Advances in Discrete Dislocations Dynamics and Multiscale Modeling

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.

[1]  V. S. Deshpandea,et al.  Discrete dislocation plasticity analysis of the wedge indentation of films , 2006 .

[2]  Lallit Anand,et al.  A constitutive model for hcp materials deforming by slip and twinning: application to magnesium alloy AZ31B , 2003 .

[3]  D. Bacon A Method for Describing a Flexible Dislocation , 1967, October 1.

[4]  Hussein M. Zbib,et al.  Multiscale dislocation dynamics simulations of shock compression in copper single crystal , 2005 .

[5]  Steven J. Plimpton,et al.  LENGTH SCALE AND TIME SCALE EFFECTS ON THE PLASTIC FLOW OF FCC METALS , 2001 .

[6]  Harold S. Park,et al.  An introduction to computational nanomechanics and materials , 2004 .

[7]  K. Schwarz,et al.  Simulation of dislocations on the mesoscopic scale. I. Methods and examples , 1999 .

[8]  H. Zbib,et al.  Dislocation dynamics simulations of the interaction between a short rigid fiber and a glide circular dislocation pile-up , 2002 .

[9]  J. Belak On the nucleation and growth of voids at high strain-rates , 1998 .

[10]  V. Bulatov,et al.  Dislocation Image Stresses at Free Surfaces by the Finite Element Method , 2003 .

[11]  M Verdieryk Mesoscopic scale simulation of dislocation dynamics in fcc metals: Principles and applications , 1998 .

[12]  A. Needleman,et al.  A discrete dislocation analysis of rate effects on mode I crack growth , 2001 .

[13]  K. Schwarz,et al.  Simulation of dislocations on the mesoscopic scale. II. Application to strained-layer relaxation , 1999 .

[14]  Chan-Sun Shin,et al.  Numerical methods to improve the computing efficiency of discrete dislocation dynamics simulations , 2006, J. Comput. Phys..

[15]  Doris Kuhlmann-Wilsdorf,et al.  Theory of plastic deformation: - properties of low energy dislocation structures , 1989 .

[16]  F. Feyel,et al.  Discrete-Continuum Modeling of Metal Matrix Composites Plasticity , 2004 .

[17]  Huajian Gao,et al.  Indentation size effects in crystalline materials: A law for strain gradient plasticity , 1998 .

[18]  L. Kubin,et al.  Dislocation patterns and the similitude principle: 2.5D mesoscale simulations. , 2006, Physical review letters.

[19]  Hussein M. Zbib,et al.  Models for long-/short-range interactions and cross slip in 3D dislocation simulation of BCC single crystals , 1998 .

[20]  Yoshiyuki Kawazoe,et al.  Mesoscopic Dynamics of Fracture , 1998 .

[21]  Minna Karstunen,et al.  Micromechanical analysis of kinematic hardening in natural clay , 2009 .

[22]  Oliver Kraft,et al.  Discrete dislocation simulations of the plasticity of micro-pillars under uniaxial loading , 2008 .

[23]  H. Espinosa,et al.  Dislocation-source shutdown and the plastic behavior of single-crystal micropillars. , 2008, Physical review letters.

[24]  Stephen Roberts,et al.  Three-Dimensional simulation of dislocation-crack interactions in b.c.c. metals at the mesoscopic scale , 1996 .

[25]  Laurent Tabourot,et al.  Generalised constitutive laws for f.c.c. single crystals , 1997 .

[26]  Ladislas P. Kubin,et al.  New Line Model for Optimized Dislocation Dynamics Simulations , 2000 .

[27]  H. Zbib,et al.  Discrete dislocation dynamics simulation of cutting of γ′ precipitate and interfacial dislocation network in Ni-based superalloys , 2006 .

[28]  Tariq Khraishi,et al.  Localized deformation and hardening in irradiated metals: Three-dimensional discrete dislocation dynamics simulations , 2002 .

[29]  Hussein M. Zbib,et al.  On plastic deformation and the dynamics of 3D dislocations , 1998 .

[30]  D. Dimiduk,et al.  Sample Dimensions Influence Strength and Crystal Plasticity , 2004, Science.

[31]  van der Erik Giessen,et al.  Incorporating three-dimensional mechanisms into two-dimensional dislocation dynamics , 2004 .

[32]  M. Tang,et al.  Dislocation mobility and the mechanical response of b.c.c. single crystals: A mesoscopic approach , 1998 .

[33]  David L. Olmsted,et al.  Atomistic simulations of dislocation mobility in Al, Ni and Al/Mg alloys , 2005 .

[34]  Zhiqiang Wang,et al.  A parallel algorithm for 3D dislocation dynamics , 2006, J. Comput. Phys..

[35]  D. Rodney,et al.  Phase Field Methods and Dislocationss , 2000 .

[36]  William A. Curtin,et al.  Multiscale plasticity modeling: coupled atomistics and discrete dislocation mechanics , 2004 .

[37]  L. M. Brown The self-stress of dislocations and the shape of extended nodes , 1964 .

[38]  Michael D. Uchic,et al.  A methodology to investigate size scale effects in crystalline plasticity using uniaxial compression testing , 2005 .

[39]  M. Fivel,et al.  Low-strain fatigue in AISI 316L steel surface grains: a three-dimensional discrete dislocation dynamics modelling of the early cycles I. Dislocation microstructures and mechanical behaviour , 2004 .

[40]  S. Kalidindi Incorporation of deformation twinning in crystal plasticity models , 1998 .

[41]  N. Ghoniem,et al.  The Influence of Crystal Surfaces on Dislocation Interactions in Mesoscopic Plasticity: A Combined Dislocation Dynamics- Finite Element Approach , 2002 .

[42]  Tetsuya Ohashi,et al.  Numerical modelling of plastic multislip in metal crystals of f.c.c. type , 1994 .

[43]  Jaafar A. El-Awady,et al.  A self-consistent boundary element, parametric dislocation dynamics formulation of plastic flow in finite volumes , 2008 .

[44]  Michael D. Uchic,et al.  Size-affected single-slip behavior of pure nickel microcrystals , 2005 .

[45]  Lem,et al.  Dislocation mechanisms, microstructures and hardening 1 FROM DISLOCATION MECHANISMS TO DISLOCATION MICROSTRUCTURES AND STRAIN HARDENING , 2001 .

[46]  H. Zbib,et al.  Modeling planar dislocation boundaries using multi-scale dislocation dynamics plasticity , 2004 .

[47]  Huajian Gao,et al.  Geometrically necessary dislocation and size-dependent plasticity , 2003 .

[48]  Ghodrat Karami,et al.  MULTISCALE DISLOCATION DYNAMICS PLASTICITY , 2003 .

[49]  H. Zbib,et al.  Simulation of shock-induced plasticity including homogeneous and heterogeneous dislocation nucleations , 2006 .

[50]  Y. Le Bouar,et al.  Quantitative Phase Field Modeling of Precipitation Processes , 2006 .

[51]  Yu U. Wang,et al.  Phase field microelasticity modeling of dislocation dynamics near free surface and in heteroepitaxial thin films , 2003 .

[52]  A. Cottrell,et al.  LX. A mechanism for the growth of deformation twins in crystals , 1951 .

[53]  Vasily V. Bulatov,et al.  A hybrid method for computing forces on curved dislocations intersecting free surfaces in three-dimensional dislocation dynamics , 2006 .

[54]  Z. Zhuang,et al.  A multi-scale computational model of crystal plasticity at submicron-to-nanometer scales , 2009 .

[55]  D. Kuhlmann-wilsdorf Technological high strain deformation of 'wavy glide' metals and LEDS , 1995 .

[56]  A. Moulin,et al.  Simulation of Frank-Read sources in silicon , 1997 .

[57]  Robert E. Rudd,et al.  Void nucleation and associated plasticity in dynamic fracture of polycrystalline copper: an atomistic simulation , 2002 .

[58]  Mark F. Horstemeyer,et al.  Multiscale modeling of the plasticity in an aluminum single crystal , 2009 .

[59]  Hussein M. Zbib,et al.  3D dislocation dynamics: stress–strain behavior and hardening mechanisms in fcc and bcc metals , 2000 .

[60]  A. J. E. Foreman,et al.  The bowing of a dislocation segment , 1967 .

[61]  H. Brehm,et al.  A dislocation density based material model to simulate the anisotropic creep behavior of single-phase and two-phase single crystals , 2009 .

[62]  van der Erik Giessen,et al.  Incorporating three-dimensional mechanisms into two-dimensional dislocation dynamics (vol 12, pg 159, 2004) Erratum , 2004 .

[63]  I. Beyerlein,et al.  Plastic anisotropy in fcc single crystals in high rate deformation , 2009 .

[64]  E. Vanden-Eijnden,et al.  The Heterogeneous Multiscale Method: A Review , 2007 .

[65]  Ladislas P. Kubin,et al.  Simulation of dislocation patterns in multislip , 2002 .

[66]  L. Kubin,et al.  Dislocation Intersections and Reactions in FCC and BCC Crystals , 2003 .

[67]  J. Chaboche,et al.  Size effects in metal matrix composites , 2005 .

[68]  U. F. Kocks,et al.  A Mechanism for Static and Dynamic Recovery , 1979 .

[69]  Ronald E. Miller,et al.  Atomistic/continuum coupling in computational materials science , 2003 .

[70]  Athanasios Arsenlis,et al.  Enabling strain hardening simulations with dislocation dynamics , 2006 .

[71]  Ladislas P. Kubin,et al.  Homogenization method for a discrete-continuum simulation of dislocation dynamics , 2001 .

[72]  Vasily V. Bulatov,et al.  Dislocation multi-junctions and strain hardening , 2006, Nature.

[73]  Huajian Gao,et al.  Generalized stacking fault energies for embedded atom FCC metals , 2000 .

[74]  Ladislas P. Kubin,et al.  Dislocation Microstructures and Plastic Flow: A 3D Simulation , 1992 .

[75]  Thierry Hoc,et al.  Physical analyses of crystal plasticity by DD simulations , 2006 .

[76]  Nasr M. Ghoniem,et al.  Fast-sum method for the elastic field of three-dimensional dislocation ensembles , 1999 .

[77]  M. Véron,et al.  Thermodynamics, microstructures, and plasticity , 2003 .

[78]  Tariq Khraishi,et al.  Free-Surface Effects in 3D Dislocation Dynamics: Formulation and Modeling , 2002 .

[79]  Vasily V. Bulatov,et al.  A Multiscale Model of Plasticity Based on Discrete Dislocation Dynamics , 2002 .

[80]  M. Horstemeyer,et al.  Dislocation motion in magnesium: a study by molecular statics and molecular dynamics , 2009 .

[81]  Ladislas P. Kubin,et al.  Mesoscopic simulations of plastic deformation , 2001 .

[82]  Jaime Marian,et al.  Dynamic transitions from smooth to rough to twinning in dislocation motion , 2004, Nature materials.

[83]  Andrew M Minor,et al.  Mechanical annealing and source-limited deformation in submicrometre-diameter Ni crystals. , 2008, Nature materials.

[84]  Julia R. Greer,et al.  Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients , 2005 .

[85]  L E Shilkrot,et al.  Coupled atomistic and discrete dislocation plasticity. , 2002, Physical review letters.

[86]  K. Schwarz,et al.  Modelling of dislocations intersecting a free surface , 2005 .

[87]  Nasr M. Ghoniem,et al.  Affine covariant-contravariant vector forms for the elastic field of parametric dislocations in isotropic crystals , 2002 .

[88]  A. Needleman,et al.  Plasticity size effects in tension and compression of single crystals , 2005 .

[89]  Oliver Kraft,et al.  Three-dimensional dislocation dynamics simulation of the influence of sample size on the stress–strain behavior of fcc single-crystalline pillars , 2008 .

[90]  Michael D. Uchic,et al.  Contribution to size effect of yield strength from the stochastics of dislocation source lengths in finite samples , 2007 .

[91]  Benoit Devincre,et al.  Slip systems interactions in α-iron determined by dislocation dynamics simulations , 2009 .

[92]  L. Kubin,et al.  Dislocation study of prismatic slip systems and their interactions in hexagonal close packed metals: application to zirconium , 2004 .

[93]  Hussein M. Zbib,et al.  Modeling of deformation by a 3D simulation of multiple, curved dislocations , 1996 .

[94]  H. Zbib,et al.  Forces on high velocity dislocations , 1998 .

[95]  M. Fivel,et al.  Low-strain fatigue in 316L steel surface grains: a three dimension discrete dislocation dynamics modelling of the early cycles. Part 2: Persistent slip markings and micro-crack nucleation , 2006 .

[96]  N. Ghoniem,et al.  Dislocation dynamics. I. A proposed methodology for deformation micromechanics. , 1990, Physical review. B, Condensed matter.

[97]  van der Erik Giessen,et al.  GNDs in nonlocal plasticity theories: lessons from discrete dislocation simulations , 2003 .

[98]  van der Erik Giessen,et al.  Discrete dislocation plasticity: a simple planar model , 1995 .

[99]  A. Needlemana,et al.  Discrete dislocation modeling of fatigue crack propagation , 2002 .

[100]  V. Bulatov,et al.  Periodic Boundary Conditions for Dislocation Dynamics Simulations in Three Dimensions , 2000 .

[101]  N. Mott,et al.  Report of a Conference on Strength of Solids , 1948 .

[102]  F. Frank,et al.  On deformation by twinning , 1955 .

[103]  H. Zbib,et al.  Interactions between glide dislocations and parallel interfacial dislocations in nanoscale strained layers , 2007 .

[104]  Laurent Tabourot,et al.  Identification through mesoscopic simulations of macroscopic parameters of physically based constitutive equations for the plastic behaviour of fcc single crystats , 1998 .

[105]  H. Zbib,et al.  Internal structures of deformation induced planar dislocation boundaries , 2001 .

[106]  A. Needleman,et al.  Fatigue crack growth from a cracked elastic particle into a ductile matrix , 2008 .

[107]  E. B. Marin,et al.  On modelling the elasto-viscoplastic response of metals using polycrystal plasticity , 1998 .

[108]  Vasily V. Bulatov,et al.  Dislocation stress fields for dynamic codes using anisotropic elasticity: methodology and analysis , 2001 .

[109]  van der Erik Giessen,et al.  Aspects of boundary-value problem solutions with three-dimensional dislocation dynamics , 2002 .

[110]  J. Greer,et al.  Nanoscale gold pillars strengthened through dislocation starvation , 2006 .

[111]  C. A. Volkert,et al.  Size effects in the deformation of sub-micron Au columns , 2006 .

[112]  Jens Lothe John Price Hirth,et al.  Theory of Dislocations , 1968 .

[113]  P. Franciosi,et al.  The concepts of latent hardening and strain hardening in metallic single crystals , 1985 .

[114]  L. Kubin,et al.  Modeling the plastic deformation of olivine by dislocation dynamics simulations , 2007 .

[115]  Enrique Martínez,et al.  Atomistically informed dislocation dynamics in fcc crystals , 2006, Journal of the Mechanics and Physics of Solids.

[116]  J. H. Palm Stress-strain relations for uniaxial loading , 1949 .

[117]  Marc Fivel,et al.  Implementing image stresses in a 3D dislocation simulation , 1996 .

[118]  Z. Zhuang,et al.  Atypical three-stage-hardening mechanical behavior of Cu single-crystal micropillars , 2009 .

[119]  V. Bulatov,et al.  Connecting atomistic and mesoscale simulations of crystal plasticity , 1998, Nature.

[120]  A. Needleman,et al.  A discrete dislocation analysis of mode I crack growth , 2000 .

[121]  H. Zbib,et al.  Modelling of irradiation-induced hardening in metals using dislocation dynamics , 2001 .

[122]  V. S. Deshpandea,et al.  Scaling of discrete dislocation predictions for near-threshold fatigue crack growth , 2003 .

[123]  Surya R. Kalidindi,et al.  Strain hardening due to deformation twinning in α-titanium : Constitutive relations and crystal-plasticity modeling , 2005 .

[124]  H. Espinosa,et al.  Dislocation escape-related size effects in single-crystal micropillars under uniaxial compression , 2007 .

[125]  H. Zbib,et al.  Dislocation dynamics analysis of dislocation intersections in nanoscale metallic multilayered composites , 2007 .

[126]  Jaafar A. El-Awady,et al.  The role of the weakest-link mechanism in controlling the plasticity of micropillars , 2009 .

[127]  David L. McDowell,et al.  Microstructure-sensitive modeling of polycrystalline IN 100 , 2008 .

[128]  J. Chaboche,et al.  Dislocations and elastic anisotropy in heteroepitaxial metallic thin films , 2003 .

[129]  Marc Fivel,et al.  Dislocation–impenetrable precipitate interaction: a three-dimensional discrete dislocation dynamics analysis , 2003 .

[130]  Masato Kawamukai,et al.  A multiscale approach for modeling scale-dependent yield stress in polycrystalline metals , 2007 .

[131]  J. G. Sevillano Substructure and strengthening of heavily deformed single and two-phase metallic materials , 1991 .

[132]  J. Kratochvíl,et al.  Estimate of Stress in the Channel of Persistent Slip Bands Based on Dislocation Dynamics , 2007 .

[133]  A. Needleman,et al.  Surface versus bulk nucleation of dislocations during contact , 2007 .

[134]  D Rodney,et al.  The Role of Collinear Interaction in Dislocation-Induced Hardening , 2003, Science.

[135]  M. Baskes,et al.  Semi-Empirical Potential Methods for Atomistic Simulations of Metals and Their Construction Procedures , 2009 .

[136]  Hussein M. Zbib,et al.  Analysis of heterogeneous deformation and dislocation dynamics in single crystal micropillars under compression , 2010 .

[137]  L. Kubin,et al.  Second-order junctions and strain hardening in bcc and fcc crystals , 2008 .

[138]  J. Kratochvíl,et al.  Interactions of glide dislocations in a channel of a persistent slip band , 2007 .

[139]  Moe Khaleel,et al.  Size and boundary effects in discrete dislocation dynamics: coupling with continuum finite element , 2001 .

[140]  P Chadwick Theoretical and Applied Mechanics: Proceedings of the 13th International Congress of Theoretical and Applied Mechanics , 1974 .

[141]  Marc Fivel,et al.  Three-dimensional computation of the interaction between a straight dislocation line and a particle , 2005 .

[142]  U. F. Kocks,et al.  Physics and phenomenology of strain hardening: the FCC case , 2003 .

[143]  E. Voce,et al.  The relationship between stress and strain for homogeneous deformations , 1948 .

[144]  Benoit Devincre,et al.  Three dimensional stress field expressions for straight dislocation segments , 1995 .

[145]  Vito Volterra,et al.  Sur l'équilibre des corps élastiques multiplement connexes , 1907 .

[146]  Richard Alan Lesar,et al.  The importance of cross-slip in high-rate deformation , 2007 .