Abstract
Over the past few decades, discrete dislocation dynamics, a modeling framework allowing for the simulation of the collective motion and interactions of dislocations in crystalline media, has been the subject of intense development worldwide. In recent years, a series of novel numerical algorithms, chemo-mechanical frameworks, and applications have been proposed. These advances have taken the field closer to enabling predictions of the mechanical response of engineering polycrystals, e.g., textured crystalline aggregates with impurities. Further, interesting pathways have been proposed to bridge discrete dislocation dynamics simulations with harmonic transition state theory, thereby delineating potential routes for performing coarse graining from the viewpoint of thermodynamics. This chapter summarizes some of the important recent contributions in the field of discrete dislocation dynamics.
References
Anderson PM, Hirth JP, Lothe J (2017) Theory of dislocations, 3rd edn. Cambridge University Press, New York
Arsenlis A, Cai W, Tang M, Rhee M, Oppelstrup T, Hommes G, Pierce TG, Bulatov VV (2007) Enabling strain hardening simulations with dislocation dynamics. Model Simul Mater Sci Eng 15:554–595
Aubry S, Arsenlis A (2013) Use of spherical harmonics for dislocation dynamics in anisotropic elastic media. Model Simul Mater Sci Eng 21:065013
Bacon DJ (1992) Dislocations in crystals. In: Gerold Va (ed) Materials science and technology: a comprehensive treatment, vol 1. Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, pp 411–482
Bako B, Clouet E, Dupuy LM, Bletry M (2011) Dislocation dynamics simulations with climb: kinetics of dislocation loop coarsening controlled by bulk diffusion. Philos Mag 91:3173–3191
Balint DS, Deshpande VS, Needleman A, Van der Giessen E (2008) Discrete dislocation plasticity analysis of the grain size dependence of the flow strength of polycrystals. Int J Plast 24:2149–2172
Bertin N, Capolungo L (2018) A FFT-based formulation for discrete dislocation dynamics in heterogeneous media. J Comput Phys 355(Supplement C):366–384
Bertin N, Upadhyay MV, Pradalier C, Capolungo L (2015) A FFT-based formulation for efficient mechanical fields computation in isotropic and anisotropic periodic discrete dislocation dynamics. Model Simul Mater Sci Eng 56:065009
Braislford A, Bullough R (1981) The theory of sink strengths. Philos Trans R Soc Lond Ser A Math Phys Sci 302:87–137
Bulatov VV, Cai W (2006) Computer simulations of dislocations. Oxford, New York
Bulatov VV, Hsiung LL, Tang M, Arsenlis A, Bartelt MC, Cai W, Florando JN, Hiratani M, Rhee M, Hommes G, Pierce TG, de la Rubia TD (2006) Dislocation multi-junctions and strain hardening. Nature 440:1174–1178
Cai W, Bulatov VV (2006) A non-singular continuum theory of dislocations. J Mech Phys Solids 54:561–587
Capolungo L, Spearot D, Cherkaoui M, McDowell D, Qu J, Jacob K (2007) Dislocation nucleation from bicrystal interfaces and grain boundary ledges: relationship to nanocrystalline deformation. J Mech Phys Solids 55:2300–2327
Chaussidon J, Robertson C, Rodney D, Fivel M (2008) Dislocation dynamics simulations of plasticity in fe laths at low temperature. Acta Mater 56:5466–5476
Clouet E, Ventelon L, Willaime F (2009) Dislocation core energies and core fields from first principles. Phys Rev Lett 102:055502
Danas K, Deshpande VS (2013) Plane-strain discrete dislocation plasticity with climb-assisted glide motion of dislocations. Model Simul Mater Sci Eng 21:045008
de Sansal C, Devincre B, Kubin L (2010) Grain size strengthening in microcrystalline copper: a three-dimensional dislocation dynamics simulation. In: Mechanical properties of solids XI. Key engineering materials, vol 423. Trans Tech Publications, Uetikon-Zuerich, pp 25–32
Devincre B, Kubin LP (1997) Mesoscopic simulations of dislocations and plasticity. Mater Sci Eng A 234–236:8–14
de Wit R (1960) The continuum theory of stationary dislocations. Solid State Phys 10:249–292
Fan H, Aubry S, Arsenlis A, El-Awady JA (2015a) Orientation influence on grain size effects in ultrafine-grained magnesium. Scr Mater 97:25–28
Fan H, Aubry S, Arsenlis A, El-Awady JA (2015b) The role of twinning deformation on the hardening response of polycrystalline magnesium from discrete dislocation dynamics simulations. Acta Mater 92:126–139
Fan H, Aubry S, Arsenlis A, El-Awady JA (2016) Grain size effects on dislocation and twinning mediated plasticity in magnesium. Scr Mater 112:50–52
Fivel M (2008a) Discrete dislocation dynamics: principles and recent applications. In: Cazacu O (ed) Multiscale modeling of heterogenous materials: from microstructure to macro-scale properties. Wiley, New York, pp 17–36
Fivel MC (2008b) Discrete dislocation dynamics: an important recent break-through in the modelling of dislocation collective behaviour. Comptes Rendus Physique 9:427–436
Froseth A, Derlet P, Swygenhoven HV (2004) Dislocations emitted from nanocrystalline grain boundaries: nucleation and splitting distance. Acta Mater 52:5863–5870
Frost H, Ashby M (1982) Deformation mechanism maps: the plasticity and creep of metals and ceramics. Pergamon Press, Oxford
Gao S, Fivel M, Ma A, Hartmaier A (2017) 3D discrete dislocation dynamics study of creep behavior in ni-base single crystal superalloys by a combined dislocation climb and vacancy diffusion model. J Mech Phys Solids 102:209–223
Gardner DJ, Woodward CS, Reynolds DR, Hommes G, Aubry S, Arsenlis A (2015) Implicit integration methods for dislocation dynamics. Model Simul Mater Sci Eng 23:025006
Geiser J (2009) Decomposition methods for differential equations. CRC Press, Boca Raton
Geslin PA, Gatti R, Devincre B, Rodney D (2017) Implementation of the nudged elastic band method in a dislocation dynamics formalism: application to dislocation nucleation. J Mech Phys Solids 108:49–67
Ghoniem NM, Sun LZ (1999) Fast-sum method for the elastic field off three-dimensional dislocation ensembles. Phys Rev B 60:128–140
Ghoniem N, Tong S, Sun L (2000) Parametric dislocation dynamics: a thermodynamics-based approach to investigations of mesoscopic plastic deformation. Phys Rev B 61:913–927
Graham JT, Rollett AD, LeSar R (2016) Fast-fourier transform discrete dislocation dynamics. Model Simul Mater Sci Eng 24:085005
Graham JT, LeSar R, Capolungo L (2019, in preparation) Discrete dislocation dynamics based polycrystal plasticity
Greer JR, Weinberger CR, Cai W (2008) Comparing the strength of f.c.c. and b.c.c. sub-micrometer pillars: compression experiments and dislocation dynamics simulations. Mater Sci Eng A 493:21–25
Henkelman G, Jonsson H (2000) Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J Chem Phys 113:9978–9985
Hirth J, Pond R (1996) Steps, dislocations and disconnections as interface defects relating to structure and phase transformations. Acta Mater 44:4749–4763
Hirth JP, Zbib HM, Lothe J (1998) Forces on high velocity dislocations. Model Simul Mater Sci Eng 6:165–169
Hoagland RG, Hirth JP, Misra A (2006) On the role of weak interfaces in blocking slip in nanoscale layered composites. Philos Mag 86:3537–3558
Hull D, Bacon DJ (2001) Introduction to dislocations, 4th edn. Butterworth Heinemann, Oxford
Jonsson H, Mills G, Jacobsen KW (1998) Nudged elastic band method for finding minimum energy paths of transitions. In: Berne BJ, Ciccotti G, Coker DF (eds.) Classical and Quantum Dynamics in Condensed Phase Simulations, World scientific, Singapore, pp 385–404
Keralavarma S, Benzerga A (2015) High-temperature discrete dislocation plasticity. J Mech Phys Solids 82:1–22
Keralavarma SM, Cagin T, Arsenlis A, Benzerga AA (2012) Power-law creep from discrete dislocation dynamics. Phys Rev Lett 109:265504
Kombaiah B, Murty KL (2015) High temperature creep and deformation microstructures in recrystallized zircaloy-4. Philos Mag B 95:1656–1679
Kubin LP (2013) Dislocations, mesoscale simulations and plastic flow. Oxford University Press, Oxford
Kubin LP, Canova G (1992) The modelling of dislocation patterns. Scr Met Mater 27:957–962
Lebensohn RA (2001) N-site modeling of a 3D viscoplastic polycrystal using fast fourier transform. Acta Mater 49:2723–2737
Lebensohn RA, Kanjarla KA, Eisenlohr P (2012) An elasto-viscoplastic formulation based on fast fourier transforms for the prediction of micromechanical fields in polycrystalline materials. Int J Plast 32–33:59–69
Lemarchand C, Devincre B, Kubin LP (2001) Homogenization method for a discrete-continuum simulation of dislocation dynamics. J Mech Phys Solids 49:1969–1982
LeSar R (2014) Simulations of dislocation structure and response. Ann Rev Condens Matter Phys 5:375–407. https://doi.org/10.1146/annurev-conmatphys-031113-133858
Liu B, Raabe D, Roters F, Eisenlohr P, Lebensohn RA (2010) Comparison of finite element and fast Fourier transform crystal plasticity solvers for texture prediction. Model Simul Mater Sci Eng 18:085005
Liu B, Arsenlis A, Aubry S (2016) Computing forces on interface elements exerted by dislocations in an elastically anisotropic crystalline material. Model Simul Mater Sci Eng 24:055013
Madec R, Devincre B, Kubin L, Hoc T, Rodney D (2003) The role of collinear interaction in dislocation-induced hardening. Science 301(5641):1879–1882
Marinica MC, Willaime F, Mousseau N (2011) Energy landscape of small clusters of self-interstitial dumbbells in iron. Phys Rev B 83:094119
McDowell DL (1997) Evolving structure and internal state variables. Nadai award lecture. ASME IMECE, Dallas
McDowell DL (1999) Non-associative aspects of multiscale evolutionary phenomena. In: Picu R, Krempl E (eds) Proceedings 4th international conference on constitutive laws for engineering materials. Rensselaer Polytechnic Institute, Troy, pp 54–57
Michel JC, Moulinec H, Suquet P (1999) Effective properties of composite materials with periodic microstructure: a computational approach. Comput Methods Appl Mech Eng 172:109–143
Misra A, Hirth J, Hoagland R (2005) Length-scale-dependent deformation mechanisms in incoherent metallic multilayered composites. Acta Mater 53:4817–4824
Mordehai D, Clouet E, Fivel M, Verdier M (2008) Introducing dislocation climb by bulk diffusion in discrete dislocation dynamics. Philos Mag 88:899–925
Morrow BM, Anderson KR, Kozar RW, Mills M (2013) An examination of the use of the modified jogged-screw model for predicting creep behavior in zircaloy-4. Acta Inf 61:4452–4460
Moulinec H, Suquet P (1998) A numerical method for computing the overall response of nonlinear composites with complex microstructure. Comput Methods Appl Mech Eng 157:69–94
Mousseau N, Barkema GT (1998) Traveling through potential energy landscapes of disordered materials: the activation-relaxation technique. Phys Rev E 57:2419–2424
Mura T (1987) Micromechanics of defects in solids. Martinus Nijhoff, Boston
Olmsted DL, Holm EA, Foiles SM (2009) Survey of computed grain boundary properties in face-centered cubic metals090000ii: grain boundary mobility. Acta Mater 57:3704–3713
Po G, Lazar M, Chandra Admal N, Ghoniem N (2017) A non-singular theory of dislocations in anisotropic crystals. arXiv 1706:00828
Prasad Reddy GV, Robertson C, Depres C, Fivel M (2013) Effect of grain disorientation on early fatigue crack propagation in face-centred-cubic polycrystals: a three-dimensional dislocation dynamics investigation. Acta Materialia 61:5300–5310
Quek SS, Wu ZX, Zhang YW, Srolovitz DJ (2014) Polycrystal deformation in a discrete dislocation dynamics framework. Acta Mater 75:92–105
Quek SS, Chooi ZH, Wu Z, Zhang YW, Srolovitz DJ (2016) The inverse hall-petch relation in nanocrystalline metals: a discrete dislocation dynamics analysis. J Mech Phys Solids 88(Supplement C):252–266
Sangid MD, Ezaz T, Sehitoglu H, Robertson IM (2011) Energy of slip transmission and nucleation at grain boundaries. Acta Mater 59:283–296
Saroukhani S, Nguyen LD, Leung KWK, Singh CV, Warner DH (2016) Harnessing atomistic simulations to predict the rate at which dislocations overcome obstacles. J Mech Phys Solids 90:203–214
Serra A, Bacon D (1995) Computer simulation of screw dislocation interactions with twin boundaries in h.c.p. metals. Acta Met Mater 43:4465–4481
Serra A, Bacon D, Pond R (1999) Dislocations in interfaces in the h.c.p. metals090000i. Defects formed by absorption of crystal dislocations. Acta Mater 47:1425–1439
Sills RB, Aubry S (2018) Dislocation dynamics simulations of materials with complex physics. In: Andreoni W, Yip S (eds) Handbook of materials modeling, 2nd edn. Springer, Dordrecht, p xxx
Sills RB, Cai W (2014) Efficient time integration in dislocation dynamics. Model Simul Mater Sci Eng 22:025003
Sills RB, Aghaei A, Cai W (2016a) Advanced time integration algorithms for dislocation dynamics simulations of work hardening. Model Simul Mater Sci Eng 24:045019
Sills RB, Kuykendall WP, A AA, Cai W (2016b) Fundamentals of dislocation dynamics simulations. In: Weinberger CR, Tucker GJ (eds) Multiscale materials modeling for nanomechanics. Springer, Cham, p 5317
Siška F, Weygand D, Forest S, Gumbsch P (2009) Comparison of mechanical behaviour of thin film simulated by discrete dislocation dynamics and continuum crystal plasticity. Comput Mater Sci 45:793–799
Sobie C, McPhie MG, Capolungo L, Cherkaoui M (2014) The effect of interfaces on the mechanical behaviour of multilayered metallic laminates. Model Simul Mater Sci Eng 22:045007
Sobie C, Bertin N, Capolungo L (2015) Analysis of obstacle hardening models using dislocation dynamics: application to irradiation-induced defects. Met Mater Trans A 46:3761–3772
Sobie C, Capolungo L, McDowell DL, Martinez E (2017a) Modal analysis of dislocation vibration and reaction attempt frequency. Acta Mater 134:203–210
Sobie C, Capolungo L, McDowell DL, Martinez E (2017b) Scale transition using dislocation dynamics and the nudged elastic band method. J Mech Phys Solids 105:161–178
Sobie C, Capolungo L, McDowell DL, Martinez E (2017c) Thermal activation of dislocations in large scale obstacle bypass. J Mech Phys Solids 105:150–160
Vattré A (2017) Elastic strain relaxation in interfacial dislocation patterns: a parametric energy-based framework. J Mech Phys Solids 105(Supplement C):254–282
Vattré A, Pan EN (2017) Interaction between semicoherent interfaces and volterra-type dislocations in dissimilar anisotropic materials. J Mater Res 32:3947–3957
Vattré A, Devincre B, Feyel F, Gatti R, Groh S, Jamond O, Roos A (2014a) Modelling crystal plasticity by 3d dislocation dynamics and the finite element method: the discrete-continuous model revisited. J Mech Phys Solids 63:491–505
Vattré AJ, Abdolrahim N, Kolluri K, Demkowicz MJ (2014b) Computational design of patterned interfaces using reduced order models. Nat Sci Rep 4:1
Verdier M, Fivel M, Groma I (1998) Mesoscopic scale simulation of dislocation dynamics in fcc metals: principles and applications. Model Simul Mater Sci Eng 6:755–770
Wang HY, LeSar R (1995) O(N) algorithm for dislocation dynamics. Philos Mag A 71:149–164
Wang Z, Ghoniem NM, Swaminarayan S, LeSar R (2006) A parallel algorithm for 3D dislocation dynamics. J Comput Phys 219:608–621
Wang ZQ, Beyerlein IJ, LeSar R (2007) Dislocation motion in high-strain-rate deformation. Philos Mag 87(16):2263–2279
Wang J, Zhou C, Beyerlein IJ, Shao S (2014) Modeling interface-dominated mechanical behavior of nanolayered crystalline composites. JOM 66:102–113
Weygand D, Friedman LH, der Giessen EV, Needleman A (2002) Aspects of boundary-value problem solutions with three-dimensional dislocation dynamics. Model Simul Mater Sci Eng 10:437
Yin J, Barnett DM, Cai W (2010) Efficient computation of forces on dislocation segments in anisotropic elasticity. Model Simul Mater Sci Eng 18:045013
Zbib HM, de la Rubia TD, Rhee M, Hirth JP (2000) 3D dislocation dynamics: stress-strain behavior and hardening mechanisms in fcc and bcc metals. J Nucl Mater 276:154–165
Zheng Z, Balint DS, Dunne FPE (2016) Discrete dislocation and crystal plasticity analyses of load shedding in polycrystalline titanium alloys. Int J Plast 87:15–31
Zhou CZ, LeSar R (2012) Dislocation dynamics simulations of plasticity in polycrystalline thin films. Int J Plast 30–31:185–201
Zhu T, Li J, Samanta A, Leach A, Gall K (2008) Temperature and strain-rate dependence of surface dislocation nucleation. Phys Rev Lett 100:025502
Acknowledgements
RL wants to acknowledge the support of the National Science Foundation under Award Number DMR-1308430 for development of an FFT-based dislocation dynamics method. His work on polycrystal plasticity development was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Science and Engineering Division and was performed at the Ames Laboratory, which is operated for the U.S. DOE by Iowa State University under contract # DE-AC02-07CH11358. LC would like thank support from the US Department of Energy, Office of Basic Energy Sciences (OBES) FWP-06SCPE401.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this entry
Cite this entry
LeSar, R., Capolungo, L. (2018). Advances in Discrete Dislocation Dynamics Simulations. In: Andreoni, W., Yip, S. (eds) Handbook of Materials Modeling . Springer, Cham. https://doi.org/10.1007/978-3-319-42913-7_85-1
Download citation
DOI: https://doi.org/10.1007/978-3-319-42913-7_85-1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-42913-7
Online ISBN: 978-3-319-42913-7
eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics