A high-performance computational framework for fast crystal plasticity simulations

Abstract We present a new computational framework aimed at dramatically reducing time needed for crystal plasticity simulations. The framework is based on a combination of the recently developed numerical implementations of crystal plasticity in the spectral representation for obtaining the response of single crystals and specialized computer hardware that integrates a graphics-processing unit (GPU). Following a divide and conquer approach adapted here from a fast GPU8 method for matrix operations, we describe a new GPU based implementation of the spectral crystal plasticity and demonstrate its performances through a few example case studies involving a Taylor-type polycrystalline model. Using a single GPU card, the novel framework described herein provides speedup factors exceeding three orders of magnitude over the conventional crystal plasticity numerical schemes.

[1]  Hamid Garmestani,et al.  Evolution of crystal orientation distribution coefficients during plastic deformation , 2003 .

[2]  Ricardo A. Lebensohn,et al.  Integration of self-consistent polycrystal plasticity with dislocation density based hardening laws within an implicit finite element framework: Application to low-symmetry metals , 2013 .

[3]  P. Van Houtte,et al.  Application of plastic potentials to strain rate sensitive and insensitive anisotropic materials , 1994 .

[4]  M. Diehl,et al.  A spectral method solution to crystal elasto-viscoplasticity at finite strains , 2013 .

[5]  Ricardo A. Lebensohn,et al.  A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals : application to zirconium alloys , 1993 .

[6]  I. Beyerlein,et al.  A polycrystal plasticity model for predicting mechanical response and texture evolution during strain-path changes: Application to beryllium , 2013 .

[7]  T. Bieler,et al.  Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications , 2010 .

[8]  D. Fullwood,et al.  Computationally efficient database and spectral interpolation for fully plastic Taylor-type crystal plasticity calculations of face-centered cubic polycrystals , 2008 .

[9]  Surya R. Kalidindi,et al.  Spectral Approaches for the Fast Computation of Yield Surfaces and First-Order Plastic Property Closures for Polycrystalline Materials with Cubic-Triclinic Textures , 2010 .

[10]  Ricardo A. Lebensohn,et al.  Modeling mechanical response and texture evolution of α-uranium as a function of strain rate and temperature using polycrystal plasticity , 2013 .

[11]  Philip Eisenlohr,et al.  An elasto-viscoplastic formulation based on fast Fourier transforms for the prediction of micromechanical fields in polycrystalline materials , 2012 .

[12]  Jitesh H. Panchal,et al.  Key computational modeling issues in Integrated Computational Materials Engineering , 2013, Comput. Aided Des..

[13]  S. Kalidindi,et al.  Crystal plasticity simulations using discrete Fourier transforms , 2009 .

[14]  H. Bunge.  Texture Analysis in Materials Science , 1982 .

[15]  R. Asaro,et al.  Overview no. 42 Texture development and strain hardening in rate dependent polycrystals , 1985 .

[16]  Jaroslaw Knap,et al.  A call to arms for task parallelism in multi‐scale materials modeling , 2011 .

[17]  Lallit Anand,et al.  Single crystal and polycrystal elasto-viscoplasticity: Application to earing in cup drawing of F.C.C. materials , 1996 .

[18]  I. Beyerlein,et al.  Anomalous Basal Slip Activity in Zirconium under High-strain Deformation , 2013 .

[19]  Surya R. Kalidindi,et al.  Fast computation of first-order elastic–plastic closures for polycrystalline cubic-orthorhombic microstructures , 2007 .

[20]  J. Segurado,et al.  Multiscale modeling of plasticity based on embedding the viscoplastic self-consistent formulation in implicit finite elements , 2012 .

[21]  Surya R. Kalidindi,et al.  Delineation of first-order closures for plastic properties requiring explicit consideration of strain hardening and crystallographic texture evolution , 2008 .

[22]  U. F. Kocks,et al.  Application of polycrystal plasticity to sheet forming , 1994 .

[23]  G. Proust,et al.  Modeling bending of α-titanium with embedded polycrystal plasticity in implicit finite elements , 2013 .

[24]  N. Zabaras,et al.  Linear analysis of texture-property relationships using process-based representations of Rodrigues space , 2007 .

[25]  G. C. Johnson,et al.  Three-dimensional deformation process simulation with explicit use of polycrystal plasticity models , 1993 .

[26]  Richard D. Hornung,et al.  Embedded polycrystal plasticity and adaptive sampling , 2008 .

[27]  R. A. Lebensohn,et al.  Self-consistent modelling of the mechanical behaviour of viscoplastic polycrystals incorporating intragranular field fluctuations , 2007 .

[28]  Surya R. Kalidindi,et al.  Spectral calibration of crystal plasticity models , 2006 .

[29]  D. Gaston,et al.  Crystal plasticity with Jacobian-Free Newton–Krylov , 2013 .

[30]  S. Kalidindi,et al.  Application of microstructure sensitive design to structural components produced from hexagonal polycrystalline metals , 2008 .

[31]  Laurent Capolungo,et al.  Anisotropic stress–strain response and microstructure evolution of textured α-uranium , 2012 .

[32]  Surya R. Kalidindi,et al.  Building texture evolution networks for deformation processing of polycrystalline fcc metals using spectral approaches: Applications to process design for targeted performance , 2010 .

[33]  L. Anand,et al.  Crystallographic texture evolution in bulk deformation processing of FCC metals , 1992 .

[34]  Carlos N. Tomé,et al.  A dislocation-based constitutive law for pure Zr including temperature effects , 2008 .

[35]  Surya R. Kalidindi,et al.  Representation of the orientation distribution function and computation of first-order elastic properties closures using discrete Fourier transforms , 2009 .

[36]  P. Dawson,et al.  Polycrystal plasticity modeling of bulk forming with finite elements over orientation space , 1995 .