multiscale crystal plasticity modeling - micde

Multiscale crystal plasticity modeling

Dr. Veera Sundararaghavan1

1Department of Aerospace Engineering University of Michigan

Center for PRedic.ve Integrated Structural Materials Science

Materials modeling

Aerospace composite finite element models

Modeling of carbon fiber degradation

Microstructural fatigue crack growth models

Crystal plasticity

Process modeling using microstructure descriptors

Atomistic modeling of composite matrix material (epoxy)

Multiscale structural simulations laboratory, Prof Veera Sundararaghavan

3 Multiscale Structural Simulations Laboratory May 24, 2017

Real Space DFT PRISMS-‐RSDFT

Fourier Space DFT (e.g. VASP)

Atomic scale cons.tu.ve laws

Sta.s.cal Mechanics CASM

Phase Diagrams CASM/CALPHAD

Disloca.on Dynamics LLNL-‐ParaDIS

Phase Field Crystal PRISMS-‐PFC*

Phase Field PRISMS-‐PF

Crystal Plas.city PRISMS-‐Plas1city

Con.nuum Plas.city PRISMS-‐Plas1city

EXPERIMENTS(nuclea.on kine.cs, etc.)

EXPERIMENTS (slip, twinning, crack, etc.)

Mechano-‐Chemistry PRISMS-‐MC*

PRISMS Center Integrated Framework Enabling accelerated predic.ve materials science

4

Center for PRedictive Integrated Structural Materials Science

Crystal plas.city finite element

Single crystal constitutive model at element level

Equilibrium (and compatibility) across grains are enforced via Finite Element Method (FEM)

EBSD serial sec.oning

CPFE simula.ons


•  Code highlights: –  Parallel 3D crystal plas.city models

implemented over Ellip.c PDE base class –  Support for reading external microstructures

post-‐processing capabili.es (pole figures, orienta.on distribu.on func.ons, etc)

–  Demonstrates parallel performance and scaling on large-‐scale problems running on hundreds of processors.

–  Training at the PRISMS Workshop following this conference

ODF ε=0 ODF ε=-‐0.25

PRISMS CPFE

Pole Figures -‐MTex Visualiza.on -‐ Paraview

Virtual Microstructure -‐ Neper

PRISMS Center: Mg-‐RE alloys

6

Goal: To model microstructural deforma.on using CPFE and validate using grain level strain data from SEM-‐DIC

Valida.on experiments: in-‐situ strain mapping

7 Center for PRedic.ve Integrated Structural Materials Science

Quan1ta1ve local analysis of the rela1onships between microstructure and deforma1on/damage •  Approach: in-‐SEM digital image correla1on (SEM-‐DIC)

•  Full-‐field maps of deforma.on at different length scales (see Fig.) •  Slip ac.vity, twinning, strain localiza.on have been quan.ta.vely resolved during

loading

EBSD orienta.on data is mapped in PRISMS-‐CPFE, following which deforma.on fields from SEM-‐DIC and CPFE can be compared.

As received (80x80 µm) Peak aged (1000x1000 µm)


Upcoming NSF work: Modeling localiza7on using peridynamics Strain maps courtesy of the Daly lab (Alan Githens; co-‐advised by John Allison and Sam Daly).

T5 temper-‐2.91% Strain


L M

A

B

C

E

F G

H

I

K

J D

L M

A

B

C

E

F G

H

I

K

J D


Strain maps courtesy of the Daly lab (Alan Githens; co-‐advised by John Allison and Sam Daly).



A

B C

A

B C

∑↑▒𝛾↓𝑏𝑎𝑠𝑎𝑙  /∑↑▒𝛾  


Strain maps courtesy of the Daly lab (Alan Githens; co-‐advised by John Allison and Sam Daly).


T5 temper-‐ compression 4.2% Strain

LIFT-‐UTRC project: Mul.scale Modeling of Al-‐Li alloys

Crystal plas.city •  ODF •  FEM

Volume frac.ons of crystals in orienta.on space is tracked

Most efficient microstructure representa.on

Conservation principle

Solve for evolution of the ODF with deformation

Based on the Taylor hypothesis

EVOLUTION EQUATION FOR THE ODF (Eulerian)

Mul.scale modeling

Mul.scale anima.on

Multiscale Structural Simulations Laboratory

MULTISCALE INVERSE PROBLEMS

Objective: Design the initial preform such that the die cavity is fully filled and the yield strength is uniform over the external surface (shown in Figure below). Material: FCC Cu

Uniform yield strength desired on this surface

Fill cavity

Multi-objective

optimization

•  Increase Volumetric yield

• Decrease property variation

+


MULTI-SCALE DESIGN FOR OPTIMUM STRENGTH: UNOPTIMIZED

70

80

90

100

110

120

130 Large

Underfill

variation in yield strength

Yiel

d st

reng

th (

MPa

)


70

80

90

100

110

120

130 Underfill

Yiel

d st

reng

th (

MPa

)

Optimal yield strength

Optimal fill

MULTI-SCALE DESIGN FOR OPTIMUM STRENGTH: OPTIMIZED

multiscale crystal plasticity modeling - micde

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