocations

István Groma, Péter Ispanovity

Department of Materials Physics, Eötvös University Budapest,H-1517 Budapest POB 32, Hungary, email:[email protected]

ABSTRACT

Understanding the physical origin of the spontaneous emergence of dislocation patterns is a long standing challenge in dislocation theory. During the past decades several phenomenological continuum models of dislocation patterning were proposed, but none of them are derived from microscopy considerations. In this paper we present a 2D continuum theory that is obtained by a systematic coarse graining of the equations of motion of dislocations. It is show that in the evolution equations of the dislocation densities a diffusionlike term being neglected in the considerations suggested earlier plays a crucial role in the length scale selection of dislocation density fluctuation. It is also show that the continuum theory can be cast into the framework of phase field theories but in order to account for the flow stress one has to introduce a nontrivial dislocation mobility function.


Title: Dislocation cross-slip mechanism in FCC metals

Authors: Lei Cao, Marisol Koslowski



ABSTRACT

Cross slip in face-centered-cubic metals is an important mechanism for dislocation multiplication, strain hardening, dynamic recovery, and dislocation cell formation. The implementation of the cross-slip mechanism in a phase-field dislocation dynamics (PFDD)model is presented, demonstrated with examples of dislocation double cross slip and dislocation bypassing precipitate. Screw dislocations, which glide on adjacent planes, are found to cross-slip and annihilate each other, leading to an effective elimination of screw dislocations in materials. Moreover, the influence of dislocation cross slip on stress-strain behaviors and dislocation microstructures are investigated, in order to establish a relationship between the microstructure and mechanical properties of materials. In addition, strain rate, initial dislocations, stacking fault energy and grain boundary structure are found to have significant influences on the cross-slip process.

Dislocation pattern formation in a 2D continuum theory of dislocations

István Groma, Péter Ispanovity

Department of Materials Physics, Eötvös University Budapest,H-1517 Budapest POB 32, Hungary, email:[email protected]

ABSTRACT

Understanding the physical origin of the spontaneous emergence of dislocation patterns is a long standing challenge in dislocation theory. During the past decades several phenomenological continuum models of dislocation patterning were proposed, but none of them are derived from microscopy considerations. In this paper we present a 2D continuum theory that is obtained by a systematic coarse graining of the equations of motion of dislocations. It is show that in the evolution equations of the dislocation densities a diffusionlike term being neglected in the considerations suggested earlier plays a crucial role in the length scale selection of dislocation density fluctuation. It is also show that the continuum theory can be cast into the framework of phase field theories but in order to account for the flow stress one has to introduce a nontrivial dislocation mobility function.


A Unifying Approach towards Dislocation Microstructure in Simulation and Experiment

Stefan Sandfeld, Dominik Steinberger, Nina Gunkelmann

Institute of Materials Simulation, Department of Materials Science, Friedrich-Alexander University of Erlangen-Nuremberg, Dr.-Mack-Str. 77, 90762 Fürth,

Germany ([email protected])

ABSTRACTDislocations have been studied extensively over the last century. Predicting the behavior of systems of interacting dislocations, though, requires a detailed understanding of dislocation mechanisms and is extremely challenging because dislocations represent a true “multiscale” phenomena. For example, atomic details of the dislocation core determine how dislocations interact, the collective behavior of large numbers of dislocations is responsible for a number of emergent phenomena on very different length scales, and the macroscopic mechanical response on the specimen scale is governed by complex structure-property relationships.Thus, typically the different approaches, be it theory, experiment, or simulation, have different characteristic length scales and represent dislocation microstructures in different degrees of detail. Moreover, the transfer of information from one method or length scale to another is not straightforward, such as the “translation” of microscopy results into dislocation initial values or the information transfer between MD and DDD

We give an overview over state-of-the-art methods for characterizing dislocation microstructures. We then introduce a novel unifying ”language” for dislocation microstructures which is based on the information-rich dislocation field quantities used in Hochrainer’s Continuum Dislocation Dynamics (CDD) theory [1]: the “discrete-to-continuum” (D2C) method [2] is a systematic approach for mapping properties of discrete dislocations to well-defined continuous fields. By using orientation distributions and the minimum information principle we can mathematically compress the data, similar to the MP3 format. Based on a number of examples, we demonstrate that this data format allows to analyze quantitatively and in detail dislocation microstructures or internal energy distributions from very different experimental and simulation methods. Additionally, this allows through ensemble averages to observe emergent patterns or to easily compare data from different methods to each other. Furthermore, we show how the D2C approach can serve as foundation for systematic data mining of discrete dislocation data (from MD and DDD), which then can be readily used as input parameters for simulation methods on larger length scales.

[1] T. Hochrainer, S. Sandfeld, M. Zaiser, P. Gumbsch, Continuum dislocation dynamics: Towards a physical theory of crystal plasticity, J. Mech. and Phys. Solids, 63 (2014)

[2] S. Sandfeld and G. Po, Microstructural comparison of the kinematics of discrete and continuum dislocations models, Modelling Simul. Mater. Sci. Eng. 23 (2015)

Title: Simulating Micromechanical tests using discrete dislocation Plasticity

Authors: Edmund Tarleton1, Sylvain Queyreau2, Tom Arsenlis3

Affiliations: 1Department of Materials, University of Oxford, Parks Road, OX1 3PH,UK, [email protected]; 2University of Paris XIII, Sorbonne, Paris,France; Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA

94550, USA

ABSTRACT

Focused ion beam milling allows small scale single crystal cantilevers to be produced with cross-sectional dimensions on the order of microns which are then tested using a nan indenter allowing both elastic and plastic materials properties to be measured. EBSD allows test specimens to be milled from any desired crystal orientation. Popular tests include micro pillar compression, indentation and micro cantilever bending. Discrete dislocation plasticity is the ideal approach through which to simulate these tests and gain insight into the underlying mechanisms. However, simulating finite volumes of material with mixed traction/displacement boundary conditions accurately remains challenging. The displacement fields are only available analytically for simple cases such as triangular loops or infinite segments. Furthermore accurate resolution of tractions near a free surface requires a prohibitively fine FE mesh. Alternative methods for calculating the dislocation displacement field via the plastic strain and efficient approaches for traction calculation via analytic integration over an element surface are discussed. Comparison between 2D and 3D models and with experiments is presented as well as the implementation of GPU accelerated codes.

Edmund Tarleton acknowledge financial support from EPSRC grant EP/N007239/1


Role Of Grain Boundary Sliding In Deformation Of Polycrystalline Materials

Authors: Ajey Venkataraman1, Marissa Linne2, Samantha Daly2, Michael D. Sangid1

Affiliations: 1Purdue University, School of Aeronautics and Astronautics, 701 W Stadium Ave, West Lafayette, IN 47906, [email protected]; 2University ofMichigan, Mechanical Engineering, 2350 Hayward, Ann Arbor, MI 48109-2125

ABSTRACT

Grain boundary sliding (GBS) is an important deformation mechanism that is known to be activated at particular conditions such as high temperatures, low strain rates and small grain sizes [1]. Typically, constitutive models in literature have accounted for crystalline slip and GBS as isolated phenomena. While crystalline slip has been extensively studied (in the formof dislocation glide), GBS is relatively less understood and has been for the most part restricted to nanocrystalline materials and high-temperature loading. Several studies have found that the two deformation mechanisms operate not independently, but as simultaneous,interactive mechanisms. In the present study, crystalline slip and GBS are modeled as coupled deformation mechanisms using crystal plasticity simulations within a finite elementframework. Distinct flow and hardening laws are assigned to the grain “core” and “mantle”applied to FCC materials. The grain core accommodates dislocation glide and the grain mantle accommodates (in addition to dislocation slip) boundary sliding. The constitutive response for our model is compared to full-field strain response experimentally obtained at the microscale level. The effects of grain mantle width and grain sizes are studied. The results from this research will help improve the sophistication and accuracy of deformation modeling and significantly advance the fundamental knowledge of material behavior.

[1] Gifkins, R_C. "Grain-boundary sliding and its accommodation during creep and superplasticity." Metallurgical and Materials Transactions A 7.8 (1976): 1225-1232.

Title: Dislocations in Radiation Damage of Materials for Nuclear Energy Applications

Author: Alexander V. Barashev

Affiliations: 1 Materials Science and Technology Division, ORNL, Oak Ridge, TN 37831-6138, USA; 2 Center for Materials Processing, Department of Materials

Science and Engineering, University of Tennessee, Knoxville, TN 37996-0750, USA;e-mail: [email protected]

ABSTRACT

Current understanding of the role of dislocations in materials response to irradiation is reviewed,and critical unresolved problems are specified. The radiation-induced processes, such as swelling, radiation growth, creep and hardening, are governed by the evolution of dislocation population. Depending on the material and conditions, the density and interaction properties of dislocations with radiation defects may change dramatically during irradiation. From one hand, dislocation climb, decoration by interstitial loops, mutual annihilation of dislocations, and growth of prismatic loops of vacancy and interstitial type alter dislocation properties from those before irradiation. From another hand, primary defects are produced by energetic particles in the form of vacancies, self-interstitial atoms and their clusters, with various diffusion and interaction properties, which also makes the situation qualitatively different from that under thermal equilibrium conditions. Current understanding of the kinetics of dislocation network is described. The crucial impact of small dislocation loops executing one-dimensional random walk on the lattice and immobile prismatic loops on the microstructure development is described.

The research sponsored by the Office of Fusion Energy Sciences U.S. DOE.


Slip activity in bcc metals under uniaxial load

Roman Gröger1, Yi-Shen Lin2, Vaclav Vitek2, Tomas Kruml1, Zdenek Chlup1

1Central European Institute of Technology - Institute of Physics of Materials(CEITEC IPM), Academy of Sciences of the Czech Republic, Zizkova 22, 61662 Brno,

Czech Republic ([email protected]);2University of Pennsylvania, Department of Materials Science and Engineering,

3231 Walnut Street, Philadelphia, PA 19104, USA

ABSTRACT

Numerous computer simulations carried out in the past two decades have shown that the cores of 1/2⟨111⟩ screw dislocations in bcc metals are not planar. The motion of these dislocations thus depends not only on the Schmid stress but also on certain other (non-glide) components of the applied stress tensor. Despite the same crystal structure of all bcc metals, the slip activity of individual {110}⟨111⟩ systems is different for materials of the VB and VIB groups. Here, we present direct molecular statics simulations of uniaxially loaded single crystals of Ta (group VB) and W (group VIB) using the new generation of Bond Order Potentials for these metals to investigate the dependence of the activity of all 1/2⟨111⟩ screw dislocations on the character (tension, compression) and orientation of the applied load. These atomistic studies are complemented by the results of our recent uniaxial tests on millimeter-sized single crystals of high purity deformed at low temperatures. We discuss under which conditions the atomistic simulations of isolated screw dislocations provide fairly accurate predictions of slip activity and when the correlation with slip traces is much worse. In the latter case, we propose a computational model that can be used to understand the effect of long-range strain fields of other dislocations on the yield stress.

STEM Optical Sectioning for Imaging Edge and Screw Displacements in Dislocation Core Structures

Peter D Nellist1,2, Hao Yang1, Juan G Lozano1, Timothy J Pennycook1,2,3, David Hernandez Maldonado1,2 and Peter B Hirsch1

1University of Oxford, Department of Materials, Parks Rd, Oxford OX1 3PH, UK;2EPSRC SuperSTEM Facility, Daresbury Laboratory, Warrington, WA4 4AD, UK;3Now at University of Vienna, Faculty of Physics, Boltzmanngasse 5, A-1090 Vienna,

Austria.

ABSTRACT

Aberration corrected transmission electron microscopes with sub-angstrom resolution have advanced our knowledge of the atomic structure of edge dislocations, which are viewed end-on with the tensile or compressive strain normal to the dislocation being clearly visible. Atomic displacements associated with screw dislocations however cannot be observed in end-on images because the helicoidal screw displacements are parallel to the viewing direction. Here we show how “optical sectioning” in high-angle annular dark-field (HAADF) scanning transmission electron microscope (STEM) imaging can be used to image screw displacements in the core structure of dislocations at atomic resolution. In optical sectioning, the reduced depth of focus of aberration corrected microscopes is utilized to extract information along the beam direction by focusing the electron probe at specific depths within the sample. A depth resolution of just a few nanometres is possible. We first show direct detection of the depth-dependent strain due to the Eshelby twist associated with dislocations containing a screw component in thin STEM samples. The measurement of the magnitude of the displacement confirms the screw Burgers vector for dislocations in GaN [1] and allows the identification of a new dissociation reaction associated with mixed [c+a] dislocations [2]. We go on to show that the helicoidal displacements around a screw can be imaged with the dislocation lying transverse to the electron beam by optically sectioning the plane containing the dislocation. This novel technique is applied to the study of the c-component in the dissociation reaction of a mixed [c+a] dislocation in GaN that was previously been observed end-on [3]. Finally we discuss how the optical sectioning approach may be used to study the delocalization of screw dislocations in body-centred cubic metals.

[1] J. G. Lozano, et al. Phys. Rev. Lett. 113 (2014) 135503. “Direct Observation of Depth-Dependent Atomic Displacements Associated with Dislocations in Gallium Nitride”

[2] P.B. Hirsch et al., Philosophical Magazine, 93 (2013) 3925. “The dissociation of the [a+c]dislocation in GaN”

[3] H. Yang, et al., Nat Commun, 6 (2015) 7266. “Imaging screw dislocations at atomic resolution by aberration-corrected electron optical sectioning”


Understanding of brittle to ductile transition in nano-lamellar phase: case of the Ti2AlN phase.

Antoine Guitton1, W. Sylvain1, C. Zehnder2, S. Schröders2, S. Korte-Kerzel2, Anne Joulain1, Ludovic Thilly1, Christophe Tromas1

1: Pprime Institute – Department of Materials Physics and MechanicsUPR 3346

CNRS – University of Poitiers – ENSMASP2MI, Boulevard Marie et Pierre Curie, BP 30179

86962 Futuroscope Chasseneuil CedexFrance

2: Institute of Physical Metallurgy and Metal Physics, RWTH Aachen University,Germany

ABSTRACT

MAX phases combine properties of both ceramics and metals which makes them attractive for a potentially wide range of applications. Concerning their mechanical properties MAX phases are elastically stiff, have rather low yield strength and low density. They present a brittle to ductile transition (BDT) at about 800°C whose origin remains unclear.We present here a multi-scale experimental study of deformation mechanisms of the Ti2AlN MAX phase below and above the BDT [1-2].

Small scale mechanical tests, associated with AFM and SEM observations of the slip lines allows studying the elementary deformation mechanisms in individual grains. Cyclic loading in spherical nanoindentation tests and in micro-pillar compression tests are performed at room temperature to understand the origin of the hysteretic behavior observed in the mechanical response of MAX phases.

In a second part, the evolution of plasticity mechanisms with temperature in MAX phase has been investigated at two different scales. Macroscopic compression tests have been performedunder confining pressure at room temperature and at 900°C. A detailed dislocation analysis by TEM revealed the presence of configurations never observed before in MAX phases: dislocations interactions confined in the basal plane at room temperature and cross-slip from basal plane to prismatic or pyramidal planes at 900°C are evidenced. Nanoindentation tests have been performed from room temperature to 800°C. The dislocation structures around the indents have been characterized by AFM and TEM observations. Here again, an evolution of the plasticity mechanisms is observed below and above the BDT.

[1] Guitton, A., Joulain, A., Thilly, L. & Tromas, C., Dislocation analysis of Ti2AlN deformed at room temperature under confining pressure. Philos. Mag. 92, 4536–4546(2012).

[2] Guitton, A., Joulain, A., Thilly, L. & Tromas C., Evidence of dislocation cross-slip in MAX phase deformed at high temperature, Scientific Report, 4 : 6358 (2014)

Dislocation Patterns under Monotonic Loading of FCC Crystals





ABSTRACT

We report on the prediction of the dislocation patterns in FCC crystals under monotonicloading using continuum dislocation dynamics theory published in the authors’ early work [1].In this density-based framework, the dislocation density evolution is governed by the transport, cross-slip and reactions of dislocations, which are captured by kinetic equations derived based on statistical mechanics principles. A novel finite element method customized to adapt to FCC single crystals has been used to solve the dislocation kinetic equations coupled with crystal mechanics. Within this framework, the cross slip process anddislocation-dislocation reactions at short range are treated using a Monte Carlo approach in the continuum frame. The continuum model is illustrated to have the ability to take the data obtained from discrete dislocation simulation as parameters in the curl-type kinetic equations to address cross-slip and short range reaction issues. The simulations are implemented for monotonic loading along different directions and the results of stress-train curve, the average dislocation density evolution, emerging dislocation and slip patterns, and similitude law attempted from the results will be presented. A special attention is given to the analysis of the observed dislocation patterns and comparison with TEM observation in the literature.



In-situ deformation of micro-objects combined with x-ray diffraction as a tool to uncover the elementary plasticity

mechanisms: on the role of dislocation nucleation in the brittle-to-ductile transition of semi-conductors and MAX phases

W. Sylvain1, Anne Joulain1, Christophe Tromas1, Ludovic Thilly1

Vincent Jacques2, Dina Carbone3, Rudy Ghisleni4, Christoph Kirchlechner5

Steven Van Petegem6, Helena Van Swygenhoven6

1Pprime Institute – CNRS – University of Poitiers – ENSMASP2MI, Boulevard Marie et Pierre Curie, BP 30179

86962 Futuroscope Chasseneuil Cedex, France2Laboratoire de Physique des Solides, CNRS-Université Paris-Sud, Orsay, France

3European Synchrotron Radiation Facility, Grenoble, France4EMPA, Thun, Switzerland

5Erich Schmid Institute of Materials Science, Austrian Academy of Sciences, Austria6 Neutrons and X-rays for Mechanics of Materials , Paul Scherrer Institute, Villigen,

Switzerland

ABSTRACT

In-situ deformation of micro-pillars combined with x-ray diffraction is used to uncover elementary plasticity mechanisms in various materials, notably within the context of the brittle-to-ductile transition (BTDT) appearing in semi-conductors or MAX phases.To study the role of dislocation nucleation in the BTDT of semiconductors, InSb single-crystalline micro-pillars have been fabricated by FIB milling. Coherent x-ray micro-diffraction was used to detect and count phase defects (stacking faults, SFs) preliminarily introduced by deformation of micro-pillars. Diffraction patterns exhibit peak splitting in agreement with the presence of a few SFs located in the deformed pillars. Simulations of coherent diffraction patterns show that not only the number of defects but also the size of the defected volume influences the maximum intensity of the pattern, allowing for a precise counting of defects [1]. Diffraction measurements were then performed in-situ, during compression, to detect the first plastic events.Ti2AlN is a ternary nitride belonging to the MAX phases, with a complex nano-layered hexagonal lattice with very high c/a ratio (∼4.5). MAX phases combine some of the best properties of metals (machinability, damage tolerance, etc.) and ceramics (high specific stiffness, high temperature resistance, etc.). Their deformation mode consists of kink and shear bands as well as grain delamination, attributed to the nano-layered structure where basal dislocation slip is mostly operative, except at high temperature [2]. The micro-mechanism suggested to explain these properties is the incipient kink band (IKB). But to date, direct evidence for the existence of IKBs, is lacking. Single-crystalline micro-pillars have been fabricated by FIB milling and in-situ compressed under micro-focused x-ray beam. The simultaneous recording of the applied compressive stress-strain curve and of the Laue patterns allows associating the onset of plasticity and/or non-linear elasticity, with the local lattice characteristics.

[1] Physical Review Letters, 111 (2013), 065503[2] Scientific Reports, 4 (2014), 6358

First Principles Modeling of <c+a> Dislocation Geometry and Interactions With Solutes in Mg Alloys.

Authors: Daniel Buey1, Lou Hector Jr2 and Maryam Ghazisaeidi1

Affiliations: 1 Department of Materials Science and Engineering, Ohio State University. 2041 College Rd, Columbus, OH 43210

2General Motors R&D

ABSTRACT

Predicting mechanical properties of new alloys requires understanding the atomic-scale mechanisms of plasticity with an accurate account for chemistry change. First principles modeling of dislocation core structures and interactions with solutes, is a fundamental step towards quantitative and predictive design of new alloys for enhanced and tailored properties. For example, activation of the pyramidal <c+a> slip mode—with an order of magnitude higher critical stress than the basal slip mode-- enhances room temperature ductility of Mg alloys. We compute the core structure and energy of edge and screw <c+a> dislocations using density functional theory (DFT) in combination with lattice Green’s function boundary conditions. Both dislocations dissociate into two half <c+a> partials separated by a stacking fault on the (1-212) plane. The edge dislocationpyramidal II core structure is then used to study the effect of Y solutes at several positions inside the dislocation core. The presence of Y in several of these sites modifies the core structure as follows. When placed inside the partial dislocation cores, Y severely distorts the surrounding bonds. On the other hand when Y is put on the stacking fault region, separating the partials, the dissociation distance can change by about the magnitude of the <c+a> Burgers vector, often accompanied by lowering the energy. We then used a modified Labusch-type solid solution strengthening model to predict the stress required to move the dislocation in the presence of Y from first-principles interaction energies.


Title: Introduction of Precisely Controlled Dislocations into SRF Cavity Nb Sheet and Their Impact on Local Superconducting Properties

Authors: Mingmin Wang1, Di Kang1, Zuhawn Sung2, Peter J. Lee2, Anatolii A. Polyanskii2,Christopher C. Compton3, Thomas R. Bieler1*

Affiliations: 1Department of Chemical Engineering and Materials Science, Michigan State University;

*Corresponding author: Office 3527 Engineering Bldg, [email protected]; 2Applied Superconductivity Center at the National High Magnetic Field Laboratory, Florida State University; 3National Superconducting Cyclotron Laboratory, Michigan State University

ABSTRACT

Formation of superconducting radio frequency (SRF) cavities from Nb sheets introduces microstructural defects such as dislocations and low-angle grain boundaries that can serve as favorable sites for pinning centers [1] for magnetic flux that can degrade cavity performance. Therefore, effects of dislocations on magnetic flux trapping behavior in strained single- and bi-crystal Nb samples were investigated in order to develop a theory for predicting which orientations will produce undesirable defects by tensile deformation. Orientations were chosen to favor specific slip systems, which generate dislocations with special angles with respect to the grain boundaries, sample surface, or magnetic field direction. These model samples have deformation that is similar to that expected in typical cavity forming processes. Laue X-ray and EBSD-OIM crystallographic analyses were used to characterize grain orientations and microstructural defects obtained experimentally, and the generated defect structures were confirmed by OIM and electron channeling contrast imaging (ECCI). Cryogenic magneto-optical imaging was used to directly observe the penetration of magnetic flux into the deformed Nb at about 5-8 K, and relationships between flux penetration and dislocation and grain boundary defect structures were identified.

[1] Matsushita, T., "Flux pinning in superconductors," Springer (2007) Research supported by DOE/OHEP (contract number DE-FG02-09ER41638 at MSU, and DE-SC0009960 at FSU) and the State of Florida. We also thank Chris Compton at FRIB for providing the Nb slice.

Title: Non-linear elastodynamic effects of dislocation generation and motion in shock waves

Authors: Jeffrey T. Lloyd and John D. Clayton

Impact Physics Branch, US Army Research Laboratory, Aberdeen Proving Ground, MD, 21005

[email protected].

ABSTRACT

For approximately 50 years, plate impact experiments have been used to investigate governing relations for dislocation motion and evolution at extreme loading rates; however, barring a limited number of investigations, the contribution of dynamic elastic waves emitted from generated and accelerated dislocations has been neglected. The limited number of cases that considered transient elastodynamic effects used a linear elastic framework, which gives rise to limited interaction between the shock front and dislocations within it. The objective of this work is to quantify the influence of waves emitted from the generation and motion of dislocations in the shock with the shock front in a non-linear elastic material, i.e., a material that becomes stiffer when compressed. Shock front dissipation and stress relaxation are analyzed for idealized dislocation configurations within an analytical framework. The following physics are included, and their effects are quantified: crystal structure; dislocation generation rate; mean dislocation velocity; and the ratio of wave speed in compressed versus uncompressed material. Based on these findings, a new relation between elastic precursor decay and dislocation evolution is proposed, which includes these non-linear elastic wave effects. Physical quantities of interest that are inferred from experiments, such as dislocation density and shock dissipation, are then re-examined using this new formulation.


Atomistic Studies on the Role of Interface Curvature on Dislocation – Interface Interactions

Julien Guénolé, Aruna Prakash, Erik Bitzek

Department of Materials Science and Engineering, Institute 1Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Germany

[email protected]

ABSTRACT

Interfaces play a decisive role in the deformation of any polycrystalline metal or precipitate-strengthened alloy. Since processes like dislocation nucleation, absorption, transmission or pinning take place at the atomic scale, atomistic simulations have played a key role in studying grain- and interphase boundaries (IPBs), and their interactions with dislocations. However, most of the detailed studies on dislocation – interface interactions were performed on quasi-two dimensional simulation setups with straight dislocation lines interacting with perfectly planar interfaces, or on nanocrystalline materials generated by Voronoi tessellation,which creates planar grain boundaries (GBs) with unrealistic GB topologies.Here we give an overview on our recent atomistic studies on dislocation – interface interactions, with the focus on non-planar boundaries and more realistic GB topologies. While controlled studies on dislocations interacting with various high-angle GBs in a bicrystal setup are used to show the importance of GB curvature on slip transmission through GBs, simulations on realistic superalloy samples reveal the importance of interface curvature on the misfit dislocation network and subsequent interactions with matrix dislocations [1].Simulations on nanocrystalline samples with different degrees of GB curvature as well as different GB network topologies finally demonstrate that depending on the GB topology certain deformation mechanisms can be overemphasized or completely suppressed in the simulations.

[1] A. Prakash, J. Guénolé, J. Wang, J. Müller, E. Spiecker, MJ. Mills, I. Povstugar, P. Choi, D. Raabe, E. Bitzek, Atom probe informed simulations of dislocation-precipitate interactions reveal the importance of local interface curvature, Acta Mater. 92, 33 (2015)

In Situ Monitoring of Dislocation Proliferation using Ultrasound

Vicente Salinas1, Fernando Lund1, Nicolás Mujica1, Rodrigo Espinoza-González2

1Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile, [email protected];

2Departamento de Ciencia de los Materiales, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Tupper 2069, Santiago, Chile.

ABSTRACT

Ultrasound (US) has been in use for decades as a nondestructive testing tool [1]. The reason is that, because of the low energies involved, US can penetrate deep into a material without affecting it. The detection of cracks and flaws in solid materials in service is a major field of application [2]. The propagation of cracks causes brittle fracture and one concern is to detect them before they reach a critical size for catastrophic propagation. Another mode of failure is ductile failure or plastic yield, which is governed by the proliferation of dislocations [3]. Can US be used as a nondestructive testing tool for the plastic behavior of materials in the same way that it is used to test for brittle fracture? We here report results of local insitu measurements of the speed of shear waves, vT, in aluminum under standard testing conditions (traction test), as a function of externally applied stress. There is a clear decrease in vT at the yield stress, consistent with a proliferation of dislocations. These measurements provide a quantitative, continuous relation between dislocation density and externally applied stress, and paves the way for the development of US as a diagnostic tool of dislocation density for metallic pieces in service where other methods, such as X-ray diffraction (XRD) and transmission electron microscopy (TEM) are not available because of their destructive nature on preparation of samples.

[1] C.-H. Chen, “Ultrasonic and Advanced Methods for Nondestructive Testing and Material Characterization”, World Scientific, Singapore (2007).[2] P. O. Moore, D. Kishoni, G. L. Workman, “Nondestructive Testing Handbook, Third Edition: Volume 7”, Ultrasonic Testing (UT), (2007).[3] Lawn, B.R., “Fracture of Brittle Solids”, Cambridge Solid State Science Series, 2nd Edn. (1993).

We acknowledge the support of Fondecyt Grant 1130382 and Fondecyt postdoctoral Grant 3160164.


The role of dislocation density in micron-scale plastic deformation

Authors: Péter D. Ispánovity, Ádám Hegyi, Dániel Tüzes, Péter Szabó, István Groma

Affiliation: Eötvös University, Department of Materials Physics, Pázmány P. stny. 1/A, H-1117 Budapest, Hungary, [email protected]

ABSTRACT

Micron-scale plasticity is characterized by large intermittent strain bursts and a strong dependence of the specimen strength on its physical dimensions (size effects). A lot of effort has been made to understand the effect of the specimen size, but much less attention has been paid to the role of the initial dislocation density. We present a systematic experimental study of micropillar compressions performed on ensembles of identically fabricated specimens witha range of initial dislocation densities and pillar sizes. It is found, that not only the pillar strength, but also strain hardening behavior is strongly dependent on the initial density. In addition, at large densities traditional size effect of yield stress is replaced by a size effect inthe strength fluctuations. Dislocation dynamics simulations complement the experimental work. First, the parameters of a stochastic continuum model are set based on discrete dislocation simulations and a weakest link argument for the microplastic regime. Then this stochastic model is applied for finite systems of different size and initial dislocation density.The good qualitative match between the model and the experiments highlight the importance of the initial dislocation density in the plasticity of micron-scale objects.

[1] P. D. Ispánovity, Á. Hegyi, I. Groma, G. Györgyi, K. Ratter és D. Weygand, Average yielding and weakest link statistics in micron-scale plasticity, Acta Mater. 61, 6234 (2013)

Financial supports of the European Commission (CIG-321842), Hungarian Scientific and Research Fund (PD-105256 and K-105335) and the Hungarian Academy of Sciences (János Bolyai Scholarship) are gratefully acknowledged.

Title: Work Hardening and Athermal Strain Rate Effects in Face-Centered Cubic Metals

Authors: Wei Cai1, Ryan B. Sills2,1, Amin Aghaei1

Affiliations: 1Department of Mechanical Engineering, Stanford University, CA 94350, USA, [email protected]; 2Sandia National Laboratories, Livermore, CA 94551, USA.

ABSTRACT

The stress-strain response of single crystal copper loaded in single and multi-slip over strain rates ranging from 10 to 104 s-1 is studied using dislocation dynamics (DD) simulations. Employing a recently developed time integration scheme [1], shear strains in excess of 1% are attained routinely and repeatedly, so that a systematic investigation on the relation between the unit mechanisms and work hardening rate is now possible.

The stress-strain response depends on the ratio of the strain rate and initial dislocation density, with two regimes observed. When the ratio is large, yield is followed by a sharp yield drop and strain softening. In this regime, it is useful to think of individual dislocations as carriers of plasticity. The predicted stress-strain curves compare relatively well with experiments on single crystals at high strain rates, although significant experimental scatter exists.

When the ratio of strain rate and initial dislocation density is small, no yield drops are observed and strain hardening occurs when loaded in multi-slip. In this regime, the interactions between dislocations become more important. When the ratio is sufficiently small, we find that the 0.1% yield strength obeys the Taylor relation. Hardening rates observed under [001] loading are consistent with stage II of the quasi-static shear stress-strain response of face-centered cubic metals, on the order of μ/200 [2].

By changing rules on unit mechanisms in DD simulations, we determine the role of different dislocation reactions on the hardening rate. We have found that Lomer locks are the most important junction type for hardening, with collinear junctions second most important. Other types of junctions do not contribute appreciably to the work hardening rate. Short-ranged elastic interactions also make a small contribution to hardening.

[1] R. B. Sills, A. Aghaei, and W. Cai, Advanced Time Integration Algorithms for Dislocation Dynamics Simulations of Work Hardening, Submitted to Modelling Simul. Mater. Sci. Eng. (2015).

[2] U. F. Kocks and H. Mecking, Physics and phenology of strain hardening: the FCC case,Prog. Materials Science, 48, 171-273 (2003).

This work was supported by Sandia National Laboratories (R.B.S.) and by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award No. DE-SC0010412 (W.C.). Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.


Title: The influence of structural changes on the critical size

of crystals upon mechanical milling

Authors: Yifei Zeng and Marisol Koslowski



ABSTRACT

Mechanical milling is a common process in many industries to reduce particle size. For instance, some active pharmaceutical ingredients need to be micronized to achieve desired functions. However, size reduction is not the only outcome of mechanical milling. During the process of high energy milling, severe plastic deformation and solid state transformations may also occur. Experiments show that the critical particle size upon milling is influenced by temperature, but there is also correlation among critical size and structural changes, such as defects multiplications and solid state transformations. We will present a model that takes into account plastic deformation, polymorph transformations, amorphization and fracture to predict the critical size uponmilling of molecular crystals and its relation to structural changes.

Back Stress Analysis of Hardening in Sub-50nm Si Nanocubes

Authors: Eric D. Hintsala1,3, Andrew J. Wagner2,3, William W. Gerberich3, K. Andre Mkhoyan3

Affiliations:1Hysitron, Inc., 9625 W 76th St, Eden Prairie, MN, USA, email:

[email protected];2Intel Corporation, Hillsboro, OR, USA;

3University of Minnesota, Department of Chemical Engineering and Materials Science,Minneapolis, MN, USA.

ABSTRACT

It is well understood that internal stress fields are crucial towards accurate determination of dislocation nucleation and kinetics, one of the most critical being the back stress from previously emitted dislocations. Yet, discrete analysis of back stress effects on flow stress in a controlled experiment have not progressed very far, due primarily to experimental challenges. A model experiment for such an analysis would involve simple loading of a defect-free single crystal with well-defined crystallographic orientation. Such an experiment is presented, where silane plasma synthesized Si nanocubes (NCs) with sub-50 nm dimensions are uniaxially compressed in-situ a FEI Technai F30 transmission electron microscope (TEM) operating at 200keV using a specially stabilized Hysitron PI-95 PicoIndenter. Stress/strain was calculated at the contact surfaces and the resulting curves show an upper/lower yield phenomena, followed by softening and eventual hardening at ~50% strain. This late hardening onset could be explained by eventual confinement of the natural corner truncations of the NC, which then was used as the basis for a classical back stress analysis [1] adapted specifically for a cubic geometry. This analysis was further guided by observations of activated {111} slip planes emanating from the center of contact towards the opposing NC corner at yield containing partial dislocations, confirmed by post-mortem dark field and high resolution TEM. The calculated back stress, when subtracted from the applied stress, suggests a constant effective stress for continued dislocation emission, as has been suggested by many [2].

[1] J.D. Eshelby, F.C. Frank, F.R.N. Nabarro, XLI. The equilibrium of linear arrays of dislocations, Philos. Mag. 42 (1951)

[2] P.B. Hirsch, S.G. Roberts, The brittle-ductile transition in silicon, Philos. Mag. A 64(1991)

This work was partially supported by NSF MRSEC under awards DMR-0819885 and DMR-1420013. The authors would like to thank Doug Stauffer and Ryan Major of Hysitron.







ABSTRACT


Back Stress Analysis of Hardening in Sub-50nm Si Nanocubes

Authors: Eric D. Hintsala1,3, Andrew J. Wagner2,3, William W. Gerberich3, K. Andre Mkhoyan3

Affiliations:1Hysitron, Inc., 9625 W 76th St, Eden Prairie, MN, USA, email:

[email protected];2Intel Corporation, Hillsboro, OR, USA;

3University of Minnesota, Department of Chemical Engineering and Materials Science,Minneapolis, MN, USA.

ABSTRACT

It is well understood that internal stress fields are crucial towards accurate determination of dislocation nucleation and kinetics, one of the most critical being the back stress from previously emitted dislocations. Yet, discrete analysis of back stress effects on flow stress in a controlled experiment have not progressed very far, due primarily to experimental challenges. A model experiment for such an analysis would involve simple loading of a defect-free single crystal with well-defined crystallographic orientation. Such an experiment is presented, where silane plasma synthesized Si nanocubes (NCs) with sub-50 nm dimensions are uniaxially compressed in-situ a FEI Technai F30 transmission electron microscope (TEM) operating at 200keV using a specially stabilized Hysitron PI-95 PicoIndenter. Stress/strain was calculated at the contact surfaces and the resulting curves show an upper/lower yield phenomena, followed by softening and eventual hardening at ~50% strain. This late hardening onset could be explained by eventual confinement of the natural corner truncations of the NC, which then was used as the basis for a classical back stress analysis [1] adapted specifically for a cubic geometry. This analysis was further guided by observations of activated {111} slip planes emanating from the center of contact towards the opposing NC corner at yield containing partial dislocations, confirmed by post-mortem dark field and high resolution TEM. The calculated back stress, when subtracted from the applied stress, suggests a constant effective stress for continued dislocation emission, as has been suggested by many [2].

[1] J.D. Eshelby, F.C. Frank, F.R.N. Nabarro, XLI. The equilibrium of linear arrays of dislocations, Philos. Mag. 42 (1951)

[2] P.B. Hirsch, S.G. Roberts, The brittle-ductile transition in silicon, Philos. Mag. A 64(1991)

This work was partially supported by NSF MRSEC under awards DMR-0819885 and DMR-1420013. The authors would like to thank Doug Stauffer and Ryan Major of Hysitron.







ABSTRACT


Using Phase Field Dislocation Dynamics to Understand the Formation, Expansion, and Interaction of Partial Dislocations in

Deformed Nano-crystals

William J. Joost1,2, Abigail Hunter1, Irene J. Beyerlein1

1 Los Alamos National Laboratory, Los Alamos, NM 87545, USA2Vehicle Technologies Office, U.S. Department of Energy, Washington, DC 20585, USA

[email protected]

ABSTRACT

Dislocation motion and interaction with obstacles largely controls the mechanical behavior of materials; however, the complexity of these processes presents challenges for both experimental and computational techniques. In this study, we apply phase field dislocation dynamics (PFDD) simulations to explore and quantify the interaction of dislocations with grain boundaries and other dislocations, and to provide insight into the hardening behavior of FCC metals. In general, the phase field approach evolves a system through minimization of total energy, where the energy is described as a function one or more scalar order parameters that are associated with particular quantities of interest. In the PFDD model, the order parameters are defined in terms of perfect Burgers vectors for each active slip system. The PFDD model is able to describe features such as partial dislocations, stacking faults, and twins by incorporating the generalized stacking fault energy surfaces (i.e. the γ-surface) determined from ab-initio density functional theory (DFT) calculations. PFDD simulations thereby offer a route towards understanding dislocation motion and interaction within an energy minimization framework that naturally account for various characteristics of the system. Using a combination of PFDD simulation results and insight from the experimental literature, we describe the relationships between grain size, features of the stacking fault energy surface, partial dislocation activity, and ultimately mechanical behavior in several FCC metals. We further demonstrate how dislocation characteristics strongly affect the behavior of nano-crystalline metals and the interactions between dislocations, with significant implications for materials design.

This work was supported in part by Los Alamos National Laboratory’s Institute of Materials Science.


Disorientations, dislocations and slip systems

Wolfgang Pantleon

Technical University of Denmark, Department of Mechanical Engineering. Section of Materials and Surface Engineering, Produktionstorvet 425, 2800 Kongens Lyngby,

[email protected].

ABSTRACT

By means of electron backscatter diffraction (EBSD), local orientations of the crystalline lattice are conveniently determined and individual grains identified. The set of orientations gathered from an individual grain is analyzed in two different manners: (i) from the disorientations between neighboring measuring points the local geometrically necessary dislocation content is resolved and (ii) the entire orientation distribution (micro orientation distribution) within a grain is investigated. For the latter a rigorous scheme based on quaternions has been proposed which allows determination of the dominant disorientation axes and a quantification of the orientation spread along different axes. From the anisotropy of the orientation spread and the main rotation axis insight is gained in the activation of individual slip systems in plastically deformed grains. This is illustrated for grains in tensiledeformed polycrystalline copper. For compatible deformation, (full constraint) Taylor theory requires simultaneous activation of either six or eight slip systems in dependence on grain orientation. In the case of six slip systems, from the single degree of freedom in slip activity a specific dominant disorientation axis is predicted, which is actually not confirmed byexperimental observations. For instance, grains with a <111> direction along the tensile axis have a tendency of showing disorientations around the tensile axis instead of perpendicular to it. From the experimentally determined disorientation axis the pattern of selected slip systems is revealed and the different activities traced to the interaction and mutual suppression of different slip systems. This analysis of the global activation of slip systems within a grain is complemented by the geometrically necessary dislocation density resolved from the local disorientations allowing determination of slip and dislocation patterning on different scales.

Stability of Eshelby Dislocations in FCC Crystalline Nanowires

Authors: Seunghwa Ryu1, Wei Cai2

Affiliations: 1Department of Mechanical Engineering, KAIST, Daejeon 34141, Korea; [email protected], 2Department of Mechanical Engineering, Stanford University,

Stanford 94305, USA; [email protected]

ABSTRACT

The thermally activated escape of Eshelby dislocation in face-centered-crystal (FCc) nanowires are investigated by combining atomistic and continuum models. The energy barriers for the dislocation escape from face-centered-cubic <110> nanowires are predicted from atomistic models as a function of nanowire radius, escape location, and surface step orientation. The dissociation of dislocation into partials has a significant effect on the energy barrier. The dislocation prefers to escape from the end of nanowire with an extended node, where the dissociation width is greater than the equilibrium width in the bulk. The energy barrier is further lowered if the surface step aligns with the dislocation’s slip plane. A continuum line tension model that accounts for partial dislocations is constructed and benchmarked against atomistic predictions for FCC nanowires. The continnum model is then used to make predictions on the stability of Eshelby dislocations over a wide range of nanowire radii.

S. R. acknowledges the support of the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2013R1A1A1010091). The work is partly supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering under Award No. DE-SC0010412 (W.C.). We wish to thank William Kuykendall for discussions on the derivations of the line tension model.


Three-dimensional Quantitative Dislocation Analysis and the High Temperature Creep Behavior of Ni-Base Single Crystal

Superalloys

Leonardo Agudo Jácome

Federal Institute for Materials Science and Testing (BAM), Dept. Materials Engineering, D-12205, Berlin, Germany.

ABSTRACT

The realistic description of plastic deformation caused by dislocations demands the representative measurement of their features, e.g., Burgers vector, slip plane, line direction and density. In the case of bulk deformation of technical alloys, reliable data must be ensured for large regions. Nonetheless, the (thin) filiform nature of dislocations and also the heterogeneity in some microstructures additionally require flexible analysis techniques that resolve the details of their interactions. Strong and clear channeling contrasts, faint extinction contours and the absence of chromatic aberration make scanning transmission electron microscopy (STEM) an ideal imaging mode in wide and thick regions of TEM foils, as opposed to conventional (C)TEM [e. g. 1,2]. It is the purpose of this contribution to show howSTEM can be applied for quantitative measurement of dislocation features. Furthermore, anew tool will be presented, which enables the three-dimensional (3D) reconstruction, visualization and quantification of dislocation densities and directions from stereo-pairs. The application of these techniques will be shown on a monocrystalline Ni-base superalloy, an important class of structural materials that has been implemented in the first row blades of gas turbines. The examples are extracted from specimens subjected to creep deformation at high temperature and low stress under various macroscopic deformation geometries.

[1] D.M. Maher, D.C. Joy, The formation and interpretation of defect images from crystalline materials in a scanning electron microscope, Ultramicroscopy, 1, 239 (1976)

[2] L. Agudo Jácome, G. Eggeler, A. Dlouhý, Advanced scanning transmission stereoelectron microscopy of structural and functional engineering materials, 122, 48 (2012)

The Deutsche Forschungsgemeinschaft (DFG) is acknowledged for funding through project AG 191/1-1. Gunther Eggeler, Antonín Dlouhý and Pedro Portella are acknowledged for fruitful discussions and scientific collaboration.

Multi-scale modelling of high-temperature deformation mechanisms in Co-Al-W-based superalloys.

H. Hasan, D. Dye, P.D. Haynes and V.A. Vorontsov

Department of Materials, Imperial College London, Prince Consort Road, South Kensington, London, United Kingdom, SW7 2BP

ABSTRACT

Since their discovery nearly ten years ago, Co-Al-W-based superalloys have emerged as the frontrunner materials to replace the ubiquitous Ni-based superalloys used in gas turbines. The study of deformation mechanisms in these alloys is of paramount importance for acceleratingthe identification of optimal alloy compositions, saving both time and money during the development process. The chemical ordering present in the γ' intermetallic phase precipitates,which grant the superalloys their superb high-temperature strength, gives rise to complex dislocation interactions. Dislocation configurations can feature a variety of possible planar fault structures, and their associated surface energies can play key role in defining theobserved mechanical properties. In order to accurately model this complexity, we have calculated Gamma-surfaces for Co-Al-W superalloys using the Density Functional Theory, as implemented in CASTEP. Also known as Generalised Stacking Fault energies, these 2D energy surfaces describe the energy cost of associated with local atomic displacements at the dislocation core. The effect of composition on the Gamma-surface topography was also studied. These ab initio data were incorporated into a Phase Field Dislocation Dynamics model to investigate the meso-scale interactions of the dislocations with the microstructure of the alloys over a range of loading conditions. The phase field approach has also been extended to investigate the effects of solute atom segregation to the site of the stacking faults during high-temperature creep and the resulting influence on the deformation resistance.


Hydroforming and failure of a large grain pure niobium tube

Aboozar Mapar1,2, Thomas R. Bieler2, Farhang Pourboghrat3,4

1Dep. of mechanical engineering, Michigan State University, East Lansing, MI 48824, Email: [email protected]; 2Dep. of chemical engineering and materials science, Michigan State University, East Lansing, MI 48824; 3Dep. of Integrated Systems

Engineering, Ohio State University, Columbus OH 43210; 4Dep. of Mechanical and Aerospace Engineering, Ohio State University, Columbus OH 43210.

ABSTRACT

The deformation and failure of a large grain pure Nb tube that was made from a fine grain polycrystalline sheet is examined. The polycrystalline Nb sheet was bent into a tube shape and electron beam welded along the seam. The tube was passed through a hot-zone in a vacuum furnace to grow the grains, resulting in an oligo crystal with a single orientation in the middle and a few elongated large grains parallel to axis of the tubeon either side. This was verified with Laue camera measurements of grain orientations along the axis and around the circumference at regular positions about 25 mm apart. Subsequently, the tube was deformed in a tube hydroforming machine. The deformation was very inhomogeneous and ended with failure in the large grain in the middle of the tube. Analysis of the measured deformation behavior of the Nb tube was compared with a crystal plasticity finite element model calibrated from single crystal samples. The insights gained from the experiment and modeling are used to discuss the how microstruactural features and dislocation slip related phenomena led to the observed failure within the large grain.

Dislocation density-based crystal plasticity modeling of single crystal Niobium

Tias Maiti, Mingmin Wang, Di Kang, Philip Eisenlohr, Thomas Bieler

Chemical Engineering and Material Science, Michigan State University, East Lansing 48824 MI, USA

ABSTRACT

Constitutive models based on thermally-activated stress-assisted dislocation kinetics have been successful in predicting deformation behavior of crystalline materials, particularly in face-centered cubic (FCC) metals. In body-centered cubic (BCC) metals success has been more or less limited,owing to ill-defined nature of slip planes and non-planar spreading of ½ <1 1 1> screw dislocationcores. As a direct consequence of this, bcc metals show strong dependence of flow stress ontemperature and strain-rate, and violation of Schmid law [1]. Most of the work on crystal plasticity of Niobium revolves around constitutive models of phenomenological descriptions, which do not capture effectively the macroscopic multi-stage hardening behavior and evolution of crystallographic texture from a physical point of view. We present high resolution full-field crystal plasticity deformation simulations of single crystal Niobium under tensile and compressive loading with an emphasis on multi-stage hardening, orientation dependence, and the violation of non-Schmid behavior. A physics based material model with atomistically derived parameters for non-Schmid flow rule and kink-pair mechanism (kink-pair nucleation and their lateral propagation) is used for this purpose. The results are then compared with in-situ measurements under tensile and compressive loading.

[1] E. Schmid, W. Boas, Plasticity of Crystals, Springer, J., Berlin, 1935.


Characterization of Misfit Dislocation at the Ferrite/Cementite Interface in Pearlitic Steel

Authors: Jaemin Kim1, Keonwook Kang2, and Seunghwa Ryu1

Affiliations: 1Department of Mechanical Engineering, KAIST, Daejeon 34141, Korea; [email protected], 2Department of Mechanical Engineering, Yonsei University, Seoul

03722, Korea; [email protected]

ABSTRACT

The misfit dislocation at the ferrite/cmenetite interfaces (FCI) for different orientation relationships (ORs) are key information to understand the phase transformation and mechanical properties of pearlitic steels. Yet, the detailed characteristics of misfit dislocation remain unresolved. With the aid of modified atomically-informed Frank-Bilby (mAIFB) method, we characterize the misfit dislocation structures and calculate the interface energiesof five ORs (Bagaryatsky, Isaichev, Pitsch-Petch, Near Bagaryatsky and Near Pitsch-Petch). The interface free energies of five OR computed from atomic simulation indicate the non-existence of Bagaryatsky and Pitsch-Petch OR. The detailed information of misfit dislocation network for five ORs at the FCI are revealed with the mAIFB method.

We acknowledge the support of the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2013R1A1A1010091 and 2013R1A1A2063917).

Title: Orowan Looping with Platelet-like Precipitates in OveragedAluminum-Copper Alloys

Authors: Ryan B. Sills1,2, Wei Cai2

Affiliations: 1Sandia National Laboratories, Livermore, CA 94551, USA, [email protected]; 2Department of Mechanical Engineering, Stanford University, CA

94350, USA.

ABSTRACT

The Orowan looping behavior with platelet-like precipitates is studied using a newly-developed dislocation dynamics model [1]. In this model, precipitates are treated as ellipsoids of arbitrary aspect ratio and arbitrary lattice mismatch (eigenstrain). Orowan loops form after collisions are detected between dislocation segments and precipitates, making the loopingalgorithm robust regardless of the time step size. The Orowan looping process is studied for the case of overaged aluminum-copper alloys, which have precipitates with an aspect ratio of about 30 and a highly non-dilatational misfit [2]. Two different looping regimes are observed. When precipitates are oriented so their major axis is parallel to the dislocation line, the Bacon-Kocks-Scattergood relation using the harmonic average of the separation distance and the precipitate diameter as the elastic outer cut-off radius holds well. In other orientations, however, the looping process is controlled by the formation of dipoles across the precipitates. A new analytical model is developed for the dipole-controlled regime and is shown to match the simulation results well. Additionally, the misfit field is shown to increase or decrease the stress necessary for looping, depending on the orientation and spacing of the precipitates.Using experimental measurements of precipitate sizes, realistic precipitate microstructures of overaged aluminum-copper are generated, and the stress-strain response is studied.

[1] R. B. Sills. Dislocation Dynamics of Face-Centered Cubic Metals and Alloys. Ph.D. Thesis, Stanford University (2016).

[2] A. Biswas, D. J. Siegel, C. Wolverton, and D. N. Seidman. Precipitates in AlCu alloys revisited: Atom-probe tomographic experiments and first-principles calculations of compositional evolution and interfacial segregation. Acta Materialia, 59, 6187–6204,(2011).

This work was supported by Sandia National Laboratories (R.B.S.) and by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award No. DE-SC0010412 (W.C.). Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. This work was performed under a Laboratory Directed Research and Development (LDRD) project 165724.


Subsurface Dislocation Slip Analysis using 3D Crystal Plasticity with a Non-local Constitutive Description

Chen Zhang1, Philip Eisenlohr1, Thomas R. Bieler1, Martin A. Crimp1,Carl J. Boehlert1 and Ruqing Xu2

1 Chemical Engineering and Material Science, Michigan State University, East Lansing, MI, 48824-1226, USA.

2 Advanced Photon Source, Argonne National Laboratory, Lemont, IL, 60439, USA

[email protected]

ABSTRACT

To understand the influence of subsurface dislocation slip activity on tomographic features observed during experiments, a crystal plasticity fast-Fourier-transform (CPFFT) based computational analysis of a Ti-5Al-2.5Sn specimen deformed under uniaxial tension at room temperature was performed in this study. Similar to previous study [1], a realistic 3D microstructure was reconstructed based on Electron Backscatter Diffraction (EBSD) and Differential Aperture X-Ray Microscopy (DAXM) data. A non-local constitutive description was used in this CPFFT study to simulate the slip transfer across grain boundaries. To validate the CPFFT simulation results, simulated strain tensors were compared with experimental measurements extracted from DAXM data. The slip transfer that occurred near grain boundaries was characterized using Schmid factor and various geometric slip transfer factors. Correlation between the simulated subsurface slip transfer and the tomographic features observed in experiment were attempted to further the understanding of heterogeneous plastic deformation in polycrystalline materials.

[1] C. Zhang, H. Li, P. Eisenlohr, W. Liu, C.J. Boehlert, M.A. Crimp, T.R. Bieler, Effect of realistic 3D microstructure in crystal plasticity finite element analysis of polycrystalline Ti-5Al-2.5Sn, International Journal of Plasticity, Volume 69, Elsevier (2015)

This research was supported by DOE/BES grant DE-FG02-09ER46637, and the DAXM characterization at the Advanced Photon Source was supported by DOE contract DE-AC02-06CH11357.

Crystal Plasticity based Modeling and Experimental Analysis of Slip Transfer in Commercial Purity Titanium

H. Phukan1, C. Zhang1, P. Eisenlohr1,T.R. Bieler1 , C.J. Boehlert1, M.A. Crimp1, R. Xu2

1 Department of Chemical Engineering and Materials Science, Michigan State University, USA , [email protected]

2 Advanced Photon Source (APS), Argonne National Laboratory, USA

ABSTRACT

In this study, the deformation behavior of commercially pure hexagonal titanium is characterized in a three-dimensional microstructure. The specimen has a “soft” texture, where the c-axis of most grains is highly inclined to the loading direction, thus strongly favoring activation of prismatic slip systems. Differential Aperture X-ray Microscopy (DAXM) has been used to examine the strain evolution of surface and underlying grains during in-situ four point bending. Based on this data, geometrically necessary dislocation (GND) content in the vicinity of grain boundaries is evaluated. The results are compared to crystal plasticity simulations carried out using a spectral based model of the same volume of microstructure. Comparison of evaluated GND content near boundaries and geometric slip transfer parameters are made to gain understanding of the influence of grain boundaries on heterogeneous deformation.

[1] J. Luster and M.A. Morris, “Compatibility of deformation in two-phase Ti-Al alloys: Dependence on microstructure and orientation relationships.”, Metal. and Mat. Trans. A (1995), 26(7), pp. 1745-1756.

[2] Wenge Yang, B.C Larson, J.Z Tischler, G.E Ice, J.D Budai, W Liu, Differential-aperture X-ray structural microscopy: a submicron-resolution three-dimensional probe of local microstructure and strain, Micron, Volume 35, Issue 6, August 2004, Pages 431-439

This work is supported by NSF-DMR 1108211, and use of the Advanced Photon Source supported by DOE/BES.


Title: Characterization of Dislocation Motion Across Grain Boundaries in Commercially Pure Tantalum

Authors: Bret E. Dunlap1, Philip Eisenlohr1, Thomas R. Bieler1, David T. Fullwood2, Brian Jackson2, Martin A. Crimp1

Affiliations: 1Michigan State University, Department of Chemical Engineering and Material Science, [email protected]; 2Brigham Young University, Department of

Mechanical Engineering

To understand heterogeneous deformation in polycrystalline metals, it is necessary to understand the manner in which dislocations carrying plasticity interact with grain boundaries. In this study, the dislocation configurations developed around nanoindentsand the interaction of these plastic zones with grain boundaries has been examined in body-centered cubic tantalum using electron channeling contrast imaging (ECCI) to directly reveal the residual dislocation distributions associated with the indents.Nanoindentation was carried out far from and near to grain boundaries to induce single and bi-crystal deformation. Orientations of grains and misorientations across grain boundaries were characterized using electron backscattered diffraction (EBSD).Topographies resulting from nanoindentation were mapped using atomic force microscopy (AFM). ECCI was then used to characterize the dislocation types and morphologies generated around the single crystal and grain boundary indents. Densities of geometrically necessary dislocations (GNDs) were determined from cross-correlation EBSD using OpenXY [1]. GND maps generated from cross-correlation EBSD replicate the ECCI observed dislocation distributions. The effect that grain boundaries play on topography transfer was determined by comparing single crystal and bi-crystal AFM topography measurements. Dislocation build-up and transfer across the grain boundary was examined using ECCI and cross-correlation EBSD. The crystallographic details of the incoming and outgoing dislocations were assessed in order to study the geometrical conditions associated with the shear transfer at boundaries.

[1] - OpenXY, Brigham Young University, GitHub.com, 2015

Identification of Activated Slip Systems in High Purity SingleCrystal Niobium Used for Particle Accelerator Cavities

D. Kang1, D.C. Baars1, A. Mapar2, T.R. Bieler1, F. Pourboghrat2, C.C. Compton3

1Department of Chemical Engineering and Materials Science, 428 South Shaw Lane,2527 Engineering Bldg., Michigan State University (MSU), East Lansing, MI 48824,

[email protected];2Department of Mechanical Engineering, MSU, East Lansing, MI 48824;

3Facility for Rare Isotope Beams, East Lansing, MI 48824

ABSTRACT

Slip during plastic deformation of body-centered cubic (bcc) metals is governed by motion of screw dislocations due to their having higher lattice friction than edge dislocations. While it is generally believed that slip occurs primarily on {110} planes at the atomic scale, macroscopic slip planes for bcc metals are affected by factors including temperature, strain rate, strain history, and non-Schmid effects [1]. High purity niobium (Nb) has been used over the past couple decades to build particle accelerator cavities that are operated in the superconducting state. Cavities are typically formed by a process that involves deep drawing, electron beam welding, and heat treatment. Understanding slip and dislocation behavior along the cavity fabrication path is crucial since the resulting dislocation substructure can affect cavity performance in various ways. As an initial study towards this goal, two groups of Nb single crystals, with and without a prior heat treatment, were deformed to about 40% engineering strain in uniaxial tension. Significant differences in flow stresses and observed slip systems between the two groups were identified, likely due to the removal of preexisting dislocations. Crystal plasticity modeling of the stress-strain behavior suggests that non-Schmid effects are small in Nb, and that the deep drawing process may be approximated with a Schmid model. As dislocations are known to reduce thermal conductivity at 2-4K, and can trap magnetic flux that creates local hot spots during operation, further understanding of slip behavior of Nb will guide development of processing paths that can enhance the performance of SRF cavities.

[1] C.R. Weinberger, B.L. Boyce, and C.C. Battaile, Slip planes in bcc transition metals, International Materials Reviews 58, 296 (2013)

This work was supported by the U.S. Department of Energy, Office of High Energy Physics, through Grant No. DE-SC0009962.


Boundary Layer Formation in Continuum Dislocation Dynamics

Christoph Reuber1, Philip Eisenlohr2, Franz Roters1

1Max-Planck-Institut für Eisenforschung GmbH,Max-Planck-Str. 1, 40237 Düsseldorf, Germany

2Chemical Engineering and Materials Science, Michigan State University,428 S Shaw Ln, East Lansing, 48824 MI, USA

ABSTRACT

A comparative study between discrete and continuum dislocation dynamics (DDD and CDD) for the analytically tractable case of a circular plastic inclusion of varying size within an elastic medium is carried out in two dimensions under single slip conditions. The CDD formulation distinguishes signed edge and screw dislocation types [1], explicitly treats formation and destruction of dislocation dipoles, and considers the dislocation flux in the (non-)local density evolution. The continuum model matches the discrete dislocation dynamics results to a large extent. Mesh-dependent density oscillations develop in CDD due to an instability in the governing partial differential equations when introducing a density-dependent flowstress. Geometrically (fixed number of dislocations) and kinematically (fixed plastic capacity) invariant changes to the size of the plastic inclusion are investigated. The formation of a boundary layer with reduced plastic slip is observed for the small inclusion in DDD. It is demonstrated that this feature depends on the spatial distribution of dislocations normal to the slip plane and can be mimicked within CDD by introducing a backstress term that is inversely proportional to the (average) spacing between active slip planes.

[1] A. Arsenlis, D.M. Parks, Modeling the evolution of crystallographic dislocation density in crystal plasticity. J. Mech. Phys. Solids, 50, 1979–2009 (2002)

Work Hardening by Grain Boundary Transformation in Multilayer Nanopillars

Tomotsugu Shimokawa1, Tomoaki Niiyama1, Kenji Higashida2

1Faculty of Mechanical Engineering, Kanazawa University, Kakuma-machi, Kanazawa, Ishikawa 920-1192, Japan, [email protected]

2Department of Materials Science and Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan

ABSTRACT

Conventional work hardening mechanisms established based on dislocation-dislocation interactions in coarse-grained materials hardly operate in nanostructured materials because of the limited space for dislocation structure formation. Here we propose a new concept of “grain boundary transformation induced plasticity (GB-TRIP)” to realize high strength and high ductility in nanostructured materials that strength should be controlled by the dislocation generation at grain boundaries. If an equilibrium grain boundary structure contains a portion of the Burgers vector component of a lattice dislocation, the first dislocation generation from a site of the grain boundary can change the grain boundary structure [1] from which the following dislocation is hardly generated; hence, the next dislocation should be generated at other sites of the grain boundary or other grain boundaries. Consequently, the grain boundary transformation results in the suppression of localized plastic deformation causes the necking.We demonstrate the new concept through atomic simulations. We first investigate the inherent properties of various Al and Cu tilt grain boundaries about dislocation source hardening at grain boundaries by grain boundary transformation using bicrystal models with different grain sizes and then consider the effect of the new concept of GB-TRIP on ductility of nanostructured materials by performing tensile loading tests of multilayered nanopillarspecimens. Similar to the Lüders band propagation, plastic deformation clearly propagatesalong the specimen due to GB-TRIP; hence, the new concept of GB-TRIP impacts on the defect design by the grain boundary engineering [2] to nanostructured materials.

[1] T. Shimokawa, Asymmetric ability of grain boundaries to generate dislocations under tensile or compressive loadings, Physical Review B, 82, 174122 (2010)

[2] T. Watanabe, S. Tsurekawa, The control of brittleness and development of desirable mechanical properties in polycrystalline systems by grain boundary engineering, Acta Materialia, 47, 4171 (1999)


Determination of superlattice stacking fault energies in multi-component superalloys.

V.A. Vorontsov1 and C.M.F. Rae2

1Department of Materials, Imperial College London, Prince Consort Road, South Kensington, London, United Kingdom, SW7 2BP; 2Department od Materials Science

and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge, United Kingdom, CB3 0FS

ABSTRACT

Superalloy single crystals, used in the manufacture of gas turbine blades, can accumulate a substantial amount of plastic strain in a relatively short time when subjected to conditions that favour primary creep. This presents a challenge when aero engines are operated at full power during take-off, climb to cruising altitude and thrust reversal whereby these materials are subjected to comparatively high stresses. These stresses are not sufficiently high to allow the cutting of the L12 ordered intermetallic phase precipitates by paired a/2<110> dislocations bounding antiphase boundaries, as is observed during macroscopic yield. Instead, the precipitates are sheared by widely extended a<112> dislocations that form low-energy superlattice stacking faults (SSFs). The susceptibility of superalloys to primary creep is strongly dependent on their composition. Understanding of the compositional effects on the SSF energies is therefore of great importance to the design of future alloys. Ab initiocalculations can provide limited insight into these effects, but are computationally expensive.In this work we employ Transmission Electron Microscopy (TEM) in conjunction with the Phase Field Model of Dislocations (PFMD) [1] to investigate the formation of SSF nodes [2]on superdislocation networks in Ni- and Co-Al-W-based superalloys. We use PFMD to evaluate the effect of stacking fault energies on the geometry of the SSF nodes and apply this insight to experimental evaluation of SSF energies from TEM imaging of the nodes in orderto investigate the compositional dependencies and influence on primary creep behaviour.

[1] V.A. Vorontsov, R.E. Voskoboinikov and C.M.F. Rae, Shearing of γ′ precipitates in Ni-base superalloys: A phase field study incorporating the effective γ-surface, Philosophical Magazine, 92, (2012), 608.

[2] G.S. Hillier, C.M.F. Rae and H.K.D.H. Bhadeshia, Extrinsic and intrinsic nodes in the gamma prime phase of a single crystal superalloy, Acta Metallurgica, 36, (1988), 95

Modeling the Bauschinger Effect and cyclic hardening in Single Crystals from Dislocation Dynamics Simulations

S. Queyreau 1 and B. Devincre 2

1 LSPM-CNRS, UPR 3407, Universite Paris XIII, 93430 Villetaneuse, France2 LEM-CNRS/ONERA, UMR104, 29 av de la Division Leclerc, 92322 Chatillon, France

[email protected]

ABSTRACT

Bauschinger Effect (B.E.) is defined from simple forward and reverse loading tests, and is manifested by the reverse flow curve exhibiting a reduced elastic limit, a well-rounded appearance of the initial plastic portion and a permanent softening with respect to the forward hardening curve. Investigation of B.E. is of particular interest for the understanding of cyclic deformation and for the modeling of kinematic hardening in crystal plasticity. Today, existing interpretations of the B.E. and cyclic hardening are dominated by phenomenological model that are based on the concepts of long-range internal stress (backstress) and/or easy glide at strain reverse induced by partial microstructure dissolution. However, such interpretations are in many regards not consistent with the B.E. observed in single crystals.

In this study, the B.E. of Ni and Cu single crystals is investigated with the help of 3D dislocation dynamics simulations. Among the different elementary features controlling the strain hardening, we show that the junction strength and the mobile dislocation mean free path are key physical parameters to understand the dislocation microstructure asymmetry upon load path changes. A new model based on the short-range properties we observed in DD simulation is proposed. This model, whose parameters are directly calculated from simulations, captures quantitatively many details of existing experiments on Baushinger and cyclic loading in single crystals.


Interaction of edge dislocations with Cu enriched precipitates in BCC Iron matrix

Xinfu He, Yankun Dou, Lixia Jia, Dongjie Wang, Shi Wu, Wen Yang

China Institute of Atomic Energy, Beijing, China

ABSTRACT

Due to a very small solubility of Copper (Cu) in body centered cubic Iron (BCC Fe), Cu enriched precipitation may take place at elevated temperatures or irradiation condition relevant for technological applications of Fe-based Cu-containing steels. Formation of Cu precipitates, in turn, results in hardening, originating from the dislocation-precipitate interaction, and dangerous loss of ductility. The hardening of copper enriched precipitates(including other elements such as Ni, Mn) is the major factor of embrittlement of reactor pressure vessels. The interaction between Cu enriched precipitates (with size of 1~6nm) and an edge dislocation in BCC Fe was investigated in this study using atomistic computer simulations in a wide temperature range. The atomic structures of Cu enriched precipitates were obtained by Metropolis Monte Carlo (MMC) method. We found that the critical resolved shear stress (CRSS) for the dislocation unpinning increases with increasing a precipitate size, and is strongly depended on the precipitate structure and ambient temperature.

Dislocation Mediated Plasticity in Hydrogen Charged Metals: Coupled Non-Linear Finite Element and Discrete Dislocation Dynamics Simulations

Authors: Zahra Molaeinia and Jaafar A. El-Awady1

Affiliations: Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA; 1email: [email protected]

ABSTRACT

For decades, it has been presumed that for metals in high-pressure hydrogen (H) environments, intergranular fracture is mainly driven by hydrogen-enhanced decohesion (HEDE) at the grain boundary (GB) with limited role of dislocation plasticity. However, recent experimental observations show a very dense dislocation microstructure forming underneath the intergranular fractured surface to depths of several micrometers in Ni and Fe. These findings suggest the need for a critical assessment of the effect of H on the collective behavior of dislocations, which is hard to identify through direct experiments. To address this, here we present a new framework in which a non-linear finite element method (FEM) is coupled with two-dimensional (2D) dislocation dynamics (DD) to model collectively H-diffusion, dislocation-H interactions, and dislocation microstructure evolution under plain strain conditions. The H-local concentration in the crystal at any time step is computed by solving the stress-dependent diffusion equations in the FEM continuum filed. In these simulations both the stress relaxation associated with the hydrogen induced volume and the elastic moduli changes due to H-atoms are accounted for. The H-induced stress field on the dislocation network in the 2D DD is then computed by modeling the H concentration as a continuous distribution of dilatation lines having strengths that are proportional to the local hydrogen concentration. The first and the second order terms of the H-atom interaction energies are accounted for. The method is employed to study the effect of the initial H-concentration and the initial dislocation density on the plastic deformation of single crystal Niobium. The simulations results show that H leads to decreasing the elastic interactions between dislocations, which results in augmenting the mobility of the dislocations. In addition, H is observed to reduce the elastic modules of the host materials. These observations are discussed in view of subsequent failure at low strain levels.


Competition between Slipping, Twinning, and their Interactions on the Hardening Response of Magnesium: Temperature and Strain Rate Effects

Author: Jaafar El-Awady

Affiliations: Department of Mechanical Engineering, Johns Hopkins University,Baltimore, MD 21218, USA, e-mail: [email protected]

ABSTRACT

At present, the wide use of Mg alloys as a structural material is still challenging due to their poor room temperature formability. Owing to its hexagonal closed packed (HCP) structure and low crystal symmetry, complex deformation mechanisms, including dislocation-slip and twinning are typically reported. As a result, the mechanical behavior of Mg metals displays strong anisotropy and strong orientation dependence. In this talk we report on microscale in situ experiments to investigate the effect of temperatures in the range of 25-500 oC and strain rates in the range of 10−4 - 10−1 s−1 on the transformation of deformation mechanisms in Mg single crystals. An anomalous strain hardening response is observed and correlated to a size dependent transition from plasticity dominated by single twin propagation followed by massive dislocation slip, to twin-twin interactions dominated response, and finally the recovery of bulk like response. To further quantify this, we discuss the results from ahierarchical multiscale simulations method to investigate dislocation and twinning mediated plasticity in Mg. Molecular dynamics simulations are performed to identify the formation andslip of pyramidal dislocations, dislocation junctions, and dislocation twin boundary interactions. These information are subsequently used to develop a new implementation of a twin boundaries (TBs) into the framework of three-dimensional discrete dislocation dynamics (DDD) to simulate the collective evolution of dislocations and their interactions with TBs in Mg single and polycrystals. Through these simulations we report on the evolution of the mechanisms that dominate the deformation of Mg microcrystals. We also report on the influence of dislocation interactions with TB and the glide of TB dislocations on the evolution and propagation of TBs.

Molecular dynamics simulation of surface cyclic slip irreversibility in vacuum and in oxygen environments in fcc metals

Zhengxuan Fan1,2*, Olivier Hardouin Duparc1 , Maxime Sauzay2 and Boubakar Diawara3

1 LSI, UMR 7642 CNRS-CEA-X, École Polytechnique, 91128 Palaiseau Cedex, France2 CEA/DEN/DMN/SRMA/LC2M, CEA Saclay, 91190 Gif sur Yvette, France

3 LPCS, ENSCP-CNRS (UMR 7045), 75231 Paris Cedex 05, France* [email protected]

ABSTRACT

Fatigue is one of the major damage mechanisms of metals. It is characterized by strong environmental effects and wide lifetime dispersions which one should be able to understand and predict. The mechanical behaviour of surface steps naturally created by the glide of dislocations subjected to cyclic loading is assessed using molecular dynamics simulations in vacuum and in oxygen environments. Different face centred cubic metals: Al, Cu, Ag and Ni are analyzed. An atomistic reconstruction phenomenon is observed at these surface steps which can induce strong irreversibility and three different mechanisms of reconstruction are identified. All surface steps are intrinsically irreversible under usual fatigue laboratory loading amplitude without the arrival of opposite sign dislocations. A surface step is reversible only when an opposite sign dislocation subsequently glides on a nearby atomic plane. Steps created by opposite sign dislocation glides on non neighbouring planes are irreversible. The irreversibility cumulates cycle by cycle and a micro-notch is produced whichdepth increases cycle by cycle. Simulations with ambient oxygen show that it does not lead to higher irreversibility as they have no major influence on the different mechanisms linked to surface relief evolution. A rough estimation of surface irreversibility is carried out for pure edge dislocations in persistent slip bands in wavy materials. This gives an irreversibility fraction between 0.5 and 0.75 in copper. An analysis coupling surface mechanisms with the classical bulk slip irreversibility model proposed by Differt, Essmann and Mughrabi in 1986 and applied to pure screw dislocations gives an irreversibility fraction of 0.62 in copper. Similar estimations in nickel give irreversibility fractions around 0.6 and 0.8 for pure edge and screw dislocations respectively [1]. These values are in agreement with recent atomic force microscopy measurements.

[1] Z. Fan et al. Acta Materialia, 102, 149 (2016)


Dislocation Transmutation through twin interfaces in hexagonal close-packed materials

Christopher D Barrett1,2, Haitham El Kadiri1,2

1Department of Mechanical Engineering, Mississippi State University, 120 Hardy St, Mississippi State, MS, 39672; 2Center for Advanced Vehicular System, Mississippi State

University, 200 Research Blvd, Mississippi State, MS, 39762.

ABSTRACT

Dislocation transmutation is a prominent feature of plasticity in hexagonal close-packed metals. As twinning also plays a major role in deformation of these materials, transmutation at twin interfaces is particularly prevalent. Thus, to appropriately handle interactions of interfaces and dislocations in crystal plasticity and higher scales, a rigorous understanding of transmutation behavior must be captured at a discrete scale. It has recently been demonstrated that {1012} twins can completely absorb basal dislocations, actually enhancing the boundary mobility and underscoring the importance of these mechanisms. Here we demonstrate, usinginterfacial defect theory and molecular dynamics, a novel method by which transmutation mechanisms may be generally classified and predicted including the effects of applied loading and how mobile the resulting products will be. It is shown that mobile transmutation of dislocations through twin boundaries is far more prevalent than has been previously supposed, and many of these reactions enhance twin mobility. Molecular dynamics and transmission electron microscopy provide validation of the method predictions.

Kink pair production and dislocation motion

S.P. Fitzgerald1

1Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, [email protected]

ABSTRACT

The motion of extended defects called dislocations controls the mechanical properties of crystalline materials such as strength and ductility. Under moderate applied loads, this motion proceeds via the thermal nucleation of kink pairs [1]. The nucleation rate is known to be a highly nonlinear function of the applied load (up to the fortieth power! [2]), and its calculation has long been a theoretical challenge. In this talk, a stochastic path integral approach is used to derive a simple, general, and exact formula for the rate. The predictions are in excellent agreement with experimental [3] and computational [4] investigations, and unambiguously explain the origin of the observed extreme nonlinearity. A simple analytical formula relating force and velocity, suitable for implementation in discrete dislocation dynamics simulations, is provided. The results can also be applied to other systems modelled by an elastic string interacting with a periodic potential, such as Josephson junctions in superconductors.

[1] Hirth, JP and Lothe, J, “Theory of dislocations”, John Wiley & Sons (1982)[2] Altshuler, TL and Christian, “The mechanical properties of pure iron tested in

compression over the temperature range 2 to 293 degrees K”, Phil. Trans. Roy. Soc. London A 261 253—287 (1967)

[3] APL Turner and T Vreeland Jr., “The effect of stress and temperature on the velocity of dislocations in pure iron monocrystals”, Acta Met, 18 1225—1235 (1970)

[4] Gilbert, MR and Queyreau, S and Marian, J, “Stress and temperature dependence of screw dislocation mobility in α-Fe by molecular dynamics”, Phys. Rev. B 84, 174103 (2011)



Author: Stefanos Papanikolaou

Affiliation: Department of Mechanical Engineering, Hopkins Extreme Materials Institute, The Johns Hopkins University, 3400 N Charles St, Baltimore, MD, 21218, USA

Email: [email protected]

ABSTRACT

The experimental stress-strain curves, obtained from uniaxial compression tests on crystalline nanopillars, display two features that are distinctly different from bulk behavior: the yield strength is size dependent and plastic deformation comes with strain bursts or stress drops (depending on loading conditions). The increase in strength with decreasing pillar size has been attributed to unconventional mechanisms such as single-arm sources and dislocation nucleation from the surface. [1] The other side of the coin --stochastic plastic slip-- is largely unexplored, but it has been shown to display strong strain-rate sensitivity [2]. The phenomenon appears reminiscent of avalanches [3] in granular piles, but available theories are almost exclusively focused on continuum frameworks. Since continuum theories fail to describe size dependent behavior in compression, the link between size dependence and intermittent plasticity has remained elusive. In this talk, I will present a realistic but minimal discrete dislocation plasticity model [4] for the elasto-plastic deformation of nanopillars that is consistent with the main experimental observations of nanopillar compression experiments, not only for strengthening but also for the main statistical features of plastic events. The implications of this model for the uniaxial compression of bulk crystals will be discussed.

[1] M. D. Uchic, P. A. Shade, D. M. Dimiduk, Plasticity of micrometer-scale single crystals in compression, Annu. Rev. Mater. Sci. 39 (2009) p.361.

[2] S. Papanikolaou, D. M. Dimiduk, W. Choi, J. P. Sethna, M. D. Uchic, C. F. Woodward, S. Zapperi, Quasi-periodic events in crystal plasticity and the self-organized avalanche oscillator, Nature 490 (2012) p.517.

[3] S. Papanikolaou, F. Bohn, G. Durin, R. L. Sommer, S. Zapperi, and J. P. Sethna, Universality beyond power laws and the average avalanche shape, Nature physics 7, (2011) p.316.

[4] S. Papanikolaou, H. Song, E. Van der Giessen, Strengthening and plastic events in crystals: The role of dislocation surface sources, arxiv:1511.04613, (under review Nature Commun.)

We would like to acknowledge financial support from the NWO through a VIDI Grant(NWO) as well as the DOE-BES Mechanical Behavior and Irradiation Effects program.

Thermodynamically Consistent Continuum Dislocation Dynamics

Thomas Hochrainer1,2, Alireza Ebrahimi1

1BIME, University of Bremen, IW3, Am Biologischen Garten 2, 28359 Bremen, Germany;

2MAPEX Center for Materials and Processes, University of Bremen, Bremen, Germany.

ABSTRACT

Dislocation based modeling of plasticity is one of the central challenges at the crossover ofmaterials science and continuum mechanics. Developing a continuum theory of dislocationsrequires the solution of two long standing problems: (i) to represent dislocation kinematics in terms of a reasonable number of variables and (ii) to derive averaged descriptions of thedislocation dynamics (i.e. material laws) in terms of these variables. The kinematic problem(i) was recently solved through the introduction of continuum dislocation dynamics (CDD) based on dislocation alignment tensors [1]. A free energy formulation may be used to solve the dynamic closure problem (ii) in CDD. For the lowest order CDD variant for curved dislocations in a single slip situation a thermodynamically consistent average dislocation velocity is found to comprise five mesoscopic shear stress contributions [2]; among these aback-stress term and a line-tension term, both of which have already been postulated for CDD. A new stress contribution occurs which is missing in earlier CDD models including the statistical continuum theory of straight parallel edge dislocations by Groma and co-workers [3]. Two further stress contributions arise from the curvature of dislocations. Results obtained from employing the resulting crystal plasticity theory as materials subroutine in the finite element program ABAQUS are used to analyze the effects from the mesoscopic shear stress contributions on the plastic response in small scale testing. Discrete dislocation simulations serve as benchmark to assess the importance of the observed effects.

[1] T. Hochrainer, Multipole expansion of continuum dislocation dynamics in terms of alignment tensors, Philos. Mag., 95(12), 1321 (2015)

[2] T. Hochrainer, Thermodynamically consistent continuum dislocation dynamics, J. Mech. Phys. Solids, accepted for publication (2016)

[3] I. Groma, F.F. Csikor, M. Zaiser, Spatial correlations and higher-order gradient terms in a continuum description of dislocation dynamics, Acta Mater. 51, 1271 (2003)

The authors gratefully acknowledge funding by the German Science Foundation DFG under project HO 4227/3-1 and the DFG Research Unit ‘Dislocation based plasticity’ FOR 1650 under project HO 4227/5-1.



Author: Stefanos Papanikolaou

Affiliation: Department of Mechanical Engineering, Hopkins Extreme Materials Institute, The Johns Hopkins University, 3400 N Charles St, Baltimore, MD, 21218, USA


ABSTRACT

The experimental stress-strain curves, obtained from uniaxial compression tests on crystalline nanopillars, display two features that are distinctly different from bulk behavior: the yield strength is size dependent and plastic deformation comes with strain bursts or stress drops (depending on loading conditions). The increase in strength with decreasing pillar size has been attributed to unconventional mechanisms such as single-arm sources and dislocation nucleation from the surface. [1] The other side of the coin --stochastic plastic slip-- is largely unexplored, but it has been shown to display strong strain-rate sensitivity [2]. The phenomenon appears reminiscent of avalanches [3] in granular piles, but available theories are almost exclusively focused on continuum frameworks. Since continuum theories fail to describe size dependent behavior in compression, the link between size dependence and intermittent plasticity has remained elusive. In this talk, I will present a realistic but minimal discrete dislocation plasticity model [4] for the elasto-plastic deformation of nanopillars that is consistent with the main experimental observations of nanopillar compression experiments, not only for strengthening but also for the main statistical features of plastic events. The implications of this model for the uniaxial compression of bulk crystals will be discussed.

[1] M. D. Uchic, P. A. Shade, D. M. Dimiduk, Plasticity of micrometer-scale single crystals in compression, Annu. Rev. Mater. Sci. 39 (2009) p.361.

[2] S. Papanikolaou, D. M. Dimiduk, W. Choi, J. P. Sethna, M. D. Uchic, C. F. Woodward, S. Zapperi, Quasi-periodic events in crystal plasticity and the self-organized avalanche oscillator, Nature 490 (2012) p.517.

[3] S. Papanikolaou, F. Bohn, G. Durin, R. L. Sommer, S. Zapperi, and J. P. Sethna, Universality beyond power laws and the average avalanche shape, Nature physics 7, (2011) p.316.

[4] S. Papanikolaou, H. Song, E. Van der Giessen, Strengthening and plastic events in crystals: The role of dislocation surface sources, arxiv:1511.04613, (under review Nature Commun.)

We would like to acknowledge financial support from the NWO through a VIDI Grant(NWO) as well as the DOE-BES Mechanical Behavior and Irradiation Effects program.

Thermodynamically Consistent Continuum Dislocation Dynamics

Thomas Hochrainer1,2, Alireza Ebrahimi1


2MAPEX Center for Materials and Processes, University of Bremen, Bremen, Germany.

ABSTRACT

Dislocation based modeling of plasticity is one of the central challenges at the crossover ofmaterials science and continuum mechanics. Developing a continuum theory of dislocationsrequires the solution of two long standing problems: (i) to represent dislocation kinematics in terms of a reasonable number of variables and (ii) to derive averaged descriptions of thedislocation dynamics (i.e. material laws) in terms of these variables. The kinematic problem(i) was recently solved through the introduction of continuum dislocation dynamics (CDD) based on dislocation alignment tensors [1]. A free energy formulation may be used to solve the dynamic closure problem (ii) in CDD. For the lowest order CDD variant for curved dislocations in a single slip situation a thermodynamically consistent average dislocation velocity is found to comprise five mesoscopic shear stress contributions [2]; among these aback-stress term and a line-tension term, both of which have already been postulated for CDD. A new stress contribution occurs which is missing in earlier CDD models including the statistical continuum theory of straight parallel edge dislocations by Groma and co-workers [3]. Two further stress contributions arise from the curvature of dislocations. Results obtained from employing the resulting crystal plasticity theory as materials subroutine in the finite element program ABAQUS are used to analyze the effects from the mesoscopic shear stress contributions on the plastic response in small scale testing. Discrete dislocation simulations serve as benchmark to assess the importance of the observed effects.

[1] T. Hochrainer, Multipole expansion of continuum dislocation dynamics in terms of alignment tensors, Philos. Mag., 95(12), 1321 (2015)

[2] T. Hochrainer, Thermodynamically consistent continuum dislocation dynamics, J. Mech. Phys. Solids, accepted for publication (2016)

[3] I. Groma, F.F. Csikor, M. Zaiser, Spatial correlations and higher-order gradient terms in a continuum description of dislocation dynamics, Acta Mater. 51, 1271 (2003)

The authors gratefully acknowledge funding by the German Science Foundation DFG under project HO 4227/3-1 and the DFG Research Unit ‘Dislocation based plasticity’ FOR 1650 under project HO 4227/5-1.


Continuum Dislocation Dynamics Simulations of Micro-Scale Plasticity

Alireza Ebrahimi1, Thomas Hochrainer1,2


2MAPEX Center for Materials and Processes, University of Bremen, Bremen, Germany

ABSTRACT

Continuum Dislocation Dynamics (CDD) [1] provides flux-type evolution equations of dislocation variables which can capture the kinematics of moving curved dislocations. The lowest order closure of CDD is based on only three internal variables per slip system. The evolution equations of dislocation variables are closed with the definition of the dislocation velocity which is defined to be dependent on the resolved shear stress and mesoscopic stress contributions. The plastic slip rate is connected to the total dislocation flux via Orowan's law, and therefore CDD defines a dislocation density based material law for crystal plasticity.

In the current contribution we present an implementation of CDD as a materials subroutine (UMAT) for ABAQUS, using the crystal plasticity framework DAMASK [2]. We provide simulations of bending of micro-beams and torsion of micro-pillars in multiple slip orientations which are compared to discrete dislocation dynamics (DDD) simulations [3]. The size-effects in micro-testing are obtained from CDD in close correspondence to DDD simulations. Furthermore, details of the dislocation microstructure and the distribution of accumulated plastic slip from CDD show unique features of DDD simulations, such asdislocation pile-ups in the center of the beam, reduced plasticity towards the free surface, and a missing elastic core.

[1] T. Hochrainer, S. Sandfeld, M. Zaiser, P. Gumbsch (2014). Continuum dislocation dynamics: Towards a physical theory of crystal plasticity, J. Mech. Phys. Solids, 63, 167-178

[2] F. Roters, P. Eisenlohr, C. Kords, D.D. Tjahjanto, M. Diehl, D. Raabe (2012). IUTAM Symposium on Linking Scales in Computations, Procedia IUTAM 3 , 3-10

[3] C. Motz, D. Weygand, J. Senger, P. Gumbsch (2008). , Acta Materialia, 56, 1942–1955

The authors gratefully acknowledges funding by the German Science Foundation DFG under project HO 4227/3-1 and the DFG Research Unit ‘Dislocation based plasticity’ FOR 1650 under project HO 4227/5-1

Mapping Dislocations In Diamond CrystalsUsing Dark-Field X-ray Microscopy With 200 nm Resolution

Anders C. Jakobsen1, Hugh Simons1, Wolfgang Pantleon2, Jürgen Härtwick3, Carsten Detlef3, Henning F. Poulsen1

1NEXMAP, DTU Fysik, Technical University of Denmark, Fysikvej 1, 2800 Kgs. Lyngby, Denmark; 2DTU Mekanik, Technical University of Denmark,

Produktionstorvet 425, 2800 Kgs. Lyngby, Denmark; 3ESRF, 71 avenue des Martyrs, Grenoble 38000, France

[email protected]

ABSTRACT

We present the case of using dark field x-ray microscopy to map dislocations in 3D. With an angular resolution of ~ 5 μrad and a spatial resolution currently below 200 nm, the dark field x-ray microscope can zoom in on an ensemble of embedded dislocations and provide spatialmaps with a time resolution of order minutes. Furthermore, components of the elastic strain and rotation field around the dislocations can be mapped and the Burgers vectors revealed.Effects of dynamical scattering are overcome by full field imaging and novel contrast methods. First results from a 17 keV study at the European Synchrotron Radiation Facility of dislocations within a 400 μm thick diamond sample will be presented and potential applications outlined.


Mechanical behaviors of ferritic/martensitic steels after irradiation under a mixed spectrum of high energy proton and

spallation neutron

Yong Dai, Kun Wang, Min Xia, Peter Derlet, Maximo Victoria

Paul Scherrer Institute, 5232 Villigen PSI, Switzerland

ABSTRACT

Various ferritic/martensitic (FM) steels investigated in the fusion reactor materials program have been irradiated in a wide dose range of 5-20 dpa (displacement per atom) at temperatures up to 450 °C under a spectrum of high energy proton and spallation neutron in the Swiss Spallation Neutron Source. Due to spallation reactions induced by high energy (570 MeV)protons, helium and hydrogen are produced at high rates of 70-90 appm / dpa and 300-400 appm / dpa, respectively.

The results of mechanical test demonstrate strong hardening and embrittlement effects on the FM steels induced by the irradiation, which are much more pronounced as compared to fission neutron irradiations when dose is above ~10 dpa [1, 2]. The hardening and embrittlement effects should be mainly attributed to the high-density defect clusters, dislocation loops and helium bubbles produced by irradiation, while the role of hydrogen and irradiation-induced precipitates is not clear. The irradiated FM steels may fail in differentfracture modes: ductile, quasi-cleavage and intergranular, which depend essentially on parameters such as irradiation dose, helium concentration, irradiation temperature, test temperature etc. The deformation mechanisms behind different fracture modes have beeninvestigated by conducting TEM observation on samples extracted from various regions, particularly directly on fracture surfaces of tensile tested specimens using the FIB technique. The results reveal that in quasi-cleavage fractured specimens defect-free dislocation channels are formed, while in ductile fractured specimens they are hardly detected. In specimens failed in intergranular fracture mode, or occasionally, in specimens with cleavage fracture mode,deformation twins have been widely observed. The formation of twins is preceded by a phase transformation mechanism, rather than by dislocation motion. The intergranular fracture could be attributed to a combined effect of strong hardening in matrix, contributed by both defect clusters and high-density small helium bubbles, and grain-boundary softening, by helium.

[1] Yong Dai, Werner Wagner, Materials researches at the Paul Scherrer Institute for developing high power spallation targets, Journal of Nuclear Materials, 389, (2009) 288.

[2] Y. Dai, G. R. Odette and T. Yamamoto, Chapter 1.06: The Effects of Helium in Irradiated Structural Alloys, in “Comprehensive Nuclear Materials”, ed. by R.J.M. Konings, Elsevier Ltd (2012)

Strength of Fe Single-Crystalline Nanoparticles under Compression

Roman Kositski1, Oleg Kovalenko2, Seok-Woo Lee3, Julia R. Greer4, Eugen Rabkin2 and Dan Mordehai1

[email protected]

1 Department of Mechanical Engineering, Technion – Israel Institute of Technology, 32000, Haifa, Israel

2 Department of Materials Science and Engineering, Technion – Israel Institute of Technology, 32000, Haifa, Israel

3 Department of Materials Science and Engineering & Institute of Materials Science, University of Connecticut, CT, United States

4 Division of Engineering and Applied Science, California Institute of Technology Pasadena, CA 91125, United States

ABSTRACT

In this work, Fe pristine single crystalline nanoparticles, formed by solid state dewetting on a hard sapphire substrate [1], are employed to study nucleation-controlled plasticity [2]. It was found experimentally that under compression, nanoparticles deforms continuously up to compressive stresses in the GPa regime, followed by a limited strain burst. We usedmolecular dynamic (MD) simulations to gain insight on the mechanisms governing the deformation on the atomic level. During compression, we identified nucleation of ½<111>{110} dislocations at the top vertices of the nanoparticle and their glide towards the bottom of the nanoparticle, until being arrested by the rigid substrate. Compressing further,more dislocations nucleate on at the same nucleation sites, gliding on close parallel slip planes. As a result, two independent pile-ups form inside the particle. The deformation during the pile-up formation is continuous, and we propose that the continuous deformation in the experiments is pseudo-elastic, with an apparent reduced effective elastic modulus. The strain burst observed in the stress-strain curves is attributed to the break-down of the pile-up, and we consider this stress as the apparent yielding point, at which the deformation is irreversible. We studied the effect of size on the strength of the particles by varying the nanoparticle dimensions and lateral proportions. As the size of the particle increases, the strength of the nanoparticle decreases and the apparent yield stress obeys a power law with size. We suggest that the size effect is controlled by two competing mechanisms, the effect of size on the stress needed to nucleate new dislocations and the number of dislocations the particle can accommodate in each pile-up.

[1] O. Kovalenko, J. R. Greer, E. Rabkin. "Solid-state dewetting of thin iron films on sapphire substrates controlled by grain boundary diffusion." Acta Materialia 61.9 (2013)

[2] R. Kositski, D. Mordehai. "Depinning-controlled plastic deformation during nanoindentation of BCC iron thin films and nanoparticles." Acta Materialia 90 (2015)

This work was supported by the Israel Science Foundation, Grant No. 1656/12, and by the US-Israel Binational Science Foundation, Grant No. 2010148.


Nanoindentation of Thin-Films and Nanoparticles

Roy Shyamal, Roman Kositski, Dan Mordehai

Department of Materials Engineering, Technion—Israel Institute of Technology, 32000 Haifa, Israel

ABSTRACT

Metallic materials can drastically change mechanical properties when their size and shape is reduced to the nanoscale. One of the most common techniques to study mechanical properties at the nanoscale is nanoindentation. In this talk we examine how the size and shape of defect-free nanoparticles affect the mechanical response to nanoindentation. Experiments on Au nanoparticles showed that they become easier to indent as they are smaller, but thin-films of the same height are much harder to indent [1]. With large scale Molecular Dynamics (MD) simulations, we show how the lateral dimensions of FCC specimens give rise to size effect in indentation through the competition between dislocation accumulation beneath the indent and depletion on free surfaces. In particular, the lack of lateral dimensions (thin-films) promotes a dense dislocation network in the plastic zone beneath the indent. We examine the importance of dislocation mechanisms, such as nucleation and cross-slip, on the indentation force and the effect of size. In addition, we studied nanoindentation of α-Fe (BCC lattice structure) thin-films and nanoparticles in MD simulations [2]. In contrast to FCC metals, the effect of size was reduced substantially. We show that dislocations are strongly pinned to the indent and that the strength of these specimens is controlled by their depinning. The dislocation depinning mechanism poorly depends on the size or dimensionality of the specimens.

[1] D. Mordehai, M. Kazakevich, D.J. Srolovitz, E. Rabkin, Nanoindentation size effect in single-crystal nanoparticles and thin films: A comparative experimental and simulation study, Acta Materialia, 59, 2309 (2011).

[2] R. Kositski, D. Mordehai, Depinning-controlled plastic deformation during nanoindentation of BCC iron thin films and nanoparticles, Acta Materialia, 90, 370(2015).

This work was supported by the Israel Science Foundation, Grant No. 1656/12


Alon Malka-Markovitz, Dan Mordehai


ABSTRACT

Cross-slip is a dislocation mechanism by which screw dislocations can change their glide plane. This thermally activated mechanism is an important mechanism in plasticity and understanding the activation barrier for cross-slip in a general stress condition is essential to construct reliable cross-slip rules in dislocation models. In this work we developed a line-tension model for cross-slip of stressed screw dislocations in FCC metals. Different descriptions of the elastic field around the partial dislocation are examined. The dislocation dissociation widths in the primary and cross-slip planes during cross-slip are calculated and the results are compared with atomistic simulations of the minimum energy path for cross-slip. The comparison between the line-tension and the atomistic models allows us to quantify rules for the activation barrier for cross-slip in a general stress field and to relate it to materials properties. We discuss how the stress-dependent activation barriers for cross-slip can be incorporated in dislocation dynamics, in order to simulate cross-slip of screw dislocation in complex dislocation structures.


Nanoindentation of Thin-Films and Nanoparticles

Roy Shyamal, Roman Kositski, Dan Mordehai


ABSTRACT

Metallic materials can drastically change mechanical properties when their size and shape is reduced to the nanoscale. One of the most common techniques to study mechanical properties at the nanoscale is nanoindentation. In this talk we examine how the size and shape of defect-free nanoparticles affect the mechanical response to nanoindentation. Experiments on Au nanoparticles showed that they become easier to indent as they are smaller, but thin-films of the same height are much harder to indent [1]. With large scale Molecular Dynamics (MD) simulations, we show how the lateral dimensions of FCC specimens give rise to size effect in indentation through the competition between dislocation accumulation beneath the indent and depletion on free surfaces. In particular, the lack of lateral dimensions (thin-films) promotes a dense dislocation network in the plastic zone beneath the indent. We examine the importance of dislocation mechanisms, such as nucleation and cross-slip, on the indentation force and the effect of size. In addition, we studied nanoindentation of α-Fe (BCC lattice structure) thin-films and nanoparticles in MD simulations [2]. In contrast to FCC metals, the effect of size was reduced substantially. We show that dislocations are strongly pinned to the indent and that the strength of these specimens is controlled by their depinning. The dislocation depinning mechanism poorly depends on the size or dimensionality of the specimens.

[1] D. Mordehai, M. Kazakevich, D.J. Srolovitz, E. Rabkin, Nanoindentation size effect in single-crystal nanoparticles and thin films: A comparative experimental and simulation study, Acta Materialia, 59, 2309 (2011).

[2] R. Kositski, D. Mordehai, Depinning-controlled plastic deformation during nanoindentation of BCC iron thin films and nanoparticles, Acta Materialia, 90, 370(2015).

This work was supported by the Israel Science Foundation, Grant No. 1656/12


Alon Malka-Markovitz, Dan Mordehai


ABSTRACT

Cross-slip is a dislocation mechanism by which screw dislocations can change their glide plane. This thermally activated mechanism is an important mechanism in plasticity and understanding the activation barrier for cross-slip in a general stress condition is essential to construct reliable cross-slip rules in dislocation models. In this work we developed a line-tension model for cross-slip of stressed screw dislocations in FCC metals. Different descriptions of the elastic field around the partial dislocation are examined. The dislocation dissociation widths in the primary and cross-slip planes during cross-slip are calculated and the results are compared with atomistic simulations of the minimum energy path for cross-slip. The comparison between the line-tension and the atomistic models allows us to quantify rules for the activation barrier for cross-slip in a general stress field and to relate it to materials properties. We discuss how the stress-dependent activation barriers for cross-slip can be incorporated in dislocation dynamics, in order to simulate cross-slip of screw dislocation in complex dislocation structures.


Analyses of Creep using High-Temperature Discrete Dislocation Plasticity

Chris A. Greer1, Shyam M. Keralavarma2, A. Amine Benzerga1,3

1Department of Aerospace Engineering, Texas A&M University, 77843 TX2Department of Aerospace Engineering, IIT Madras, Chennai, India

3Department of Materials Science & Engineering, Texas A&M University, 77843 TX

ABSTRACT

A framework for solving problems of dislocation-mediated plasticity coupled with point-defect diffusion is presented [1]. Plastic flow arises due to the collective motion of a large number of discrete dislocations. Both glide and diffusion-mediated climb motions are accounted for. Time scale separation is contingent upon the existence of quasi-equilibrium dislocation configurations. A variational principle is used to derive the coupled governing equations for point-defect diffusion and dislocation climb. Superposition is used to obtain the mechanical fields in terms of the infinite-medium discrete dislocation fields and an image field that enforces the boundary conditions while the point-defect concentration is obtained by solving the stress-dependent diffusion equations on the same finite-element grid. Core-level boundary conditions for the concentration field are avoided by invoking an approximate, yet robust kinetic law [2]. Aspects of the formulation are general but its implementation in a simple plane strain model enables the modeling of high-temperature phenomena such as creep[3], recovery and relaxation. Simulations depict transitions from diffusional to power-law creep, in keeping with long-standing phenomenological theories of creep.

[1] S.M. Keralavarma, A.A. Benzerga, High-temperature discrete dislocation plasticity,Journal of the Mechanics and Physics of Solids, 82, 1-22 (2015)

[2] D. Mordehai, E. Clouet, M. Fivel, M. Verdier, Introducing dislocation climb by bulk diffusion in discrete dislocation dynamics, The Philosophical Magazine, 88, 899-926(2008)

[3] S.M. Keralavarma, T. Cagin, A. Arsenlis, A.A. Benzerga, Power-law creep from discrete dislocation dynamics, Physical Review Letters, 109, 265504 (2012)

Support from the Lawrence Livermore National Security, LLC under Master Task Agreements No. B599687 and B602391, LLNL under Contract DE-AC52-07NA27344 is acknowledged. CAG and AAB also acknowledge support from the Texas Institute for Advanced Studies (TIAS) and the NSF IMI grant DMR-0844082 through the International Institute for Multifunctional Materials for Energy Conversion at Texas A&M University.

Effects of taper on micropillar compression: A discrete dislocation simulation

Authors: Babak Kondori1, A. Needleman1, A. Amine Benzerga1,2

Affiliations: 1 Department of Materials Science & Engineering, Texas A&M University, College Station, TX, 77843-3003

2 Department of Aerospace Engineering, Texas A&M University, College Station, TX,77843-3141

Corresponding Author: Babak Kondori, [email protected]

ABSTRACT

Two dimensional discrete dislocation simulations, enhanced by a set of physically based rules to mimic three dimensional processes of dislocation activity, are used to investigate the effects of taper on micropillar plasticity in the high dislocation density regime. Pillars with material properties of Al and a height to diameter ratio of 3 are loaded in compression. The mechanical response of the compressed pillars with mid-height diameters of D = 0.4, 0.8, 1.6, 3.2 μm and taper angles of 0 and 5 degrees are studied. The flow strengths of the pillars showa strong size dependence, regardless of their taper angle. However, in an average sense, the size effect is more prominent in the pillars with larger taper angles. It is also observed that the size effect becomes more pronounced as deformation proceeds. The study of the local arrangement of dislocations and their Burgers vectors indicates that the build-up of effective GND density, with the associated development of local strain gradients, is one of the origins of the size effect in pillars. Higher average effective GND densities in tapered pillars compared with their untapered counterparts rationalizes the typically higher flow strength of tapered specimens. For the smallest pillars, the stochastic nature of the deformation response is enhanced as the taper angle is increased. Limited available dislocation sources, the dependence of flow strength on the activation stress and the location of sources in the tip region of small pillars are identified as the sources of the observed scatter in flow strength.

Support from the Texas Institute for Advanced Studies (TIAS) at Texas A&M University is gratefully acknowledged.


Simulations of orientation dependence of strain-hardening, strain-burst characteristics and dislocation microstructure evolution in

20, 6µm size Ni microcrystals

S.I. Rao*,@, D.M. Dimiduk, A.Hussein#, J.A. El-Awady#,T.A. Parthasarathy*, M.D. Uchic, A.Mortensen@,

C. Woodward and W.A. Curtin@

Air Force Research Laboratory, Materials and Manufacturing Directorate, AFRL/MLLM Wright-Patterson AFB, OH 45433-7817

*UES, Inc., 4401 Dayton-Xenia Rd, Dayton, OH 45432-1894

#Johns Hopkins University, Baltimore, MD

@ Institute of Mechanical Engineering, EPFL, Lausanne, Switzerland

[email protected]

ABSTRACT

3D dislocation dynamics simulations are used to investigate strain-hardening characteristics, dislocation microstructure evolution with strain, and strain-burst characteristics in large 20, 6µm size Ni microcrystals under three different loading axes: 111, 001 and 110. Previous atomistic simulation results are used to implement three different mechanisms of cross-slip in the dislocation dynamics code: intersection, surface and bulk (at jogs) cross slip. The microcrystals are initially populated randomly with Frank-Read sources, 20 or 6µm in size, having initial dislocation densities of ~5 X 1011/m2

using free-surface boundary conditions. Three different loading axes, <111>, <001> and <110>, are explored for shear strains of ~0.05 and final dislocation densities of ~ 1013/m2.The orientation dependence of initial strain hardening rates and dislocation microstructure evolution with strain are discussed. The effect of cross-slip on dislocation microstructure evolution and strain-burst characteristics is also discussed. A mechanism for dislocation microstructure evolution as a function of orientation of deformation in fcc single crystals is suggested. The simulated strain hardening and dislocation microstructure evolution results are compared with experimental data under similar loading conditions from bulk single-crystal Ni,Cu.

Strain Hardening in Multilayered Thin Films

Jian Wang1, Amit Misra2,

1University of Nebraska-Lincoln, Department of Mechanical and Materials Engineering;

2University of Michigan, Ann Arbor, Department of Materials Science & Engineering;<[email protected]>.

ABSTRACT

Experimental results indicate that multilayered thin films have unusual properties such as high strength, measurable plasticity and high strain hardening rate when both layers are nanoscale.Furthermore, the strength and strain hardening rate show a pronounced size effect, depending not only on the layer thickness but also on the layer thickness ratio. We analyze the strain hardening behavior of nanoscale multilayers using a three-dimensional crystal elastic–plastic model that describes plastic deformation based on the evolution of dislocation density in metal and ceramic layers according to confined layer slip mechanism. These glide dislocations nucleate at interfaces, glide inside layers and are deposited at interfaces that impede slip transmission. The high strain hardening rate is ascribed to the closely spaced dislocation arrays deposited at interfaces and the load transfer that is related to the layerthickness ratio of metal and ceramic layers [1]. The measurable plasticity implies the plastically deformable ceramic layer in which the dislocation activity is facilitated by the interaction force among the deposited dislocations within interface and in turn is strongly related to the layer thickness of the hard phase.

1. J. Wang; A. Misra; Strain hardening in nanolayered thin films, Current Opinion in Solid State and Materials Science. 2014;18(1):19-28.


Dislocation-based fracture within nonlocal anisotropic elasticity

Mahmoud Mousavi1, Alexander M. Korsunsky2

Department of Civil and Structural Engineering, Box 12100, Aalto University, FI-00076Aalto, Finland1

Multi-Beam Laboratory for Engineering Microscopy, Department of Engineering Science, University of Oxford, OX1 3PJ, UK2

ABSTRACT

Dislocations are a subject of common interest in different disciplines in solid mechanics. Within fracture mechanics, crystal dislocations play a role of the fundamental object that governs the physics of plastic deformation and fracture, while they can also bemacroscopically treated within continuum mechanics as basic elementary objects involved in mathematical fracture modeling. The latter is referred to as distributed dislocation technique [1] or dislocation-based fracture mechanics. This approach is quite well-established within classical elasticity [2].Eringen's theory of nonlocal elasticity of Helmholtz type provides nonsingular stress fields for dislocation within anisotropic elasticity [3]. In this presentation, the distributed dislocation technique is applied for the analysis of anisotropic materials weakened by cracks withinEringen's theory of nonlocal elasticity. The corresponding dislocation density functions are evaluated using the proper crack-face boundary conditions. The nonlocal stress field within a plane weakened by cracks is also determined. The stress singularity of the classical linear elasticity is removed by the introduction of the nonlocal theory of elasticity. The crack opening displacement will also be discussed within this nonlocal framework. Having formulated the general anisotropic case, special case of orthotropic material will be presented.

[1] D. Hills, P. Kelly, D. Dai, A.M. Korsunsky, “Solution of crack problems: the distributeddislocation technique”, Springer (1996).

[2] J. Weertman, Dislocation based fracture mechanics, World Scientific, Singapore (1996).[3] M. Lazar, E. Agiasofitou, Screw dislocation in nonlocal anisotropic elasticity, Int. J. Eng.

Sci. 49, 1404–1414 (2011).

Annihilation, Sources and Junctions in Continuum Dislocation Dynamics

Mehran Monavari, Stefan Sandfeld and Michael Zaiser

Institute of Materials Simulation (WW8), FAU, Dr.-Mack-Str. 77 90732 Fürth [email protected]

ABSTRACT

The dynamics of dislocations as curved line like objects depends on their orientation and curvature. A full representation of dislocation orientation and curvature is given by the higher dimensional dislocation orientation distribution function (DODF). In Continuum Dislocation Dynamics (CDD) theory, the DODF is represented by a series of harmonic moments called symmetric alignment tensors. The evolution of these tensors describes the glide motion of curved dislocation lines in a density-based setting. Using DODF moments instead of the full function reduces the computational cost tremendously while it allows to capture many important features of the microstructure such as GND and SSD densities and the associated orientations and curvature. However determining the rate ofstrongly orientation dependent mechanisms such as dislocation annihilation and multiplication needs the access to DODF.In this paper we apply the ’Maximum Information Entropy Principle’ (MIEP) to reconstruct the DODF from the CDD alignment tensors. The resulting approximate DODF is used to evaluate the rates of dislocation annihilation and multiplication and thus to incorporate these processes into CDD. Later we use CDD to investigate the role of junction formation, dislocation annihilation and multiplication in view of the emergence of dislocation patterns in cyclic deformation of face-centred cubic metals.


In situ TEM investigation of deformation micro-mechanisms and dislocation mobility in titanium

Barkia B. 1,*, Couzinié J.P 1, Guillot I. 1, Doquet V. 2

1: Institut de Chimie et des Matériaux Paris-Est, UMR 7182, CNRS/UPEC, Thiais, France.

2: Laboratoire de Mécanique des Solides, UMR 7649, CNRS, École Polytechnique, Palaiseau, France.

* Corresponding author at: Grande voie de vignes, CentraleSupélec/MMSMat, Châtenay Malabry, 92290, France.

E-mail address: [email protected]

ABSTRACT

Deformation mechanisms and dislocation kinetics of two commercially pure titanium batches with different oxygen content were investigated by in situ TEM tensile tests. It has been shown that the deformation is mainly accommodated with <a> type screw dislocations glide. The movement of screw segments is jerky and consists of a succession of very quick jumps. The dislocation motion can be inhibited by the formation of intrinsic obstacles (macro-kinks). Dislocation multiplication is mainly controlled by double-cross slip mechanism. The activation of dislocations along the grain boundary and the inter-granular localized sources are the main dislocation emission mechanisms. The oxygen solutes reduce the waiting time and contract the jumping distance between two stable positions during the locking-unlocking mechanism. The presence of impurities (individual or clusters of solute atoms) causes a change in dislocation structure from uniform to banded and slow down kinks promoting the initiation of cross-kinkas proposed by Caillard et al. [1]. The latter mechanism triggers the dislocation multiplication (loop formation) by double-cross mechanism and increases the strain hardening.

[1] D. Caillard, M. Legros, A. Couret, Extrinsic obstacles and loop formation in deformed metals and alloys, Phil. Mag., 93, 203, (2013).

Deformation mechanisms of nanotwinned Al

X. Zhang, S. Xue, D. Bufford, Yue Liu, and H. Wang

School of Materials Engineering, Purdue University, West Lafayette, IN,


Abstract

Nanotwinned metals have been extensively studied as they typically exhibit high strength

and ductility. Prior studies focus on twins in metallic materials with low stacking fault energy,

such as Cu, Ag and stainless. Recent studies show that growth twins or stacking faults can also be

introduced into Al with high stacking fault energy. In this poster we present strategies to introduce

growth twins into epitaxial and nanocrystalline Al. In nanocrystalline Al, there appers to be an

optimum film thickness that promote the nucleation and growth of nanotwins. In epitaxial

nanotwinned Al, the predominant growth defects are incoherent twin boundaries. In situ

nanoindentation studies show that nanotwinned Al with high density incoherent twin boundaries

has high strength and prominent work hardening.


Dislocations and hydrogen: Nanoscale hydrides and pipe diffusion in palladium

Authors: Dallas R. Trinkle1, Emily J. Schiavone1, Brent J. Heuser2

Affiliations: 1Materials Science and Engineering, Univ. Illinois, Urbana-Champaign ([email protected]);

2 Nuclear, Plasma, and Radiological Engineering, Univ. Illinois, Urbana-Champaign

ABSTRACT

Studying the fundamental behavior of hydrogen in metals, like palladium, requires a combina-tion of computation and experimental techniques. In palladium, hydrogen occupies octahedral sites and dislocation cores, which act as nanoscale H traps—forming Cottrell atmospheres that are metal-hydride-like at low temperatures. Using a combination of first-principles meth-ods with atomic and mesoscale modeling, we can model the formation of the atmosphere and low temperature nanoscale hydrides, while in situ inelastic neutron scattering and small-angle neutron scattering measure vibrational changes and hydrides dimensions at the nanoscale [1].To understand the dynamics of hydrogen at a dislocation core, we compute the diffusion pathway below and inside a partial dislocation, and estimate changes in barriers away from the dislocation using the elastic strain [2]. We use this data for kinetic Monte Carlo studies of hydrogen pipe diffusion at different temperatures, and compare with new quasielastic neutron scattering measurements for a direct measurement of hydrogen pipe diffusion in Pd [3].

[1] D. R. Trinkle, H. Ju, B. J. Heuser, T. J. Udovic, Nanoscale-hydride formation at disloca-tions in palladium: Ab initio theory and inelastic neutron scattering measurements, Phys. Rev. B 83, 174116 (2011)

[2] E. J. Schiavone and D. R. Trinkle, Ab initio modeling of quasielastic neutron scattering of hydrogen pipe diffusion in palladium, Phys. Rev. B 94, 054114 (2016)

[3] B. J. Heuser, D. R. Trinkle, N. Jalarvo, J. Serio, E. J. Schiavone, E. Mamontov, M. Tyagi,Direct Measurement of Hydrogen Dislocation Pipe Diffusion in Deformed Polycrystalline Pd Using Quasielastic Neutron Scattering, Phys. Rev. Lett. 113, 025504 (2014)

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