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Computationally Efficient Crystal Plasticity Simulations Using Spectral Databases

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Handbook of Materials Modeling

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Abstract

Crystal plasticity models allow incorporation of physics of plastic deformation at length scales smaller than a single crystal or individual grains in a polycrystalline sample. As such, they present an important avenue for improving the fidelity of multiscale modeling and simulation for a variety of phenomena involving plastic deformations in crystalline materials. However, crystal plasticity models are extremely computationally expensive, limiting their adoption by materials development community and manufacturing industries. In this chapter, a spectral database approach is presented to carry out the computations involved in the crystal plasticity framework in a highly efficient manner. In this approach, the important variables of interest from crystal plasticity computations can be stored in precomputed databases based on discrete Fourier transforms (DFTs). Although the database generation requires one-time high computational cost, it dramatically reduces the computational cost in all subsequent computations. Several case studies illustrating the benefits of this approach are presented in this chapter.

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References

  • ABAQUS (2010). Providence, RI, USA., © Dassault Systèmes Simulia Corp

    Google Scholar 

  • Adams BL, Kalidindi S, Fullwood DT (2013) Microstructure-sensitive design for performance optimization. Butterworth-Heinemann, Waltham

    Google Scholar 

  • Adzima F, Balan T, Manach PY, Bonnet N, Tabourot L (2017) Crystal plasticity and phenomenological approaches for the simulation of deformation behavior in thin copper alloy sheets. Int J Plast 94:171–191

    Article  Google Scholar 

  • Alharbi HF, Kalidindi SR (2015) Crystal plasticity finite element simulations using a database of discrete Fourier transforms. Int J Plast 66:71–84

    Article  Google Scholar 

  • Al-Harbi HF, Knezevic M, Kalidindi SR (2010) Spectral approaches for the fast computation of yield surfaces and first-order plastic property closures for polycrystalline materials with cubic-triclinic textures. Cmc Comput Mater Continua 15(2):153–172

    Google Scholar 

  • Asaro RJ, Needleman A (1985) Overview no. 42 texture development and strain hardening in rate dependent polycrystals. Acta Metall 33(6):923–953

    Article  Google Scholar 

  • Bachu V, Kalidindi SR (1998) On the accuracy of the predictions of texture evolution by the finite element technique for fcc polycrystals. Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing 257(1):108–117

    Article  Google Scholar 

  • Barlat F (2007) Constitutive modeling for metals. In: Advanced methods in material forming, pp 1–18, Springer, Berlin/Heidelberg

    Google Scholar 

  • Bronkhorst CA, Kalidindi SR, Anand L (1992) Polycrystalline plasticity and the evolution of crystallographic texture in FCC metals. Philos Trans R Soc London, Ser A 341:443–477

    Article  ADS  Google Scholar 

  • Bunge HJ, Esling C (1984) Texture development by plastic deformation. Scr Metall 18(3):191–195

    Article  Google Scholar 

  • Callister WD Jr (2007) Materials science and engineering : an introduction. Wiley, New York

    Google Scholar 

  • Chockalingam K, Tonks MR, Hales JD, Gaston DR, Millett PC, Zhang L (2013) Crystal plasticity with Jacobian-free Newton–Krylov. Comput Mech:1–11

    Google Scholar 

  • Gupta A, Bettaieb MB, Abed-Meraim F, Kalidindi SR (2018) Computationally efficient predictions of crystal-plasticity based forming limit diagrams using a spectral database. Int J Plast 103:168–187

    Article  Google Scholar 

  • Kalidindi SR, Anand L (1994) Macroscopic shape change and evolution of crystallographic texture in pre-textured FCC metals. J Mech Phys Solids 42(3):459–490

    Article  ADS  Google Scholar 

  • Kalidindi SR, Duvvuru HK (2005) Spectral methods for capturing crystallographic texture evolution during large plastic strains in metals. Acta Mater 53(13):3613–3623

    Article  Google Scholar 

  • Kalidindi SR, Schoenfeld SE (2000) On the prediction of yield surfaces by the crystal plasticity models for fcc polycrystals. Mater Sci Eng A 293(1–2):120–129

    Article  Google Scholar 

  • Kalidindi SR, Bronkhorst CA, Anand L (1992) Crystallographic texture evolution in bulk deformation processing of fcc metals. J Mech Phys Solids 40(3):537–569

    Article  ADS  Google Scholar 

  • Kalidindi SR, Bhattacharyya A, Doherty RD (2004) Detailed analysis of grain-scale plastic deformation in columnar polycrystalline aluminum using orientation image mapping and crystal plasticicty models. Proc Math Phys Eng Sci 460(2047):1935–1956. http://www.jstor.org/stable/4143061

    Article  Google Scholar 

  • Kalidindi SR, Duvvuru HK, Knezevic M (2006) Spectral calibration of crystal plasticity models. Acta Mater 54(7):1795–1804

    Article  Google Scholar 

  • Kalidindi SR, Knezevic M, Niezgoda S, Shaffer J (2009) Representation of the orientation distribution function and computation of first-order elastic properties closures using discrete Fourier transforms. Acta Mater 57(13):3916–3923

    Article  Google Scholar 

  • Knezevic M, Kalidindi SR (2017) Crystal plasticity modeling of microstructure evolution and mechanical fields during processing of metals using spectral databases. JOM 69(5):830–838

    Article  ADS  Google Scholar 

  • Knezevic M, Savage DJ (2014) A high-performance computational framework for fast crystal plasticity simulations. Comput Mater Sci 83:101–106

    Article  Google Scholar 

  • Knezevic M, Kalidindi SR, Fullwood D (2008a) Computationally efficient database and spectral interpolation for fully plastic Taylor-type crystal plasticity calculations of face-centered cubic polycrystals. Int J Plast 24(7):1264–1276

    Article  Google Scholar 

  • Knezevic M, Kalidindi SR, Mishra RK (2008b) Delineation of first-order closures for plastic properties requiring explicit consideration of strain hardening and crystallographic texture evolution. Int J Plast 24(2):327–342

    Article  Google Scholar 

  • Knezevic M, Al-Harbi HF, Kalidindi SR (2009) Crystal plasticity simulations using discrete Fourier transforms. Acta Mater 57(6):1777–1784

    Article  Google Scholar 

  • Kocks UF, Mecking H (2003) Physics and phenomenology of strain hardening: the FCC case. Prog Mater Sci 48(3):171–273

    Article  Google Scholar 

  • Lebensohn RA (2001) N-site modeling of a 3D viscoplastic polycrystal using fast Fourier transform. Acta Mater 49(14):2723–2737

    Article  Google Scholar 

  • Lebensohn RA, Liu Y, Ponte Castañeda P (2004) On the accuracy of the self-consistent approximation for polycrystals: comparison with full-field numerical simulations. Acta Mater 52(18):5347–5361

    Article  Google Scholar 

  • Lebensohn RA, Tome CN, Castaneda PP (2007) Self-consistent modelling of the mechanical behaviour of viscoplastic polycrystals incorporating intragranular field fluctuations. Philos Mag 87(28):4287–4322

    Article  ADS  Google Scholar 

  • Lebensohn RA, Brenner R, Castelnau O, Rollett AD (2008) Orientation image-based micromechanical modelling of subgrain texture evolution in polycrystalline copper. Acta Mater 56(15):3914–3926

    Article  Google Scholar 

  • Lubliner J (2008) Plasticity theory. Dover, New York

    Google Scholar 

  • Marciniak Z, Kuczynski K (1979) Forming limit curve for bending processes. Int J Mech Sci 21(10):609–621

    Article  Google Scholar 

  • Marciniak Z, Kuczynski K, Pokora T (1973) Influence of plastic properties of a material on forming limit diagram for sheet-metal in tension. Int J Mech Sci 15(10):789–800

    Article  Google Scholar 

  • Molinari A, Canova GR, Ahzi S (1987) A self consistent approach of the large deformation polycrystal viscoplasticity. Acta Metall 35(12):2983–2994

    Article  Google Scholar 

  • Needleman A, Asaro RJ, Lemonds J, Peirce D (1985) Finite element analysis of crystalline solids. Comput Methods Appl Mech Eng 52(1–3):689–708

    Article  ADS  Google Scholar 

  • Pan J, Rice JR (1983) Rate sensitivity of plastic-flow and implications for yield-surface vertices. Int J Solids Struct 19(11):973–987

    Article  Google Scholar 

  • Raabe D, Wang Y, Roters F (2005) Crystal plasticity simulation study on the influence of texture on earing in steel. Comput Mater Sci 34(3):221–234

    Article  Google Scholar 

  • Roters F, Eisenlohr P, Hantcherli L, Tjahjanto DD, Bieler TR, Raabe D (2010) Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: theory, experiments, applications. Acta Mater 58(4):1152–1211

    Article  Google Scholar 

  • Taylor GI (1938) Plastic strain in metals. J Inst Met 62:307–324

    Google Scholar 

  • Van Houtte P (1994) Application of plastic potentials to strain rate sensitive and insensitive anisotropic materials. Int J Plast 10(7):719–748

    Article  Google Scholar 

  • Van Houtte P, Li S, Seefeldt M, Delannay L (2005) Deformation texture prediction: from the Taylor model to the advanced Lamel model. Int J Plast 21(3):589–624

    Article  Google Scholar 

  • Zecevic M, McCabe RJ, Knezevic M (2015a) Spectral database solutions to elasto-viscoplasticity within finite elements: application to a cobalt-based FCC superalloy. Int J Plast 70:151–165

    Article  Google Scholar 

  • Zecevic M, McCabe RJ, Knezevic M (2015b) A new implementation of the spectral crytsal plasticity framework in implicit finite elements. Mech Mater 84:114–126

    Article  Google Scholar 

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Acknowledgments

Akash Gupta, Evdokia Popova and Surya R. Kalidindi gratefully acknowledge support received for this work from the Office of Naval Research (ONR) under the award number N00014-15-1-2478 (Dr. William M. Mullins, program manager).

Author information

Authors and Affiliations

  1. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    Surya R. Kalidindi, Akash Gupta & Evdokia Popova

  2. TCS Research, Tata Consultancy Services, Tata Research Development and Design Centre, Pune, India

    Akash Gupta

  3. UMI 2958, Georgia Tech-CNRS, Metz, France

    Akash Gupta

Authors
  1. Surya R. Kalidindi
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  2. Akash Gupta
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  3. Evdokia Popova
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Corresponding author

Correspondence to Surya R. Kalidindi .

Editor information

Editors and Affiliations

  1. Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Wanda Andreoni

  2. Department of Nuclear Science & Engineering , Massachusetts Institute of Technology , Cambridge, MA, USA

    Sidney Yip

Section Editor information

  1. Department of Mechanical Engineering, Stanford University, Stanford, CA, USA

    Wei Cai

  2. Dept. of Mechanical Engineering, Johns Hopkins Univeristy, Baltimore, MD, USA

    Somnath Ghosh

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Kalidindi, S.R., Gupta, A., Popova, E. (2018). Computationally Efficient Crystal Plasticity Simulations Using Spectral Databases. In: Andreoni, W., Yip, S. (eds) Handbook of Materials Modeling . Springer, Cham. https://doi.org/10.1007/978-3-319-42913-7_16-1

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  • DOI: https://doi.org/10.1007/978-3-319-42913-7_16-1

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  • 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

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