Modelling crystal plasticity by 3D dislocation dynamics and the finite element method: The Discrete-Continuous Model revisited

Abstract A unified model coupling 3D dislocation dynamics (DD) simulations with the finite element (FE) method is revisited. The so-called Discrete-Continuous Model (DCM) aims to predict plastic flow at the (sub-)micron length scale of materials with complex boundary conditions. The evolution of the dislocation microstructure and the short-range dislocation–dislocation interactions are calculated with a DD code. The long-range mechanical fields due to the dislocations are calculated by a FE code, taking into account the boundary conditions. The coupling procedure is based on eigenstrain theory, and the precise manner in which the plastic slip, i.e. the dislocation glide as calculated by the DD code, is transferred to the integration points of the FE mesh is described in full detail. Several test cases are presented, and the DCM is applied to plastic flow in a single-crystal Nickel-based superalloy.

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

[2]  Christopher R. Weinberger,et al.  A non-singular continuum theory of dislocations , 2006 .

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

[4]  J. G. Sevillano.  Flow Stress and Work Hardening , 2006 .

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

[6]  F. Feyel,et al.  Predicting size effects in nickel-base single crystal superalloys with the Discrete-Continuous Model , 2010 .

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

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

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

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

[11]  F. Nabarro,et al.  CXXII. The synthesis of elastic dislocation fields , 1951 .

[12]  A. El-Azab,et al.  On the elastic boundary value problem of dislocations in bounded crystals , 2008 .

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

[14]  Marc Fivel,et al.  Introducing dislocation climb by bulk diffusion in discrete dislocation dynamics , 2008 .

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

[16]  Benoit Devincre,et al.  Orientation dependence of plastic deformation in nickel-based single crystal superalloys: Discrete–continuous model simulations , 2010 .

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

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

[19]  Alberto M. Cuitiño,et al.  Nanoscale phase field microelasticity theory of dislocations: model and 3D simulations , 2001 .

[20]  Y. Shibutani,et al.  IUTAM Symposium on Mesoscopic Dynamics of Fracture Process and Materials Strength , 2004 .

[21]  S. S. Shishvan,et al.  Plane-strain discrete dislocation plasticity incorporating anisotropic elasticity , 2011 .

[22]  J. Chaboche,et al.  Coupled Meso-Macro Simulations of Plasticity: Validation Tests , 1998 .

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

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

[25]  B. Devincre,et al.  MODEL VALIDATION OF A 3D SIMULATION OF DISLOCATION DYNAMICS: DISCRETIZATION AND LINE TENSION EFFECTS , 1992 .

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

[27]  N. Ghoniem,et al.  Parametric dislocation dynamics of anisotropic crystals , 2003 .

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

[29]  B. Fedelich,et al.  On the relationship between anisotropic yield strength and internal stresses in single crystal superalloys , 2011 .

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

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

[32]  Jie Yin,et al.  Efficient computation of forces on dislocation segments in anisotropic elasticity , 2010 .

[33]  A. Needleman,et al.  Discrete Dislocation Plasticity , 2002 .

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

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

[36]  J. Tersoff,et al.  Interaction of threading and misfit dislocations in a strained epitaxial layer , 1996 .

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

[38]  Yang Xiang,et al.  A level set method for dislocation dynamics , 2003 .

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

[40]  R Madec,et al.  From dislocation junctions to forest hardening. , 2002, Physical review letters.

[41]  A. Needleman,et al.  MULTISCALE PHENOMENA IN MATERIALS-EXPERIMENTS AND MODELING RELATED TO MECHANICAL BEHAVIOR , 2003 .

[42]  Ted Belytschko,et al.  A new fast finite element method for dislocations based on interior discontinuities , 2007 .

[43]  Benoit Devincre,et al.  Dislocation dynamics simulations of precipitation hardening in Ni-based superalloys with high γ′ volume fraction , 2009 .

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

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

[46]  Toshio Mura,et al.  Micromechanics of defects in solids , 1982 .

[47]  L. Kubin,et al.  Dislocation dynamics in confined geometry , 1999 .

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

[49]  A Arsenlis,et al.  Power-law creep from discrete dislocation dynamics. , 2012, Physical review letters.

[50]  J. Chaboche,et al.  Multiscale modelling of plastic deformation , 1999 .

[51]  Yuan Gao,et al.  A hybrid multiscale computational framework of crystal plasticity at submicron scales , 2010 .

[52]  B. Devincre,et al.  Boundary problems in DD simulations , 2002 .

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