Abstract
Dislocation dynamics (DD) is a modeling approach for the study of crystal plasticity wherein individual dislocation lines are discretized and their motion in the crystal is simulated. This chapter provides an overview of the basic features of the DD methodology and a guide for how to run DD simulations. Each of the basic building blocks, in terms of both dislocation physics and numerics, is first discussed. Three case studies are then presented, showing how to set up a simulation, ensure solution convergence, and extract key outputs. The major DD codes are briefly reviewed, discussing their major features and differences. Finally, the relation of DD to material models at other length and time scales is discussed, along with current challenges and research topics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
R. Abbaschian, L. Abbaschian, R.E. Reed-Hill, Physical Metallurgy Principles (Cengage Learning, Stamford, CT, 2009)
S. Akarapu, H.M. Zbib, D.F. Bahr, Analysis of heterogeneous deformation and dislocation dynamics in single crystal micropillars under compression. Int. J. Plast. 26, 239–257 (2010)
R.J. Amodeo, N.M. Ghoniem, Dislocation dynamics. I. A proposed methodology for deformation micromechanics. Phys. Rev. B 41 (10), 6958–6967 (1990)
A.S. Argon, Strengthening Mechanisms in Crystal Plasticity. Oxford University Press, Oxford, 2008)
A. Arsenlis, W. Cai, M. Tang, M. Rhee, T. Oppelstrup, G. Hommes, T.G. Pierce, V.V. Bulatov, Enabling strain hardening simulations with dislocation dynamics. Model. Simul. Mater. Sci. Eng. 15, 553 (2007)
S. Aubry, A. Arsenlis, Use of spherical harmonics for dislocation dynamics in anisotropic elastic media. Model. Simul. Mater. Sci. Eng. 21, 065013 (2013)
B. Bakó, E. Clouet, L.M. Dupuy, M. Blétry, Dislocation dynamics simulations with climb: kinetics of dislocation loop coarsening controlled by bulk diffusion. Philos. Mag. 91, 3173–3191 (2011)
A.A. Benzerga, Y. Bréchet, A. Needleman, E. van der Giessen, Incorporating three-dimensional mechanisms into two-dimensional dislocation dynamics. Model. Simul. Mater. Sci. Eng. 12, 159–196 (2004)
V.V. Bulatov, W. Cai, Computer Simulations of Dislocations (Oxford University Press, Oxford, 2006)
V.V. Bulatov, F.F. Abraham, L.P. Kubin, B. Devincre, S. Yip, Connecting atomistic and mesoscale simulations of crystal plasticity. Nature 391, 669–672 (1998)
V.V. Bulatov, L.L. Hsiung, M. Tang, A. Arsenlis, M.C. Bartelt, W. Cai, J.N. Florando, M. Hiratani, M. Rhee, G. Hommes, T.G. Pierce, T.D. de la Rubia, Dislocation multi-junctions and strain hardening. Nature 440, 1174–1178 (2006)
W. Cai, V.V. Bulatov, Mobility laws in dislocation dynamics simulations. Mater. Sci. Eng. A 387, 277–281 (2004)
W. Cai, V.V. Bulatov, J.P. Chang, J. Li, S. Yip, Periodic image effects in dislocation modeling. Philos. Mag. 83, 539–567 (2003)
W. Cai, V.V. Bulatov, J. Chang, J. Li, S. Yip, Dislocation core effects on mobility, in Dislocations in Solids, ed. by F.R.N. Nabarro, J.P. Hirth, Vol. 12, Chap. 64 (Elsevier, Amsterdam, 2004), pp. 1–80
W. Cai, A. Arsenlis, C.R. Weinberger, V.V. Bulatov, A non-singular continuum theory of dislocations. J. Mech. Phys. Solids 54, 561–587 (2006)
S.S. Chakravarthy, W.A. Curtin, Effect of source and obstacle strengths on yield stress: A discrete dislocation study. J. Mech. Phys. Solids 58, 625–635 (2010)
Q. Chen, X.-Y. Liu, S.B. Biner, Solute and dislocation junction interactions. Acta Mater. 56, 2937–2947 (2008)
H.H.M. Cleveringa, E. van der Giessen, A. Needleman, Comparison of discrete dislocation and continuum plasticity predictions for a composite material. Acta Mater. 45 (8), 3163–3179 (1997)
T. Crosby, G. Po, C. Erel, N. Ghoniem, The origin of strain avalanches in sub-micron plasticity of fcc metals. Acta Mater. 89, 123–132 (2015)
W.A. Curtin, R.E. Miller, Atomistic/continuum coupling in computational materials science. Model. Simul. Mater. Sci. Eng. 11, R33–R68 (2003)
V.S. Deshpande, A. Needleman, E. van der Giessen, Plasticity size effects in tension and compression of single crystals. J. Mech. Phys. Solids 53, 2661–2691 (2005)
B. Devincre, L.P. Kubin, C. Lemarchand, R. Madec, Mesoscopic simulations of plastic deformation. Mater. Sci. Eng. A 309, 211–219 (2001)
B. Devincre, L. Kubin, T. Hoc, Physical analyses of crystal plasticity by DD simulations. Scr. Mater. 54, 741–746 (2006)
B. Devincre, R. Madec, G. Monnet, S. Queyreau, R. Gatti, L. Kubin, Modeling crystal plasticity with dislocation dynamics simulations: the ‘microMegas’ code, in Mechanics of Nano-Objects. (Presses de l’Ecole des Mines de Paris, Paris, 2011), pp. 81–100
G. deWit, J.S. Koehler, Interaction of dislocations with an applied stress in anisotropic crystals. Phys. Rev. 116 (5), 1113–1120 (1959)
J.A. El-Awady, S. Bulent Biner, N.M. Ghoneim, A self-consistent boundary element, parametric dislocation dynamics formulation of plastic flow in finite volumes. J. Mech. Phys. Solids 56, 2019–2035 (2008)
H. Fan, S. Aubry, A. Arsenlis, J.A. El-Awady, The role of twinning deformation on the hardening response of polycrystalline magnesium from discrete dislocation dynamics simulations. Acta Mater. 92, 126–139 (2015)
R.S. Fertig, S.P. Baker, Simulation of dislocations and strength in thin films: a review. Prog. Mater. Sci. 54, 874–908 (2009)
M.C. Fivel, T.J. Gosling, G.R. Canova, Implementing image stresses in a 3D dislocation simulation. Model. Simul. Mater. Sci. Eng. 4, 581–596 (1996)
M.C. Fivel, C.F. Robertson, G.R. Canova, L. Boulanger, Three-dimensional modeling of indent-induced plastic zone at a mesoscale. Acta Mater. 46, 6183–6194 (1998)
A.J.E. Foreman, The bowing of a dislocation segment. Philos. Mag. 15, 1011–1021 (1967)
S. Gao, M. Fivel, A. Ma, A. Hartmaier, Influence of misfit stresses on dislocation glide in single crystal superalloys: a three-dimensional discrete dislocation dynamics study. J. Mech. Phys. Solids 76, 276–290 (2015)
D.J. Gardner, C.S. Woodward, D.R. Reynolds, G. Hommes, S. Aubry, A. Arsenlis, Implicit integration methods for dislocation dynamics. Model. Simul. Mater. Sci. Eng. 23, 025006 (2015)
N.M. Ghoniem, R. Amodeo, Computer simulation of dislocation pattern formation. Solid State Phenom. 3 & 4, 377 (1988)
N.M. Ghoniem, S.H. Tong, L.Z. Sun, Parametric dislocation dynamics: a thermodynamics-based approach to investigations of mesoscopic plastic deformation. Phys. Rev. B 61, 913 (2000)
M.R. Gilbert, S. Queyreau, J. Marian, Stress and temperature dependence of screw dislocation mobility in α-Fe by molecular dynamics. Phys. Rev. B 84, 174103 (2011)
D. Gómez-GarcÃa, B. Devincre, L.P. Kubin, Dislocation patterns and the similitude principle: 2.5D mesoscale simulations. Phys. Rev. Lett. 96, 125503 (2006)
P.A. Gordon, T. Neeraj, Y. Li, J. Li, Screw dislocation mobility in BCC metals: the role of the compact core on double-kink nucleation. Model. Simul. Mater. Sci. Eng. 18, 085008 (2010)
P.J. Guruprasad, A.A. Benzerga, Size effects under homogeneous deformation of single crystals: A discrete dislocation analysis. J. Mech. Phys. Solids 56, 132–156 (2008)
S.M. Hafez Haghighat, R. Schäublin, D. Raabe, Atomistic simulation of the a 0 < 100 > binary junction formation and its unzipping in body-centered cubic iron. Acta Mater. 64, 24–32 (2014)
A. Hartmaier, M.C. Fivel, G.R. Canova, P. Gumbsch, Image stresses in a free standing thin film. Model. Simul. Mater. Sci. Eng. 7, 781–793 (1999)
J.P. Hirth, J. Lothe, Theory of Dislocations, 2nd edn. (Krieger Publishing Company, Malabar, FL, 1992)
J. Huang, N.M. Ghoniem, Accuracy and convergence of parametric dislocation dynamics. Model. Simul. Mater. Sci. Eng. 10, 1–19 (2002)
M. Huang, L. Zhao, J. Tong, Discrete dislocation dynamics modelling of mechanical deformation of nickel-based single crystal superalloys. Int. J. Plast. 28, 141–158 (2010)
D. Hull, D.J. Bacon, Introduction to Dislocations, 4th edn. (Butterworth Heinemann, Oxford, 2009)
A.M. Hussein, S.I. Rao, M.D. Uchic, D.M. Dimiduk, J.A. El-Awady, Microstructurally based cross-slip mechanisms and their effects on dislocation microstructure evolution in fcc crystals. Acta Mater. 85, 180–190 (2015)
K. Kang, J. Yin, W. Cai, Stress dependence of cross slip energy barrier for face-centered cubic nickel. J. Mech. Phys. Solids 62, 181–193 (2014)
Y. Kawasaki, T. Takeuchi, Cell structures in copper single crystals deformed in the [001] and [111] axes. Scr. Met. 14, 183–188 (1980)
T.A. Khraishi, H.M. Zbib, Free-surface effects in 3D dislocation dynamics: formulation and modeling. ASME J. Eng. Mater. Technol. 124 (3), 342–351 (2002)
T.A. Khraishi, L. Yan, Y.L. Shen, Dynamic simulations of the interaction between dislocations and dilute particle concentrations in metal–matrix composites (MMCs). Int. J. Plast. 20, 1039–1057 (2004)
U.F. Kocks, A.S. Argon, M.F. Ashby, Thermodynamics and kinetics of slip. Prog. Mater. Sci. 19, 1–288 (1975)
L. Kubin, Dislocations, Mesoscale Simulations and Plastic Flow. (Oxford University Press, Oxford, 2013)
L.P. Kubin, G. Canova, M. Condat, B. Devincre, V. Pontikis, Y. Bréchet, Dislocation microstructures and plastic flow: a 3D simulation. Solid State Phenom. 23 & 24, 455–472 (1992)
L.P. Kubin, B. Devincre, M. Tang, Mesoscopic modelling and simulation of plasticity in fcc and bcc crystals: dislocation intersections and mobility. J. Comput.-Aided Mater. Des. 5, 31–54 (1998)
W.P. Kuykendall, W. Cai, Conditional convergence in 2-dimensional dislocation dynamics. Model. Simul. Mater. Sci. Eng. 21, 055003 (2013)
W.P. Kuykendall, W. Cai, Effect of multiple stress components on the energy barrier of crossslip in nickel (2016, in preparation)
C. Laird, Chapter 27: fatigue, in Physical Metallurgy, ed. by R.W. Cahn, P. Haasen, 4th edn. (Elsevier Science, Amsterdam, 1996), pp. 2293–2397
S.W. Lee, S. Aubry, W.D. Nix, W. Cai, Dislocation junctions and jogs in a free-standing FCC thin film. Model. Simul. Mater. Sci. Eng. 19, 025002 (2011)
J. Li, AtomEye: an efficient atomistic configuration viewer. Model. Simul. Mater. Sci. Eng. 11, 173–177 (2003)
R. Madec, B. Devincre, L.P. Kubin, From dislocation junctions to forest hardening. Phys. Rev. Lett. 89, 255508 (2002)
R. Madec, B. Devincre, L. Kubin, T. Hoc, D. Rodney, The role of collinear interaction in dislocation-induced hardening. Science 301, 1879–1882 (2003)
J. Marian, A. Caro, Moving dislocations in disordered alloys: connecting continuum and discrete models with atomistic simulations. Phys. Rev. B 74, 024113 (2006)
E. MartÃnez, J. Marian, A. Arsenlis, M. Victoria, J.M. Perlado, Atomistically informed dislocation dynamics in fcc crystals. J. Mech. Phys. Solids 56, 869–895 (2008)
MDDP: Multiscale Dislocation Dynamics Plasticity code, http://www.cmms.wsu.edu/
microMegas (mM) code, http://zig.onera.fr/mm_home_page/
R.E. Miller, L.E. Shilkrot, W.A. Curtin, A coupled atomistics and discrete dislocation plasticity simulation of nanoindentation into single crystal thin films. Acta Mater. 52, 271–284 (2004)
MODEL: Mechanics Of Defect Evolution Library, https://bitbucket.org/model/model/wiki/Home
V. Mohles, Dislocation dynamics simulations of particle strengthening. in Continuum Scale Simulation of Engineering Materials: Fundamentals – Microstructures – Process Applications, ed. by D. Raabe, F. Roters, F. Barlat, L.-Q. Chen (Wiley, Weinheim, 2004)
G. Monnet, B. Devincre, Solute friction and forest interaction. Philos. Mag. 86, 1555–1565 (2006)
D. Mordehai, E. Clouet, M. Fivel, M. Verdier, Introducing dislocation climb by bulk diffusion in discrete dislocation dynamics. Philos. Mag. 88, 899–925 (2008)
C. Motz, D. Weygand, J. Senger, P. Gumbsch, Initial dislocation structures in 3-D discrete dislocation dynamics and their influence on microscale plasticity. Acta Mater. 57, 1744–1754 (2009)
A. Needleman, E. van der Giessen, Discrete dislocation and continuum descriptions of plastic flow. Mater. Sci. Eng. A 309–310, 1–13 (2001)
NUMODIS: a Numerical Model for Dislocations, http://www.numodis.com/numodis/index.html
R.W. Nunes, J. Bennetto, D. Vanderbilt, Structure, barriers and relaxation mechanisms of kinks in the 90∘ partial dislocation in silicon. Phys. Rev. Lett. 77, 1516–1519 (1996)
D.L. Olmsted, L.G. Hector Jr., W.A. Curtin, R.J. Clifton, Atomistic simulations of dislocation mobility in Al, Ni and Al/Mg alloys. Model. Simul. Mater. Sci. Eng. 13, 371–388 (2005)
ParaDiS: Parallel Dislocation Simulator code, http://micro.stanford.edu/wiki/ParaDiS_Manuals
G. Po, N. Ghoniem, A variational formulation of constrained dislocation dynamics coupled with heat and vacancy diffusion. J. Mech. Phys. Solids 66, 103–116 (2014)
G. Po, M.S. Mohamed, T. Crosby, C. Erel, A. El-Azab, N. Ghoniem, Recent progress in discrete dislocation dynamics and its applications to micro plasticity. J. Mat. 66, 2108–2120 (2014)
W. Püschl, Models for dislocation cross-slip in close-packed crystal structures: a critical review. Prog. Mater. Sci. 47, 415–461 (2002)
S. Queyreau, B. Devincre, Bauschinger effect in precipitation-strengthened materials: A dislocation dynamics investigation. Philos. Mag. Lett. 89, 419–430 (2009)
S. Queyreau, G. Monnet, B. Devincre, Slip systems interactions in α-iron determined by dislocation dynamics simulations. Int. J. Plast. 25, 361–377 (2009)
S. Queyreau, G. Monnet, B. Devincre, Orowan strengthening and forest hardening superposition examined by dislocation dynamics simulations. Acta Mater. 58, 5586–5595 (2010)
S. Queyreau, J. Marian, M.R. Gilbert, B.D. Wirth, Edge dislocation mobilities in bcc Fe obtained by molecular dynamics. Phys. Rev. B 84, 064106 (2011)
S. Rao, T.A. Parthasarathy, D.M. Dimiduk, P.M. Hazzledine, Discrete dislocation simulations of precipitation hardening in superalloys. Philos. Mag. 84, 30, 3195–3215 (2004)
S. Rao, D.M. Dimiduk, J.A. El-Awady, T.A. Parthasarathy, M.D. Uchic, C. Woodward, Activated states for cross-slip at screw dislocation intersections in face-centered cubic nickel and copper via atomistic simulation. Acta Mater. 58, 5547–5557 (2010)
S.I. Rao, D.M. Dimiduk, T.A. Parthasarathy, M.D. Uchic, C. Woodward, Atomistic simulations of surface cross-slip nucleation in face-centered cubic nickel and copper. Acta Mater. 61, 2500 (2013)
S. Rao, D.M. Dimiduk, J.A. El-Awady, T.A. Parthasarathy, M.D. Uchic, C. Woodward, Screw dislocation cross slip at cross-slip plane jogs and screw dipole annihilation in FCC Cu and Ni investigated via atomistic simulations. Acta Mater. 101, 10–15 (2015)
I. Ryu, W.D. Nix, W. Cai, Plasticity of bcc micropillars controlled by competition between dislocation multiplication and depletion. Acta Mater. 61, 3233–3241 (2013)
K.W. Schwarz, Simulation of dislocations on the mesoscopic scale. I. Methods and examples. J. Appl. Phys. 85, 108–119 (1999)
K.W. Schwarz, Local rules for approximating strong dislocation interactions in discrete dislocation dynamics. Model. Simul. Mater. Sci. Eng. 11, 609–625 (2003)
P. Shanthraj, M.A. Zikry, Dislocation density evolution and interactions in crystalline materials. Acta Mater. 59, 7695–7702 (2011)
L.E. Shilkrot, R.E. Miller, W.A. Curtin, Coupled atomistic and discrete dislocation plasticity. Phys. Rev. Lett. 89 (2) 025501 (2002)
L.E. Shilkrot, R.E. Miller, W.A. Curtin, Multiscale plasticity modeling: coupled atomistics and discrete dislocation mechanics. J. Mech. Phys. Solids 52, 755–787 (2004)
R.B. Sills, W. Cai, Efficient time integration in dislocation dynamics. Model. Simul. Mater. Sci. Eng. 22, 025003 (2014)
R.B. Sills, W. Cai, Solute drag on perfect and extended dislocations. Philos. Mag. 96, 895–921 (2016)
R.B. Sills, A. Aghaei, W. Cai, Advanced time integration algorithms for dislocation dynamics simulations of work hardening. Model. Simul. Mater. Sci. Eng. 24, 045019 (2016)
A. Takahashi, N.M. Ghoniem, A computational method for dislocation-precipitate interaction. J. Mech. Phys. Solids 56, 1534–1553 (2008)
M. Tang, G. Xu, W. Cai, V.V. Bulatov, A hybrid method for computing forces on curved dislocations intersecting free surfaces in three-dimensional dislocation dynamics. Model. Simul. Mater. Sci. Eng. 14, 1139–1151 (2006)
TRIDIS: the edge-screw 3D Discrete Dislocation Dynamics code, http://www.numodis.com/tridis/index.html
E. van der Giessen, A. Needleman, Discrete dislocation plasticity: a simple planar model. Model. Simul. Mater. Sci. Eng. 3, 689–735 (1995)
A. Vattré, B. Devincre, A. Roos, Orientation dependence of plastic deformation in nickel-based single crystal superalloys: discrete-continuous model simulations. Acta Mater. 58, 1938–1951 (2010)
T. Vegge, T. Rasmussen, T. Leffers, O.B. Pedersen, K.W. Jacobsen, Atomistic simulations of cross-slip of jogged screw dislocations in copper. Philos. Mag. Lett. 81, 137 (2001)
M. Verdier, M. Fivel, I. Groma, Mesoscopic scale simulation of dislocation dynamics in fcc metals: Principles and applications. Model. Simul. Mater. Sci. Eng. 6, 755 (1998)
G. Wang, A. Strachan, T. Cagin, W.A. Goddard III, Molecular dynamics simulations of 1/2 a < 111 > screw dislocation in Ta. Mater. Sci. Eng. A 309–310, 133–137 (2001)
C.R. Weinberger, W. Cai, Computing image stress in an elastic cylinder. J. Mech. Phys. Solids 55, 2027–2054 (2007)
C.R. Weinberger, W. Cai, Surface-controlled dislocation multiplication in metal micropillars. Proc. Natl. Acad. Sci. 105, 38, 14304–14307 (2008)
C.R. Weinberger, S. Aubry, S.W. Lee, W.D. Nix, W. Cai, Modelling dislocations in a free-standing thin film. Model. Simul. Mater. Sci. Eng. 17, 075007 (2009)
D. Weygand, L.H. Friedman, E. van der Giessen, A. Needleman, Aspects of boundary-value problem solutions with three-dimensional dislocation dynamics. Model. Simul. Mater. Sci. Eng. 10, 437–468 (2002)
D. Weygand, M. Poignant, P. Gumbsch, O. Kraft, 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 483, 188–190 (2008)
H. Yasin, H.M. Zbib, M.A. Khaleel, Size and boundary effects in discrete dislocation dynamics: coupling with continuum finite element. Mater. Sci. Eng. A 309–310, 294–299 (2001)
S. Yefimov, I. Groma, E. van der Giessen, A comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity calculations. J. Mech. Phys. Solids 52, 279–300 (2004)
J. Yin, D.M. Barnett, W. Cai, Efficient computation of forces on dislocation segments in anisotropic elasticity. Model. Simul. Mater. Sci. Eng. 18, 045013 (2010)
C. Zhou, R. LeSar, Dislocation dynamics simulations of plasticity in polycrystalline thin films. Int. J. Plast. 30–31, 185–201 (2012)
X.W. Zhou, R.B. Sills, D.K. Ward, R.A. Karnesky, Atomistic calculation of dislocation core energy in aluminum (2016 in preparation)
Acknowledgements
We wish to thank Dr. Benoit Devincre for useful discussions. This work was supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award No. DE-SC0010412. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Sills, R.B., Kuykendall, W.P., Aghaei, A., Cai, W. (2016). Fundamentals of Dislocation Dynamics Simulations. In: Weinberger, C., Tucker, G. (eds) Multiscale Materials Modeling for Nanomechanics. Springer Series in Materials Science, vol 245. Springer, Cham. https://doi.org/10.1007/978-3-319-33480-6_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-33480-6_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-33478-3
Online ISBN: 978-3-319-33480-6
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)