a facility for simulating the dynamic response of materials · dislocation loop slip plane. michael...
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![Page 1: A facility for simulating the dynamic response of materials · dislocation loop slip plane. Michael Ortiz MRS 11/04 Dislocation field theory. Michael Ortiz MRS 11/04 General dislocations](https://reader033.vdocuments.net/reader033/viewer/2022060802/608676b6ee09145dd0662f6f/html5/thumbnails/1.jpg)
Michael OrtizPisa 09/06
Multiscale modeling of materials: (1) Dislocation structures → polycrystals
M. OrtizM. OrtizCalifornia Institute of Technology
Scuola Normale di Pisa September 15, 2006
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Michael OrtizMRS 11/04
Metal plasticity − Multiscale hierarchy
Lattice defects, EoS
Dislocation dynamics
Subgrainstructures
length
time
mmnm µm
µsns
ms
Polycrystals
Engineeringapplications
Ultimate goal: Ascertain macroscopic behavior from first principles
Continuum
Quantum mechanical
Discrete
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Michael OrtizMRS 11/04
Classical view of crystal lattices
Simple cubic(SC)
Body-centered cubic(BCC)
Face-centered cubic(FCC)
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Michael OrtizMRS 11/04
Straight dislocations: 2D view
slip plane
dislocationcore
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Michael OrtizMRS 11/04
Straight dislocations: 2D view
Burgerscircuit C
Burgersvector
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Michael OrtizMRS 11/04
Discreteness of crystallographic slip
Slip traces on crystal surface(AFM, C. Coupeau)
Slip occurs on discrete planes!
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Michael OrtizMRS 11/04
Dislocations and crystallography
The 12 slip systems of fcc crystals
(Schmidt and Boas nomenclature):
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Michael OrtizMRS 11/04
General linear elastic dislocations
elastic deformationplastic deformation
dislocation loop
slip plane
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Michael OrtizMRS 11/04
Dislocation field theory
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Michael OrtizMRS 11/04
General dislocations − Energy
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Michael OrtizMRS 11/04
Straight dislocations – Energy
Screw dipoleof size r
in square lattice,applied stress
logarithmicdivergence!
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Michael OrtizMRS 11/04
Straight dislocations – Mobility
Kink
lattice friction
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Michael OrtizMRS 11/04
Dislocation transport and plasticity
slip planes
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Michael OrtizMRS 11/04
Dislocation transport and plasticity
expandingdislocation
loop
dislocation velocity
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Michael OrtizMRS 11/04
Obstacles − Topological obstructions
(Humphreys and Hirsch ’70)Impenetrable obstacles
pinningpoints
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Michael OrtizMRS 11/04
Junctions − Strong latent hardening
LatticeOrientation
PrimaryTest Lattice
OrientationSecondary
Test
PrimaryTest
SecondaryTest
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Michael OrtizMRS 11/04
Dislocation structures - Fatigue
Labyrinth structure in fatiguedcopper single crystal(Jin and Winter ´84)
Nested bands in copper single crystalfatigued to saturation
(Ramussen and Pedersen ´80)
Dipolar dislocation walls
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Michael OrtizMRS 11/04
Dislocation lamellar structures
Dislocation walls
Lamellar dislocation structurein 90% cold-rolled Ta
(DA Hughes and N Hansen, Acta Materialia,44 (1) 1997, pp. 105-112)
Dislocation walls
Lamellar structurein shocked Ta
(MA Meyers et al., Metall. Mater. Trans.,
26 (10) 1995, pp. 2493-2501)
Lamellar dislocation structures at large strains
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Michael OrtizMRS 11/04
Dislocation structures – Pile-ups
LiF plate impact experiment.Dislocation pile-ups at surfaces
and grain boundaries(G Meir and RJ Clifton, J. Appl. Phys.,
59 (1) 1986, pp. 124-148)
Dislocationpile ups
Dislocation pile-upat Ti grain boundary
(I. Robertson)
Effect of grain boundaries, surfaces
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Michael OrtizMRS 11/04
Dislocation structures – Effect of strain
X1
x1
x2
Die Exit
Shear Plane
X2
ϕ
Die EntryEqual Channel
Angular Extrusionprocess
(Beyerlein, Lebensohnand Tome, LANL, 2003)
Route C Route A
Increasin
g d
eform
ation
Evolution of dislocation structures in Cu specimen. Lamellar width:
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Michael OrtizMRS 11/04
Dislocation structures – Scaling laws
Pure nickel cold rolled to 90%Hansen et al. Mat. Sci. Engin.
A317 (2001).
Lamellar width and misorientation angle as a function of deformatation
Hansen et al. Mat. Sci. Engin. A317 (2001).
Scaling of lamellar width and misorientation angle with deformation
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Michael OrtizMRS 11/04
Dislocation structures – Scaling laws
Classical scaling laws of crystal plasticity
Taylor scaling(SJ Basinski and ZS Basinski,
Dislocations in Solids,FRN Nabarro (ed.)
North-Holland, 1979.)
Hall-Petch scaling(NJ Petch,
J. Iron and Steel Inst.,174, 1953, pp. 25-28.)
Taylor hardening(RJ Asaro,
Adv. Appl. Mech.,23, 1983, p. 1.)