An efficient 2D discrete dislocation Dynamics-XFEM coupling framework and its application to polycrystal plasticity

Abstract A new efficient framework coupling the two dimensional (2D) discrete dislocation dynamics (DDD) and the extended finite element method (XFEM) is developed for modeling the dynamic evolution of multiple dislocations in crystalline materials with abundant interfaces/surfaces. By a specially introduced stress calculation scheme with cut-off radius and virtual elements, the present algorithm can capture interaction between neighboring dislocations accurately although no time-consuming dislocation-core enrichment is employed. Since it is not sensitive to the FE mesh size and large XFEM time step can be used, its efficiency is evidently improved compared with other DDD frameworks. Due to the merits of XFEM itself, the present DDD-XFEM scheme can treat intractable surface/interface problems conveniently, with no additional image stress calculation as in the DDD-FEM superposition framework and special plastic-strain distribution near the surfaces/interfaces as in the discrete-continuous method (DCM) needed. For these, it can be used to model plastic behaviors of crystals with abundant interfaces/surfaces (i.e. grain/phase boundaries and crack/void surfaces). To show the ability of present DDD-XFEM scheme, it is used to simulate the mechanical responses of polycrystalline aluminum with assumed rigid and penetrable grain boundaries. A three-stage model for dislocation penetrating through grain boundary (DPTGB) is suggested. The results show that the present DDD-XFEM scheme can capture the formation of dislocation pile-ups and thus the Hall-Petch effect successfully. The DPTGB can decrease the flow stress and hardening rate evidently; moreover, it can weaken the grain size effect and may enhance the cyclic stress relaxation of polycrystals greatly.

[1]  E. Holm,et al.  Comparing grain boundary energies in face-centered cubic metals: Al, Au, Cu and Ni , 2010 .

[2]  Cédric Pradalier,et al.  A FFT-based formulation for efficient mechanical fields computation in isotropic and anisotropic periodic discrete dislocation dynamics , 2015 .

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

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

[5]  Akiyuki Takahashi,et al.  A computational method for dislocation-precipitate interaction , 2008 .

[6]  H. Duan,et al.  The depth dependent hardness of bicrystals with dislocation transmission through grain boundaries: A theoretical model , 2017 .

[7]  Y. Liu,et al.  Creep behavior as dislocation climb over NiAl nanoprecipitates in ferritic alloy: The effects of interface stresses and temperature , 2015 .

[8]  G. Monnet,et al.  Modeling crystal plasticity with dislocation dynamics simulations: The ’microMegas’ code , 2011 .

[9]  V. Levitas,et al.  Slip of shuffle screw dislocations through tilt grain boundaries in silicon , 2019, Computational Materials Science.

[10]  F. Dunne,et al.  Mechanistic basis of temperature-dependent dwell fatigue in titanium alloys , 2017 .

[11]  Minsheng Huang,et al.  The influence of dislocation climb on the mechanical behavior of polycrystals and grain size effect at elevated temperature , 2014 .

[12]  R. LeSar,et al.  Multipole expansion of dislocation interactions: Application to discrete dislocations , 2002 .

[13]  Minsheng Huang,et al.  Discrete dislocation analyses of circular nanoindentation and its size dependence in polycrystals , 2008 .

[14]  J. Vlassak,et al.  Dislocation climb in two-dimensional discrete dislocation dynamics , 2012 .

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

[16]  Marc A. Meyers,et al.  Void growth by dislocation emission , 2004 .

[17]  Ted Belytschko,et al.  Fast integration and weight function blending in the extended finite element method , 2009 .

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

[19]  Minsheng Huang,et al.  Strengthening mechanism in micro-polycrystals with penetrable grain boundaries by discrete dislocation dynamics simulation and Hall-Petch effect , 2009 .

[20]  J. El-Awady,et al.  Grain size effects on dislocation and twinning mediated plasticity in magnesium , 2016 .

[21]  T. Záležák,et al.  High temperature dislocation processes in precipitation hardened crystals investigated by a 3D discrete dislocation dynamics , 2017 .

[22]  Nicolas Bertin,et al.  Connecting discrete and continuum dislocation mechanics: A non-singular spectral framework , 2018, International Journal of Plasticity.

[23]  P. Lin,et al.  Numerical investigations of helical dislocations based on coupled glide-climb model , 2017 .

[24]  W. Cai,et al.  Massively-Parallel Dislocation Dynamics Simulations , 2004 .

[25]  Z. Zhuang,et al.  Modeling high temperature anneal hardening in Au submicron pillar by developing coupled dislocation glide-climb model , 2017 .

[26]  W. Cai,et al.  Modeling of dislocation-grain boundary interactions in FCC metals , 2003 .

[27]  Yaxin Zhu,et al.  Simulation on crack propagation vs. crack-tip dislocation emission by XFEM-based DDD scheme , 2019, International Journal of Plasticity.

[28]  R. Hoagland,et al.  Mechanics of nanoscale metallic multilayers: From atomic-scale to micro-scale , 2009 .

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

[30]  Peter Gumbsch,et al.  Dislocation sources in discrete dislocation simulations of thin-film plasticity and the Hall-Petch relation , 2001 .

[31]  Minsheng Huang,et al.  Modeling of abnormal mechanical properties of nickel-based single crystal superalloy by three-dimensional discrete dislocation dynamics , 2014 .

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

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

[34]  Minsheng Huang,et al.  The key role of dislocation dissociation in the plastic behaviour of single crystal nickel-based superalloy with low stacking fault energy: Three-dimensional discrete dislocation dynamics modelling , 2013 .

[35]  Ted Belytschko,et al.  On XFEM applications to dislocations and interfaces , 2007 .

[36]  Julia R. Greer,et al.  Plasticity in small-sized metallic systems: Intrinsic versus extrinsic size effect , 2011 .

[37]  J. Xue,et al.  A size-dependent tensorial plasticity model for FCC single crystal with irradiation , 2015 .

[38]  V. Levitas,et al.  Amorphization induced by 60° shuffle dislocation pileup against different grain boundaries in silicon bicrystal under shear , 2019, Acta Materialia.

[39]  F. Dunne,et al.  Investigation of slip transfer across HCP grain boundaries with application to cold dwell facet fatigue , 2017 .

[40]  Dierk Raabe,et al.  Simulation of dislocation penetration through a general low-angle grain boundary , 2012 .

[41]  Minsheng Huang,et al.  Coupled DDD–FEM modeling on the mechanical behavior of microlayered metallic multilayer film at elevated temperature , 2015 .

[42]  A. Benzerga,et al.  A discrete dislocation analysis of strengthening in bilayer thin films , 2006 .

[43]  Minsheng Huang,et al.  Cylindrical nano-indentation on metal film/elastic substrate system with discrete dislocation plasticity analysis: A simple model for nano-indentation size effect , 2010 .

[44]  Z. Zhuang,et al.  Developing micro-scale crystal plasticity model based on phase field theory for modeling dislocations in heteroepitaxial structures , 2016 .

[45]  E. Arzt.  Size effects in materials due to microstructural and dimensional constraints: a comparative review , 1998 .

[46]  Ted Belytschko,et al.  An extended finite element method for dislocations in complex geometries: Thin films and nanotubes , 2009 .

[47]  Vasily V. Bulatov,et al.  Grain boundary energy function for fcc metals , 2014 .

[48]  Minsheng Huang,et al.  Discrete dislocation dynamics modelling of microvoid growth and its intrinsic mechanism in single crystals , 2007 .

[49]  Xiaoyu Jiang,et al.  Revealing the inhibition mechanism of grain size gradient on crack growth in gradient nano-grained materials , 2019, International Journal of Solids and Structures.

[50]  Jie Yin,et al.  Computing dislocation stress fields in anisotropic elastic media using fast multipole expansions , 2012 .

[51]  G. Hasson,et al.  Interfacial energies of tilt boundaries in aluminium. Experimental and theoretical determination , 1971 .

[52]  Ted Belytschko,et al.  On a new extended finite element method for dislocations: Core enrichment and nonlinear formulation , 2008 .

[53]  G. Po,et al.  A coupled dislocation dynamics-continuum barrier field model with application to irradiated materials , 2018 .

[54]  Benoit Devincre,et al.  Consistent formulation for the Discrete-Continuous Model: Improving complex dislocation dynamics simulations , 2016 .

[55]  Yong-Wei Zhang,et al.  The inverse hall–petch relation in nanocrystalline metals: A discrete dislocation dynamics analysis , 2016 .

[56]  Minsheng Huang,et al.  Cyclic Hardening Behavior of Polycrystals with Penetrable Grain Boundaries: Two-Dimensional Discrete Dislocation Dynamics Simulation , 2009 .

[57]  M. Fivel,et al.  Developing rigorous boundary conditions to simulations of discrete dislocation dynamics , 1999 .

[58]  Yinan Cui,et al.  Quantitative investigations on dislocation based discrete-continuous model of crystal plasticity at submicron scale , 2015 .

[59]  Vikram Deshpande,et al.  Climb-enabled discrete dislocation plasticity , 2014 .

[60]  James R. Rice,et al.  Ductile versus brittle behaviour of crystals , 1974 .

[61]  Giacomo Po,et al.  A non-singular theory of dislocations in anisotropic crystals , 2017, 1706.00828.

[62]  G. Po,et al.  The role of slow screw dislocations in controlling fast strain avalanche dynamics in body-centered cubic metals , 2020, International Journal of Plasticity.

[63]  A. Hartmaier,et al.  A two-dimensional dislocation dynamics model of the plastic deformation of polycrystalline metals , 2010 .

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

[65]  A. Needleman,et al.  Discrete dislocation plasticity analysis of the wedge indentation of films , 2006, Journal of the Mechanics and Physics of Solids.

[66]  A. Needleman,et al.  Discrete dislocation plasticity analysis of the grain size dependence of the flow strength of polycrystals , 2008 .

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

[68]  Minsheng Huang,et al.  An extended 3D discrete-continuous model and its application on single- and bi-crystal micropillars , 2017 .

[69]  W. Curtin,et al.  A Superposition Framework for Discrete Dislocation Plasticity , 2004 .

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

[71]  Hussein M. Zbib,et al.  A multiscale model of plasticity , 2002 .

[72]  Alan Needleman,et al.  Discrete dislocation modeling in three-dimensional confined volumes , 2001 .

[73]  J. El-Awady,et al.  Micro-scale fatigue mechanisms in metals: Insights gained from small-scale experiments and discrete dislocation dynamics simulations , 2019, Current Opinion in Solid State and Materials Science.

[74]  A. Needleman,et al.  Hybrid discrete dislocation models for fatigue crack growth , 2010 .

[75]  Minsheng Huang,et al.  Effect of interfacial dislocation networks on the evolution of matrix dislocations in nickel-based superalloy , 2018, International Journal of Plasticity.

[76]  T. Belytschko,et al.  A review of extended/generalized finite element methods for material modeling , 2009 .

[77]  Peter Gumbsch,et al.  Initial dislocation structures in 3-D discrete dislocation dynamics and their influence on microscale plasticity , 2009 .

[78]  F. Dunne,et al.  The dislocation configurational energy density in discrete dislocation plasticity , 2019, Journal of the Mechanics and Physics of Solids.

[79]  D. Dunstan,et al.  Grain size dependence of the strength of metals: The Hall–Petch effect does not scale as the inverse square root of grain size , 2014 .

[80]  P. Gilles,et al.  Finite element multi-impact simulations using a crystal plasticity law based on dislocation dynamics , 2018 .

[81]  Ted Belytschko,et al.  Elastic crack growth in finite elements with minimal remeshing , 1999 .

[82]  Alexander Hartmaier,et al.  Influence of misfit stresses on dislocation glide in single crystal superalloys: A three-dimensional discrete dislocation dynamics study , 2015 .

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

[84]  Jianqiu Zhou,et al.  Effect of grain size and misorientation angle on fatigue crack growth of nanocrystalline materials , 2016 .

[85]  F. Feyel,et al.  Modelling crystal plasticity by 3D dislocation dynamics and the finite element method: The Discrete-Continuous Model revisited , 2014 .

[86]  Joshua C. Crone,et al.  A multiply parallel implementation of finite element-based discrete dislocation dynamics for arbitrary geometries , 2014 .

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