Discrete dislocation dynamics is a numerical tool developed to model the plasticity of crystalline materials at an intermediate length scale, between the atomistic modeling and the crystal plasticity theory. In this review we show, using examples from the literature, how a discrete dislocation model can be used either in a hierarchical or a concurrent multiscale framework. In the last section of this review, we show through the uniaxial compression of microcrystal application, how a concurrent multiscale model involving a discrete dislocation framework can be used for predictive purposes.
Issue Section:
Predictive Science and Technology in Mechanics and Materials
1.
Zimmerman
, J. A.
, Gao
, H.
, and Abraham
, F. F.
, 2000, “Generalized Stacking Fault Energies for Embedded Atom FCC Metals
,” Modell. Simul. Mater. Sci. Eng.
0965-0393, 8
, pp. 103
–115
.2.
Kim
, S. -G.
, Horstemeyer
, M. F.
, Baskes
, M. I.
, Rais-Rohani
, M.
, Kim
, S.
, Jelinek
, B.
, Houze
, J.
, Moitra
, A.
, and Liyanage
, L.
, 2009, “Semi-Empirical Potential Methods for Atomistic Simulations of Metals and Their Construction Procedures
,” ASME J. Eng. Mater. Technol.
0094-4289, 131
(4
), p. 041210
.3.
Sevillano
, J. G.
, 1991, “Substructure and Strengthening of Heavily Deformed Single and Two-Phase Metallic Materials
,” J. Phys. III
1155-4320, 1
, pp. 967
–988
.4.
Horstemeyer
, M. F.
, Baskes
, M.
, and Plimpton
, S. J.
, 2001, “Length Scale and Time Scale Effects on the Plastic Flow of fcc Metals
,” Acta Mater.
1359-6454, 49
, pp. 4363
–4374
.5.
Canova
, G.
, and Kubin
, L.
, 1991, “Dislocation Microstructure and Plastic Flow: A Three Dimensional Simulation
,” Continuum Models and Discrete Systems
, Vol. 2
, G. A.
Maugin
, eds., Longman Scientific and Technical
, Harlow, UK
, pp. 93
–101
.6.
Zbib
, H. M.
, Rhee
, M.
, and Hirth
, J. P.
, 1996, “3D Simulation of Curved Dislocations: Discretization and Long Range Interactions
,” Advances in Engineering Plasticity and Its Applications
, T.
Abe
and T.
Tsuta
, eds., Pergamon
, New York
, pp. 15
–20
.7.
Zbib
, H. M.
, and Diaz de la Rubia
, T.
, 2001, “A Multiscale Model of Plasticity: Patterning and Localization
,” Material Science for the 21st Century
, Vol A
, The Society of Materials Science
, Japan
, pp. 341
–347
.8.
Rodney
, D.
, and Finel
, A.
, 2001, “Influences of Interface and Dislocation Behavior on Microstructure Evolution
,” Mater. Res. Soc. Symp. Proc.
0272-9172, 652
, pp. Y4.9.1
–6
.9.
Wang
, Y. U.
, Jin
, Y. M.
, and Khachaturyan
, A. G.
, 2003, “Phase Field Microelasticity Modeling of Dislocation Dynamics Near Free Surface and in Heteroepitaxial Thin Films
,” Acta Mater.
1359-6454, 51
, pp. 4209
–4223
.10.
Rodney
, D.
, Le Bouar
, Y.
, and Finel
, A.
, 2003, “Phase Field Methods and Dislocations
,” Acta Mater.
1359-6454, 51
, pp. 17
–30
.11.
Bronchard
, Q.
, Le Bouar
, Y.
, and Finel
, A.
, 2006, “Quantitative Phase Field Modeling of Precipitation Process
,” Adv. Eng. Mater.
1438-1656, 8
, pp. 1245
–1248
.12.
Marin
, E. B.
, and Dawson
, P. R.
, 1998, “On Modeling the Elasto-Viscoplastic Response of Metals Using Polycrystal Plasticity
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 165
, pp. 1
–21
.13.
Horstemeyer
, M. F.
, Potirniche
, G.
, and Marin
, E. B.
, 2005, “Mesoscale-Macroscale Continuum Modeling: Crystal Plasticity
,” Handbook for Materials Modeling
, S.
Yip
, ed., Springer
, Dordrecht, The Netherlands
, Chap. 3.14.
Staroselsky
, A.
, and Anand
, L.
, 2003, “A Constitutive Model for hcp Materials Deforming by Slip and Twinning: Application to Magnesium Alloy AZ31B
,” Int. J. Plast.
0749-6419, 19
, pp. 1843
–1864
.15.
Salem
, A. A.
, Kalidindi
, S. R.
, and Semiatin
, S. L.
, 2005, “Strain Hardening Due to Deformation Twinning in α-Titanium: Constitutive Relations and Crystal
,” Acta Mater.
1359-6454, 53
, pp. 3495
–3502
.16.
Groh
, S.
, Marin
, E. B.
, Horstemeyer
, M. F.
, and Zbib
, H. M.
, 2009, “Multiscale Modeling of the Plasticity in an Aluminum Single Crystal
,” Int. J. Plast.
0749-6419, 25
, pp. 1456
–1473
.17.
Bammann
, D. J.
, Chiesa
, M. L.
, and Johnson
, G. C.
, 1996, Theoretical and Applied Mechanics 1996
(Proceedings of the 19th International Congress of Theoretical and Applied Mechanics
), R.
Tatsumi
, E.
Wanabe
, and T.
Kambe
, eds., ICTAM
, Kyoto, Japan
, pp. 359
–376
.18.
Shenoy
, M.
, Tjiptowidjojo
, Y.
, and McDowell
, D.
, 2008, “Microstructure-Sensitive Modeling of Polycrystalline IN 100
,” Int. J. Plast.
0749-6419, 24
, pp. 1694
–1730
.19.
Liu
, W. K.
, Karpov
, E. G.
, Zhang
, S.
, and Park
, H. S.
, 2004, “An Introduction to Computational Nanomechanics and Materials
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 193
, pp. 1529
–1578
.20.
Curtin
, W. A.
, and Miller
, R. E.
, 2003, “Atomistic/Continuum Coupling in Computational Materials Science
,” Modell. Simul. Mater. Sci. Eng.
0965-0393, 11
, pp. R33
–R68
.21.
E
, W.
, Engquist
, B.
, Li
, X.
, Ren
, W.
, and Vanden-Eijnden
, E.
, 2004, “The Heterogeneous Multiscale Method: A Review
,” Princeton University, http://www.math.princeton.edu/multiscale/http://www.math.princeton.edu/multiscale/22.
Brown
, L.
, 1964, “The Self-Stress of Dislocations and the Shape of Extended Nodes
,” Philos. Mag.
0031-8086, 10
, pp. 441
–466
.23.
Bacon
, D.
, 1967, “A Method for Describing a Flexible Dislocation
,” Phys. Status Solidi
0031-8957, 23
, pp. 527
–538
.24.
Foreman
, A.
, 1967, “The Bowing of a Dislocation Segment
,” Philos. Mag.
0031-8086, 15
, pp. 1011
–1021
.25.
Amodeo
, R. J.
, and Ghoniem
, N. M.
, 1990, “Dislocation Dynamics. I. A proposed Methodology for Deformation Micromechanics
,” Phys. Rev. B
0163-1829, 41
, pp. 6958
–6967
.26.
Kubin
, L.
, Canova
, G.
, Condat
, M.
, Devincre
, B.
, Pontikis
, V.
, and Bréchet
, Y.
, 1992, “Dislocation Microstructures and Plastic Flow: A 3D Simulation
,” Solid State Phenom.
1012-0394, 23–24
, pp. 455
–472
.27.
Volterra
, V.
, 1907, “Sur L'Equilibre des Corps Elastiques Multiplement
,” Ann. Ecole Nom. Sup.
, 3
(24
), pp. 401
–517
.28.
Burgers
, J. M.
, 1939, “Report of a Conference of Strength of Solids
,” Proc. K. Ned. Akad. Wet.
0370-0348, 47
, pp. 283
–378
.29.
Hirth
, J.
, and Lothe
, J.
, 1982, Theory of Dislocations
, 2nd ed., Wiley
, New York
.30.
Madec
, R.
, Devincre
, B.
, and Kubin
, L.
, 2001, “New Line Model for Optimized Dislocation Dynamics Simulations
,” Mater. Res. Soc. Symp. Proc.
0272-9172, 653
, pp. Z1.8.1
–6
.31.
Devincre
, B.
, Kubin
, L.
, Lemarchand
, C.
, and Madec
, R.
, 2001, “Mesoscopic Simulations of Plastic Deformation
,” Mater. Sci. Eng., A
0921-5093, 309–310
, pp. 211
–219
.32.
Zbib
, H. M.
, Rhee
, M.
, and Hirth
, J. P.
, 1998, “On Plastic Deformation and the Dynamics of 3D Dislocations
,” Int. J. Mech. Sci.
0020-7403, 40
, pp. 113
–127
.33.
Arsenlis
, A.
, Cai
, W.
, Tang
, M.
, Rhee
, M.
, Oppelstrup
, T.
, Hommes
, G.
, Pierce
, T. G.
, and Bulatov
, V. V.
, 2007, “Enabling Strain Hardening Simulations With Dislocation Dynamics
,” Modell. Simul. Mater. Sci. Eng.
0965-0393, 15
, pp. 553
–595
.34.
Křišt'an
, J.
, and Kratochvíl
, J.
, 2008, “Estimates of Stress in the Channel of Persistent Slip Bands Based on Dislocation Dynamics
,” Special Issue of Mater. Sci. Forum
0255-5476, 567-568
, pp. 405
–408
.35.
Ghoniem
, N. M.
, and Sun
, L. Z.
, 1999, “Fast-Sum Method for the Elastic Field of Three-Dimensional Dislocation Ensembles
,” Phys. Rev. B
0163-1829, 60
, pp. 128
–40
.36.
Ghoniem
, N. M.
, Huang
, J.
, and Wang
, Z.
, 2002, “Affine Covariant-Contravariant Vector Forms for the Elastic Field of Parametric Dislocations in Isotropic Crystals
,” Philos. Mag. Lett.
0950-0839, 82
, pp. 55
–63
.37.
Schwarz
, K. W.
, 1999, “Simulation of Dislocations on the Mesoscopic Scale. I. Methods and Examples
,” J. Appl. Phys.
0021-8979, 85
, pp. 108
–119
.38.
Schwarz
, K. W.
, 1999, “Simulation of Dislocations on the Mesoscopic Scale. II. Application to Strained-Layer Relaxation
,” J. Appl. Phys.
0021-8979, 85
, pp. 120
–129
.39.
Rhee
, M.
, Stolken
, J.
, Zbib
, H. M.
, Hirth
, J. P.
, and Diaz de la Rubia
, T.
, 2001, “Dislocation Dynamics Using Anisotropic Elasticity: Methodology and Analysis
,” Mater. Sci. Eng., A
0921-5093, 309–310
, pp. 288
–293
.40.
Hirth
, J. P.
, Zbib
, H. M.
, and Lothe
, J.
, 1998, “Forces on High Velocity Dislocations
,” Modell. Simul. Mater. Sci. Eng.
0965-0393, 6
, pp. 165
–169
.41.
Zbib
, H. M.
, Shehadeh
, S.
, Khan
, S.
, and Karami
, G.
, 2003, “Multiscale Dislocation Dynamics Plasticity
,” Int. J. Multiscale Comp. Eng.
1543-1649, 1
, pp. 73
–89
.42.
Nadgorny
, E.
(1998), Progress in Materials Science, Dislocation Dynamics and Mechanical Properties
, J. W.
Christian
, P.
Haasen
, and T. B.
Massalski
, eds., (Pergamon Press
, Oxford
, Vol. 31
), p. 536
.43.
Wang
, Z. Q.
, Beyerlein
, I. J.
, and LeSar
, R.
, 2007, “The Importance of Cross-Slip in High Rate Deformation
,” Modell. Simul. Mater. Sci. Eng.
0965-0393, 15
, pp. 675
–690
.44.
Wang
, Z. Q.
, Beyerlein
, I. J.
, and LeSar
, R.
, 2009, “Plastic Anisotropy in fcc Single Crystal in High Rate Deformation
,” Int. J. Plast.
0749-6419, 25
, pp. 26
–48
.45.
Rhee
, M.
, Zbib
, H. M.
, Hirth
, J. P.
, Huang
, H.
, and de La Rubia
, T. D.
, 1998, “Models for Long/Short Range Interactions in 3D Dislocation Simulation
,” Modell. Simul. Mater. Sci. Eng.
0965-0393, 6
, pp. 467
–492
.46.
Bulatov
, V.
, Rhee
, M.
, and Cai
, W.
, 2001, “Periodic Boundary Conditions for Dislocation Dynamics Simulations in Three Dimensions
,” in Multiscale Modeling of Materials 2000
, L. P.
Kubin
, R.
Selinger
, J. L.
Bassani
, and K.
Cho
, eds. (Materials Research Society
, Warrendale, PA
, Vol. 653
), pp. z1
–z3
, .47.
Madec
, R.
, Devincre
, B.
, and Kubin
, L.
, 2003, Mesoscopic Dynamics in Fracture Process and Strength of Materials
(IUTAM Symposium
), Y.
Shibutani
and H.
Kitagawa
, eds., Kluwer Academic
, The Netherlands
.48.
Moulin
, A.
, Condat
, M.
, and Kubin
, L. P.
, 1997, “Simulation of Frank–Read Sources in Silicon
,” Acta Mater.
1359-6454, 45
, pp. 2339
–2348
.49.
Tang
, M.
, Kubin
, L. P.
, and Canova
, G. R.
, 1998, “Dislocation Mobility and the Mechanical Response of b.c.c. Single Crystals: A Mesoscopic Approach
,” Acta Mater.
1359-6454, 46
, pp. 3221
–3235
.50.
Kubin
, L. P.
, Madec
, R.
, and Devincre
, B.
, 2003, “Dislocation Intersections and Reactions in FCC and BCC Crystals
,” Mater. Res. Soc. Symp. Proc.
0272-9172, 779
, pp. W1.6
.51.
Madec
, R.
, and Kubin
, L. P.
, 2008, “Second-Order Junctions and Strain Hardening in bcc and fcc Crystals
,” Scr. Mater.
1359-6462, 58
, pp. 767
–770
.52.
Monnet
, G.
, Devincre
, B.
, and Kubin
, L. P.
, 2004, “Dislocation Study of Prismatic Slip Systems and Their Interactions in Hexagonal Close Packed Metals: Application to Zirconium
,” Acta Mater.
1359-6454, 52
, pp. 4317
–4328
.53.
Taylor
, G. I.
, 1938, “Plastic Strain in Metals
,” J. Inst. Met.
0020-2975, 62
, pp. 307
–324
.54.
Durinck
, J.
, Devincre
, B.
, Kubin
, L. P.
, and Cordier
, P.
, 2007, “Modeling the Plastic Deformation of Olivine by Dislocation Dynamics Simulations
,” Am. Mineral.
0003-004X, 92
, pp. 1346
–1357
.55.
Weygand
, D.
, Friedman
, L. H.
, Van der Geissen
, E.
, and Needleman
, A.
, 2002, “Aspects of Boundary-Value Problem Solutions With Three-Dimensional Dislocation Dynamics
,” Modell. Simul. Mater. Sci. Eng.
0965-0393, 10
, pp. 437
–468
.56.
Madec
, R.
, Devincre
, B.
, and Kubin
, L.
, 2003, “The Role of Collinear Interaction in Dislocation-Induced Hardening
,” Science
0036-8075, 301
, pp. 1879
–1882
.57.
Kristan
, J.
, and Kratochvil
, J.
, 2007, “Interactions of Glide Dislocations in a Channel of a Persistent Slip Band
,” Philos. Mag.
1478-6435, 87
, pp. 4593
–4613
.58.
Hirth
, J. P.
, Rhee
, M.
, and Zbib
, H. M.
, 1996, “Modeling of Deformation by a 3D Simulation of Multipole, Curved Dislocations
,” J. Comput.-Aided Mater. Des.
0928-1045, 3
, pp. 164
–166
.59.
Verdier
, M.
, Fivel
, M.
, and Groma
, I.
, 1998, “Mesoscopic Scale Simulation of Dislocation Dynamics in fcc Metals: Principles and Applications
,” Modell. Simul. Mater. Sci. Eng.
0965-0393, 6
, pp. 755
–770
.60.
Zbib
, H. M.
, Diaz de la Rubia
, T.
, Rhee
, M.
, and Hirth
, J.
, 2000, “3D Dislocation Dynamics: Stress-Strain Behavior and Hardening Mechanism in fcc and bcc Metals
,” J. Nucl. Mater.
0022-3115, 276
, pp. 154
–165
.61.
Khraishi
, T.
, Zbib
, H. M.
, Diaz de la Rubia
, T.
, and Victoria
, M.
, 2001, “Modeling of Irradiation in Metals Using Dislocation Dynamics
,” Philos. Mag. Lett.
0950-0839, 81
, pp. 583
–593
.62.
Khraishi
, T.
, Zbib
, H. M.
, Diaz de la Rubia
, T.
, and Victoria
, M.
, 2002, “Localized Deformation and Hardening in Irradiated Metals: Three-Dimensional Discrete Dislocation Dynamics Simulations
,” Metall. Mater. Trans. B
1073-5615, 33B
, pp. 285
–296
.63.
Shin
, C. S.
, Fivel
, M. C.
, Verdier
, M.
, and Kwon
, S. C.
, 2006, “Numerical Methods to Improve the Computing Efficiency of Discrete Dislocation Dynamics Simulations
,” J. Comput. Phys.
0021-9991, 215
(2
), pp. 417
–429
.64.
Wang
, Z.
, Ghoniem
, N.
, Swaminarayan
, S.
, and LeSar
, R.
, 2006, “A Parallel Algorithm for 3D Dislocation Dynamics
, J. Comput. Phys.
0021-9991, 219
(2
), pp. 608
–621
.65.
Kuhlmann-Wilsdorf
, D.
, 1989, “Theory of Plastic Deformation: - Properties of Low Energy Dislocation Structures
,” Mater. Sci. Eng., A
0921-5093, 113
, pp. 1
–41
.66.
Kuhlmann-Wilsdorf
, D.
, 1995, “Technological High Strain Deformation of ‘Wavy Glide’ Metals and LEDS
,” Phys. Status Solidi A
0031-8965, 149
, pp. 225
–241
.67.
Van der Giessen
, E.
, and Needleman
, A.
, 1995, “Discrete Dislocation Plasticity: A Simple Planar Model
,” Modell. Simul. Mater. Sci. Eng.
0965-0393, 3
, pp. 689
–735
.68.
Cleveringa
, H. H. M.
, van der Giessen
, E.
, and Needleman
, A.
, 2000, “A Discrete Dislocation Analysis of Mode I Crack Growth
,” J. Mech. Phys. Solids
0022-5096, 48
, pp. 1133
–1157
.69.
Cleveringa
, H. H. M.
, van der Giessen
, E.
, and Needleman
, A.
, 2001, “A Discrete Dislocation Analysis of Rate Effects on Mode I Crack Growth
,” Mater. Sci. Eng., A
0921-5093, 317
, pp. 37
–43
.70.
Deshpande
, V. S.
, Needleman
, A.
, and van der Giessen
, E.
, 2003, “Scaling of Discrete Dislocation Predictions for Near-Threshold Fatigue Crack Growth
,” Acta Mater.
1359-6454, 51
, pp. 4637
–4651
.71.
Deshpande
, V. S.
, Needleman
, A.
, and van der Giessen
, E.
, 2005, “Plasticity Size Effects in Tension and Compression of Single Crystals
,” J. Mech. Phys. Solids
0022-5096, 53
, pp. 2661
–2691
.72.
Benzerga
, A. A.
, Brechet
, Y.
, Needleman
, A.
, and Van der Giessen
, E.
, 2004, “Incorporating Three-Dimensional Mechanisms Into Two-Dimensional Dislocation Dynamics
,” Modell. Simul. Mater. Sci. Eng.
0965-0393, 12
, pp. 159
–196
.73.
Balint
, D. S.
, Deshpande
, V. S.
, Needleman
, A.
, and Van der Giessen
, E.
, 2006, “Discrete Dislocation Plasticity Analysis of the Wedge Indentation of Films
,” J. Mech. Phys. Solids
0022-5096, 54
, pp. 2281
–2303
.74.
Nicola
, L.
, Bower
, A. F.
, Kim
, K. -S.
, Needleman
, A.
, and Van der Giessen
, E.
, 2007, “Surface Versus Bulk Nucleation of Dislocations During Contact
,” J. Mech. Phys. Solids
0022-5096, 55
, pp. 1120
–1144
.75.
Gomez-Garcia
, D.
, Devincre
, B.
, and Kubin
, L. P.
, 2006, “Dislocation Patterns and the Similitude Principle: 2.5D Mesoscale Simulation
,” Phys. Rev. Lett.
0031-9007, 96
, p. 125503
.76.
Palm
, J.
, 1949, “Stress-Strain Relation for Uniaxial Loading
,” Appl. Sci. Res., Sect. A
0365-7132, 1
, pp. 198
–210
.77.
Voce
, E.
, 1948, “The Relation Between Stress and Strain for Homogeneous Deformation
,” J. Inst. Met.
0020-2975, 74
, pp. 537
–562
.78.
Bulatov
, V.
, Abraham
, F. F.
, Kubin
, L.
, Devincre
, B.
, and Yip
, S.
, 1998, “Connecting Atomistic and Mesoscale Simulations of Crystal Plasticity
,” Nature (London)
0028-0836, 391
, pp. 669
–672
.79.
Marian
, J.
, Cai
, W.
, and Bulatov
, V. V.
, 2004, “Dynamic Transitions in Dislocation Motion: From Smooth to Rough to Twinning
,” Nature Mater.
1476-1122, 3
, pp. 158
–163
.80.
Olmsted
, D. L.
, Hector
, L. G.
, Jr., Curtin
, W. A.
, and Clifton
, R. J.
, 2005, “Atomistic Simulations of Dislocation Mobility in Al, Ni and Al/Mg Alloys
,” Modell. Simul. Mater. Sci. Eng.
0965-0393, 13
, pp. 371
–388
.81.
Bulatov
, V. V.
, Hsiung
, L. L.
, Tang
, M.
, Arsenlis
, A.
, Bartelt
, M. C.
, Cai
, W.
, Florando
, J. N.
, Hiratani
, M.
, Rhee
, M.
, Hommes
, G.
, Pierce
, T. G.
, and Diaz de la Rubia
, T.
, 2006, “Dislocation Multi-Junctions and Strain Hardening
,” Nature (London)
0028-0836, 440
, pp. 1174
–1178
.82.
Martinez
, E.
, Marian
, J.
, Arsenlis
, A.
, Victoria
, M.
, and Perlado
, J. M.
, 2008, “Atomistically Informed Dislocation Dynamics in fcc Crystals
,” J. Mech. Phys. Solids
0022-5096, 56
, pp. 869
–895
.83.
Groh
, S.
, Marin
, E. B.
, Horstemeyer
, M. F.
, and Bammann
, D. J.
, 2009, “Dislocation Motion in Magnesium: A Study by Molecular Statics and Molecular Dynamics
,” Model. Simul. Mater. Sci. Eng.
, accepted.84.
Kocks
, U. F.
, and Mecking
, H.
, 2003, “Physics and Phenomenology of Strain Hardening: The FCC Case
,” Prog. Mater. Sci.
0079-6425, 48
, pp. 171
–273
.85.
Kocks
, U. F.
, and Mecking
, H.
, 1979, “A Mechanism for Static and Dynamic Recovery
,” Strength of Metals and Alloys
, Pergamon
, New York
, pp. 345
–350
.86.
Mecking
, H.
, and Estrin
, Y.
, 1987, “Microstructure Related Constitutive Modeling of Plastic Deformation
,” Eighth International Symposium on Metallurgy and Material Science
, Riso, Denmark.87.
Teodosiu
, C.
, Raphanel
, J.
, and Tabourot
, L.
, 1993, “Finite Implementation of the Large Elastoplastic Deformation of Multicrystals
,” Large Plastic Deformation
, C.
Teodosiu
, J.
Raphanel
, and F.
Sidoroff
, eds., pp. 153
–168
.88.
Tabourot
, L.
, Fivel
, M.
, and Rauch
, E.
, 1997, “Generalized Constitutive Laws for f.c.c. Single Crystal
,” Mater. Sci. Eng., A
0921-5093, 234–236
, pp. 639
–642
.89.
Fivel
, M.
, Tabourot
, L.
, Rauch
, E.
, and Canova
, G.
, 1998, “Identification Through Mesoscopic Simulations of Macroscopic Parameters of Physically Based Constitutive Equations for the Plastic Behavior of fcc Single Crystals
,” J. Phys. IV
1155-4339, 8
, pp. 151
–158
.90.
Franciosi
, P.
, 1985, “The Concepts of Latent Hardening and Strain Hardening in Metallic Single Crystals
,” Acta Metall.
0001-6160, 33
, pp. 1601
–1612
.91.
Fivel
, M.
, 1997, “Etudes Numeriques a Diferentes Echelles de la Deformation Plastique des Monocristaux de Structure CFC
,” PhD dissertation, University of Grenoble.92.
Devincre
, B.
, Kubin
, L.
, and Hoc
, T.
, 2006, “Physical Analyses of Crystal Plasticity by DD Simulations
,” Scr. Mater.
1359-6462, 54
, pp. 741
–746
.93.
Queyreau
, S.
, Monnet
, G.
, and Devincre
, B.
, 2008, “Slip System Interactions in α-Iron Determined by Dislocation Dynamics Simulations
,” Int. J. Plast.
0749-6419, 25
(2
), pp. 361
–377
.94.
Preußner
, J.
, Rudnik
, Y.
, Brehm
, H.
, Völkl
, R.
, and Glatzel
, U.
, 2009, “A Dislocation Density Based Material Model to Simulate the Anisotropic Creep Behavior of Single-Phase and Two-Phase Single Crystals
,” Int. J. Plast.
0749-6419, 25
, pp. 973
–994
.95.
Ohashi
, T.
, Kawamukai
, M.
, and Zbib
, H.
, 2007, “A Multiscale Approach for Modeling Scale-Dependent Yield Stress in Polycrystalline Metals
,” Int. J. Plast.
0749-6419, 23
, pp. 897
–914
.96.
Ohashi
, T.
, 1994, “Numerical Modeling of Plastic Multislip in Metal Crystals of f.c.c. Type
,” Philos. Mag. A
0141-8610, 70
(5
), pp. 793
–803
.97.
Zbib
, H. M.
, Diaz de la Rubia
, T.
, and Bulatov
, V.
, 2002, “A Multiscale Model of Plasticity Based on Discrete Dislocation Dynamics
,” ASME J. Eng. Mater. Technol.
0094-4289, 124
, pp. 78
–87
.98.
Yasin
, H.
, Zbib
, H. M.
, and Khaleel
, M. A.
, 2001, “Size and Boundary Effects in Discrete Dislocation Dynamics: Coupling With Continuum Finite Element
,” Mater. Sci. Eng., A
0921-5093, 309–310
, pp. 294
–299
.99.
Martinez
, R.
, and Ghoniem
, N. M.
, 2002, “The Influence of Crystal Surfaces on Dislocation Interactions in Mesoscopic Plasticity: A Combined Dislocation Dynamics-Finite Element Approach
,” Comput. Model. Eng. Sci.
1526-1492, 3
, pp. 229
–243
.100.
Tang
, M.
, Xu
, G.
, Cai
, W.
, and Bulatov
, V. V.
, 2003, “Dislocation Image Stresses at Free Surfaces by the Finite Element Method
,” Thin Film Stresses and Mechanical Properties
, Vol. 795
, S. G.
Corcoran
, Y. -C.
Joo
, N. R.
Moody
, and Z.
Suo
, eds., Materials Research Society
, Warrendale, PA
, pp. U2.4.1
–5
.101.
Fivel
, M. C.
, Gosling
, T. J.
, and Canova
, G. R.
, 1996, “Implementing Image Stresses in a 3D Dislocation Simulation
,” Modell. Simul. Mater. Sci. Eng.
0965-0393, 4
, pp. 581
–596
.102.
El-Awady
, J. A.
, Biner
, S. B.
, and Ghoniem
, N.
, 2008, “A Self-Consistent Boundary Element, Parametric Dislocation Dynamics Formulation of Plastic Flow in Finite Volumes
,” J. Mech. Phys. Solids
0022-5096, 56
, pp. 2019
–2035
.103.
Liu
, X. H.
, and Schwarz
, K. W.
, 2005, “Modeling of Dislocations Intersecting a Free Surface
,” Modell. Simul. Mater. Sci. Eng.
0965-0393, 13
, pp. 1233
–1247
.104.
Khraishi
, T.
, and Zbib
, H. M.
, 2002, “Free-Surface Effects in 3D Dislocation Dynamics: Formulation and Modeling
,” ASME J. Eng. Mater. Technol.
0094-4289, 124
(3
), pp. 342
–351
.105.
Khraishi
, T.
, and Zbib
, H. M.
, 2002, “Dislocation Dynamics Simulations of the Interaction Between a Short Rigid Fiber and a Glide Dislocation Pile-Up
,” Comput. Mater. Sci.
0927-0256, 24
, pp. 310
–322
.106.
Tang
, M.
, Cai
, W.
, Xu
, G.
, and Bulatov
, V. V.
, 2006, “A Hybrid Method for Computing Forces on Curved Dislocations Intersecting Free Surfaces in Three-Dimensional Dislocation Dynamics
,” Modell. Simul. Mater. Sci. Eng.
0965-0393, 14
, pp. 1139
–1151
.107.
Van der Giessen
, E.
, and Needleman
, A.
, 2003, “GNDs in Nonlocal Plasticity Theories: Lessons From Discrete Dislocation Simulations
,” Scr. Mater.
1359-6462, 48
, pp. 127
–132
.108.
Déprés
, C.
, Robertson
, C. F.
, and Fivel
, M. C.
, 2004, “Low-Strain Fatigue in AISI 316L Steel Surface Grains: A Three-Dimensional Discrete Dislocation Dynamics Modeling of the Early Cycles I. Dislocation Microstructures and Mechanical Behavior
,” Philos. Mag.
1478-6435, 84
, pp. 2257
–2275
.109.
Depres
, C.
, Robertson
, C. F.
, and Fivel
, M. C.
, 2006, “Low-Strain Fatigue in 316L Steel Surface Grains: A Three Dimension Discrete Dislocation Dynamics Modeling of the Early Cycles. Part 2: Persistent Slip Markings and Micro-Crack Nucleation
,” Philos. Mag.
1478-6435, 86
, pp. 79
–97
.110.
Shin
, C. S.
, Fivel
, M. C.
, Verdier
, M.
, and Oh
, K. H.
, 2003, “Dislocation-Impenetrable Precipitate Interaction: A Three-Dimensional Discrete Dislocation Dynamics Analysis
,” Philos. Mag.
1478-6435, 83
, pp. 3691
–3704
.111.
Shin
, C. S.
, Fivel
, M. C.
, and Kim
, W. W.
, 2005, “Three-Dimensional Computation of the Interaction Between a Straight Dislocation Line and a Particle
,” Modell. Simul. Mater. Sci. Eng.
0965-0393, 13
, pp. 1163
–1173
.112.
Hughes
, D. A.
, Khan
, S. M. A.
, Godfrey
, A.
, and Zbib
, H. M.
, 2001, “Internal Structures of Deformation Induced Planar Dislocation Boundaries
,” Mater. Sci. Eng., A
0921-5093, 309–310
, pp. 220
–226
.113.
Khan
, S.
, Zbib
, H. M.
, and Hughes
, D.
, 2004, “Modeling Planar Dislocation Boundaries Using a Multi-Scale Approach
,” Int. J. Plast.
0749-6419, 20
, pp. 1059
–92
.114.
Shehadeh
, M. A.
, Zbib
, H. M.
, and Diaz de la Rubia
, T.
, 2005, “Multiscale Dislocation Dynamics Simulations of Shock Compression in Copper Single Crystal
,” Int. J. Plast.
0749-6419, 21
, pp. 2369
–2390
.115.
Shehadeh
, M. A.
, Bringa
, E. M.
, Zbib
, H. M.
, McNaney
, J. M.
, and Remington
, B. A.
, 2006, “Simulation of Shock-Induced Plasticity Including Homogeneous and Heterogeneous Dislocation Nucleation
,” Appl. Phys. Lett.
0003-6951, 89
, p. 171918
.116.
Akasheh
, F.
, Zbib
, H. M.
, Hirth
, J. P.
, Hoagland
, R. G.
, and Misra
, A.
, 2007, “Interactions Between Glide Dislocations and Parallel Interfacial Dislocations in Nanoscale Strained Layers
,” J. Appl. Phys.
0021-8979, 102
, p. 034314
.117.
Akasheh
, F.
, Zbib
, H. M.
, Hirth
, J. P.
, Hoagland
, R. G.
and Misra
, A.
, 2007, “Dislocation Dynamics Analysis of Dislocation Intersections in Nanoscale Metallic Multilayered Composites
,” J. Appl. Phys.
0021-8979, 101
, p. 084314
.118.
Yashiro
, K.
, Kurose
, F.
, Nakashima
, Y.
, Kubo
, K.
, Tomita
, Y.
, and Zbib
, H. M.
, 2006, “Discrete Dislocation Dynamics Simulations of γ′ Precipitate and Interfacial Dislocation Network in Ni-Based Superalloys
,” Int. J. Plast.
0749-6419, 22
, pp. 713
–723
.119.
Lemarchand
, C.
, Devincre
, B.
, and Kubin
, L. P.
, 2001, “Homogenization Method for a Discrete-Continuum Approach of Dislocation Dynamics
,” J. Mech. Phys. Solids
0022-5096, 49
, pp. 1969
–1982
.120.
Devincre
, B.
, Roos
, A.
, and Groh
, S.
, 2003, Thermodynamics, Microstructures and Plasticity
(NATO Science Series II: Mathematics, Physics and Chemistry
), 108th ed., A.
Finel
, D.
Mazière
, and M.
Véron
, eds., Kluwer
, Dordrecht, The Netherlands
.121.
Groh
, S.
, Devincre
, B.
, Kubin
, L. P.
, Roos
, A.
, Feyel
, F.
, and Chaboche
, J.-L.
, 2003, “Dislocations and Elastic Anisotropy in Heteroepitaxial Metallic Thin Films
,” Philos. Mag. Lett.
0950-0839, 83
, pp. 303
–313
.122.
Groh
, S.
, Devincre
, B.
, Feyel
, F.
, Kubin
, L.
, Roos
, A.
, and Chaboche
, J.-L.
, 2003, “Discrete-Continuum Modeling of Metal Matrix Composites Plasticity
,” Mesoscopic Dynamics in Fracture Process and Strength of Materials
, Y.
Shibutani
and H.
Kitagawa
, eds, Kluwer
, Dordrecht, The Netherlands
.123.
Groh
, S.
, Devincre
, B.
, Kubin
, L. P.
, Roos
, A.
, Feyel
, F.
, and Chaboche
, J.-L.
, 2005, “Size Effects in Metal Matrix Composites
,” Mater. Sci. Eng., A
0921-5093, 400–401
, pp. 279
–282
.124.
Liu
, Z. L.
, Liu
, X. M.
, Zhuang
, Z.
, and You
, X. C.
, “A Multi-Scale Computational Model of Crystal Plasticity at Submicron-to-Nanometer
,” Int. J. Plast.
0749-6419, 25
(8
), pp. 1413
–1608
.125.
Shilkrot
, L. E.
, Miller
, R. E.
and Curtin
, W. A.
, 2002, “Coupled Atomistic and Discrete Dislocation Plasticity
, Phys. Rev. Lett.
0031-9007, 89
, p. 025501
.126.
Shilkrot
, L. E.
, Miller
, R. E.
, and Curtin
, W. A.
, 2004, “Multiscale Plasticity Modeling: Coupled Atomistics and Discrete Dislocation Mechanics
,” J. Mech. Phys. Solids
0022-5096, 52
, pp. 755
–787
.127.
Gao
, H.
, and Huang
, Y.
, 2003, “Geometrically Necessary Dislocation and Size-Dependent Plasticity
,” Scr. Mater.
1359-6462, 48
, pp. 113
–118
.128.
Uchic
, M. D.
, Dimiduk
, D. M.
, Florando
, J. N.
, and Nix
, W. D.
, 2004, “Sample Dimensions Influence Strength and Crystal Plasticity
,” Science
0036-8075, 305
, pp. 986
–989
.129.
Uchic
, M. D.
, and Dimiduk
, D. M.
, 2005, “A Methodology to Investigate Size Scale Effects in Crystalline Plasticity Using Uniaxial Compression
,” Mater. Sci. Eng., A
0921-5093, 400–401
, pp. 268
–78
.130.
Greer
, J. R.
, Oliver
, W. C.
, and Nix
, W. D.
, 2005, “Size Dependence of Mechanical Properties of Gold at the Micron Scale in the Absence of Strain Gradients
,” Acta Mater.
1359-6454, 53
, pp. 1821
–30
.131.
Greer
, J. R.
, and Nix
, W. D.
, 2006, “Nanoscale Gold Pillars Strengthened Through Dislocation Starvation
,” Phys. Rev. B
0163-1829, 73
, p. 245410
.132.
Shan
, Z. W.
, Mishra
, R. K.
, Syed Asif
, S. A.
, Warren
, O. L.
, and Minor
, A. M.
, 2008, “Mechanical Annealing and Source-Limited Deformation in Submicrometer-Diameter Ni Crystal
,” Nature Mater.
1476-1122, 7
, pp. 115
–119
.133.
Parthasarathy
, T. A.
, Rao
, S. I.
, Dimiduk
, D. M.
, Uchic
, M. D.
, and Trinkle
, D. R.
, 2007, “Contribution to Size Effect of Yield Strength From the Stochastics of Dislocation Source Lengths in Finite Samples
,” Scr. Mater.
1359-6462, 56
, pp. 313
–316
.134.
Tang
, H.
, Schwarz
, K. W.
, and Espinosa
, H. D.
, 2007, “Dislocation Escape-Related Size Effects in Single-Crystal Micropillars Under Uniaxial Compression
,” Acta Mater.
1359-6454, 55
, pp. 1607
–1616
.135.
Weygand
, D.
, Poignant
, M.
, Gumbsch
, P.
, and Kraft
, O.
, 2008, “Three-Dimensional Dislocation Dynamics Simulation of the Influence of Sample Size on the Stress-Strain Behavior of fcc Single-Crystalline Pillars
,” Mater. Sci. Eng., A
0921-5093, 483–484
, pp. 188
–190
.136.
Senger
, J.
, Weygand
, D.
, Gumbsch
, P.
, and Kraft
, O.
, 2008, “Discrete Dislocation Simulations of the Plasticity of Micro-Pillars Under Uniaxial Loading
,” Scr. Mater.
1359-6462, 58
, pp. 587
–590
.137.
El-Awady
, J. A.
, Wen
, M.
, and Ghoniem
, M. N.
, 2009, “The Role of the Weakest-Link Mechanism in Controlling the Plasticity of Micropillars
,” J. Mech. Phys. Solids
0022-5096, 57
, pp. 32
–50
.138.
Nix
, W. D.
, and Gao
, H.
, 1998, “Indentation Size Effects in Crystalline Materials: A Law for Strain Gradient Plasticity
,” J. Mech. Phys. Solids
0022-5096, 46
, pp. 411
–25
.139.
Tang
, H.
, Schwarz
, K. W.
, and Espinosa
, H. D.
, 2008, “Dislocation-Source Shutdown and the Plastic Behavior of Single-Crystal Micropillars
,” Phys. Rev. Lett.
0031-9007, 100
, pp. 185503
.140.
Dimiduk
, D. M.
, Uchic
, M. D.
, and Parthasarathy
, T. A.
, 2005, “Size-Affected Single-Slip Behavior of Pure Nickel Microcrystals
,” Acta Mater.
1359-6454, 53
, pp. 4065
–4077
.141.
Volkert
, C.
, and Lilleodden
, E. T.
, 2006, “Size Effects in the Deformation of Sub-Micron Au Columns
,” Philos. Mag.
1478-6435, 86
, pp. 5567
–5579
.142.
Kubin
, L. P.
, and Devincre
, B.
, 1999, “From Dislocation Mechanisms to Dislocation Microstructures and Strain Hardening
,” Deformation-Induced Microstructures: Analysis and Relation to Properties
(20th Risoe Symposium
), J. B.
Bilde Sørensen
, J. V.
Carstensen
, N.
Hansen
, D.
Juul Jensen
, T.
Leffers
, W.
Pantleon
, O. B.
Pedersen
, and G.
Winther
, eds., Risoe National Laboratory
, Roskilde, Denmark
, pp. 61
–83
.143.
Madec
, R.
, Devincre
, B.
, and Kubin
, L. P.
, 2002, “Simulation of Dislocation Patterns in Multislip
,” Scr. Mater.
1359-6462, 47
, pp. 689
–695
.144.
Liu
, Z. L.
, Liu
, X. M.
, Zhuang
, Z.
, and You
, X. C.
, 2009, “Atypical Three-Stage-Hardening Mechanical Behavior of Cu Single-Crystal Micropillars
,” Scr. Mater.
1359-6462, 60
, pp. 594
–597
.145.
Akarupa
, S.
, Zbib
, H. M.
, and Bahr
, D. F.
, 2008, “Heterogeneous Deformation and Dislocation Dynamics in Single Crystal Micropillars Under Compression
,” unpublished.146.
Zbib
, H. M.
, Akarupa
, S.
, Akasheh
, F.
, Overman
, C.
, and Bahr
, D.
, 2009, “Deformation and Size Effects in Small Scale Structures
,” in Macro to Nano Scale Inelastic behavior of Materials: Plasticity, Fatigue and Fracture
, A.
Khan
and B.
Farrokh
, eds. (Proceedings of the 15th International Symposium on Plasticity and Its Current Applications
), Jan. 3–9, St. Thomas
, pp. 220
–222
.147.
Devincre
, B.
, and Roberts
, S. G.
, 1996, “Three-Dimensional Simulation of Dislocation-Crack Interactions in BCC Metals at the Mesocopic Scale
,” Acta Mater.
1359-6454, 44
, pp. 2891
–2900
.148.
Deshpande
, V. S.
, Needleman
, A.
, and van der Giessen
, E.
, 2002, “Discrete Dislocation Modeling of Fatigue Crack Propagation
,” Acta Mater.
1359-6454, 50
, pp. 831
–846
.149.
Groh
, S.
, Olarnrithinun
, S.
, Curtin
, W. A.
, Needleman
, A.
, Deshpande
, V. S.
, and Van der Giessen
, E.
, 2008, “Fatigue Crack Growth From a Cracked Elastic Particle Into a Ductile Matrix
,” Philos. Mag.
1478-6435, 88
, pp. 3565
–3583
.150.
Cottrell
, A. H.
, and Bilby
, B. A.
, 1951, “Mechanism for the Growth of Deformation Twins in Crystals
,” Philos. Mag.
0031-8086, 42
, pp. 573
–581
.151.
Christian
, J. W.
, and Mahajan
, S.
, 1995, “Deformation Twinning
,” Prog. Mater. Sci.
0079-6425, 39
, pp. 1
–157
.152.
Kalidindi
, S. R.
, 1998, “Incorporation of Deformation Twinning in Crystal Plasticity Models
,” J. Mech. Phys. Solids
0022-5096, 46
, pp. 267
–290
.153.
Belak
, J.
, 1998, “On the Nucleation and Growth of Voids at High Strain-Rates
,” J. Comput.-Aided Mater. Des.
0928-1045, 5
, pp. 193
–206
.154.
Rudd
, R. E.
, and Belak
, J. F.
, 2002, “Void Nucleation and Associated Plasticity in Dynamic Fracture of Polycrystalline Copper: An Atomistic Simulation
,” Comput. Mater. Sci.
0927-0256, 24
, pp. 148
–153
.155.
Devincre
, B.
, 1995, “Three Dimensional Stress Fields Expressions for Straight Dislocation Segments
,” Solid State Commun.
0038-1098, 93
, pp. 875
–878
.156.
Rhee
, M.
, 1998, “3-D Modeling of Dislocation Cells in Metals
,” Ph.D. thesis, Washington State University, Pullman, WA.Copyright © 2009
by American Society of Mechanical Engineers
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