journal article·2018-12Open access

Machine Learning–Based Reduce Order Crystal Plasticity Modeling for ICME Applications

Mengfei Yuan, Sean Paradiso, Bryce Meredig, Stephen R. Niezgoda

Abstract

Abstract Crystal plasticity simulation is a widely used technique for studying the deformation processing of polycrystalline materials. However, inclusion of crystal plasticity simulation into design paradigms such as integrated computational materials engineering (ICME) is hindered by the computational cost of large-scale simulations. In this work, we present a machine learning (ML) framework using the material information platform, Open Citrination, to develop and calibrate a reduced order crystal plasticity model for face-centered cubic (FCC) polycrystalline materials, which can be both rapidly exercised and easily inverted. The reduced order model takes crystallographic texture, constitutive model parameters, and loading condition as inputs and returns the stress-strain curve and final texture. The model can also be inverted and take a stress-strain curve, loading condition, and final texture as inputs and return the initial texture and constitutive model parameters as outputs. Principal component analysis (PCA) is used to develop an efficient description of the crystallographic texture. A viscoplastic self-consistent (VPSC) crystal plasticity solver is used to create the training data by modeling the stress-strain behavior and evolution of texture during deformation processing.
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Research context

OpenAlex topics: Machine Learning in Materials Science · Microstructure and mechanical properties · Composite Material Mechanics

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (72)

Show source-provided references
1. Allison J (2011) Integrated computational materials engineering: a perspective on progress and future steps. JOM 63(4):1510.1007/s11837-011-0053-y ↗
2. Agrawal A, Choudhary A (2016) Perspective: Materials informatics and big data: realization of the ”fourth paradigm” of science in materials science. Apl Materials 4(5):05320810.1063/1.4946894 ↗
3. Olson GB (1997) Computational design of hierarchically structured materials. Science 277(5330):123710.1126/science.277.5330.1237 ↗
4. Panchal JH, Kalidindi SR, McDowell DL (2013) Key computational modeling issues in integrated computational materials engineering. Comput Aided Des 45(1):410.1016/j.cad.2012.06.006 ↗
5. Asaro RJ (1983) Crystal plasticity. J Appl Mech 50(4b):92110.1115/1.3167205 ↗
6. Lebensohn R, Tomé C (1994) A self-consistent viscoplastic model: prediction of rolling textures of anisotropic polycrystals. Mater Sci Eng A 175(1-2):7110.1016/0921-5093(94)91047-2 ↗
7. Lebensohn R, Tomé C, Castaneda PP (2007) Self-consistent modelling of the mechanical behaviour of viscoplastic polycrystals incorporating intragranular field fluctuations. Philos Mag 87(28):428710.1080/14786430701432619 ↗
8. Tomé C, Lebensohn R (2007) Visco-plastic self-consistent (vpsc), Los Alamos National Laboratory (USA) and Universidad Nacional de Rosario (Argentina) 6
9. Jia N, Peng RL, Wang Y, Johansson S, Liaw P (2008) Micromechanical behavior and texture evolution of duplex stainless steel studied by neutron diffraction and self-consistent modeling. Acta Mater 56(4):78210.1016/j.actamat.2007.10.040 ↗
10. Wang H, Wu P, Tomé C, Huang Y (2010) A finite strain elastic–viscoplastic self-consistent model for polycrystalline materials. J Mech Phys Solids 58(4):59410.1016/j.jmps.2010.01.004 ↗
11. Anglin B, Gockel B, Rollett A (2016) Developing constitutive model parameters via a multi-scale approach. Integr Mater Manuf Innov 5(1):1110.1186/s40192-016-0053-4 ↗
12. Aguir H, BelHadjSalah H, Hambli R (2011) Parameter identification of an elasto-plastic behaviour using artificial neural networks–genetic algorithm method. Mater Des 32(1):4810.1016/j.matdes.2010.06.039 ↗
13. Aguir H, Chamekh A, BelHadjSalah H, Dogui A, Hambli R (2008) Identification of constitutive parameters using hybrid ann multi-objective optimization procedure. Int J Mater Form 1(1):110.1007/s12289-008-0008-1 ↗
14. White A (2012) The materials genome initiative: one year on. MRS Bull 37(08):71510.1557/mrs.2012.194 ↗
15. O’Mara J, Meredig B, Michel K (2016) Materials data infrastructure: a case study of the citrination platform to examine data import, storage, and access. JOM 68(8):203110.1007/s11837-016-1984-0 ↗
16. Taylor GI (1938) Plastic strain in metals, our. Inst Metals 62:307
17. Hill R (1965) A self-consistent mechanics of composite materials. Journal of the Mechanics and Physics of Solids 13(4):21310.1016/0022-5096(65)90010-4 ↗
18. Anand L, Kothari M (1996) A computational procedure for rate-independent crystal plasticity. J Mech Phys Solids 44(4):52510.1016/0022-5096(96)00001-4 ↗
19. 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):115210.1016/j.actamat.2009.10.058 ↗
20. Molinari A, Canova G, Ahzi S (1987) A self consistent approach of the large deformation polycrystal viscoplasticity. Acta Metall 35(12):298310.1016/0001-6160(87)90297-5 ↗
21. Segurado J, Lebensohn RA, LLorca J, Tomé CN (2012) Multiscale modeling of plasticity based on embedding the viscoplastic self-consistent formulation in implicit finite elements. Int J Plast 28(1):12410.1016/j.ijplas.2011.07.002 ↗
22. Proust G, Kalidindi SR (2006) Procedures for construction of anisotropic elastic–plastic property closures for face-centered cubic polycrystals using first-order bounding relations. J Mech Phys Solids 54(8):174410.1016/j.jmps.2006.01.010 ↗
23. Liu B, Raabe D, Roters F, Eisenlohr P, Lebensohn R (2010) Comparison of finite element and fast fourier transform crystal plasticity solvers for texture prediction. Model Simul Mater Sci Eng 18(8):08500510.1088/0965-0393/18/8/085005 ↗
24. Lebensohn RA (2001) N-site modeling of a 3d viscoplastic polycrystal using fast fourier transform. Acta Mater 49(14):272310.1016/S1359-6454(01)00172-0 ↗
25. Lebensohn RA, Rollett AD, Suquet P (2011) Fast fourier transform-based modeling for the determination of micromechanical fields in polycrystals. JOM 63(3):1310.1007/s11837-011-0037-y ↗
26. Eshelby JD (1957) The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc R Soc Lond A 241(1226):37610.1098/rspa.1957.0133 ↗
27. Eshelby JD (1959) The elastic field outside an ellipsoidal inclusion. Proc R Soc Lond A 252(1271):56110.1098/rspa.1959.0173 ↗
28. Van Houtte P (1994) Application of plastic potentials to strain rate sensitive and insensitive anisotropic materials. Int J Plast 10(7):71910.1016/0749-6419(94)90043-4 ↗
29. Kalidindi SR, Duvvuru HK, Knezevic M (2006) Spectral calibration of crystal plasticity models. Acta Mater 54(7):179510.1016/j.actamat.2005.12.018 ↗
30. Raabe D, Roters F (2004) Using texture components in crystal plasticity finite element simulations. Int J Plast 20(3):33910.1016/S0749-6419(03)00092-5 ↗
31. Kocks UF, Tomé CN (2000) HR Wenk Texture and anisotropy: preferred orientations in polycrystals and their effect on materials properties. Cambridge University Press, Cambridge
32. Kalidindi SR, Bronkhorst CA, Anand L (1992) Crystallographic texture evolution in bulk deformation processing of fcc metals. J Mech Phys Solids 40(3):53710.1016/0022-5096(92)80003-9 ↗
33. Hielscher R, Schaeben H (2008) A novel pole figure inversion method: specification of the mtex algorithm. J Appl Crystallogr 41(6):102410.1107/S0021889808030112 ↗
34. Bachmann F, Hielscher R, Schaeben H (2010) In solid state phenomena. Trans Tech Publ 160:63–68
35. Mainprice D, Hielscher R, Schaeben H (2011) Calculating anisotropic physical properties from texture data using the mtex open-source package. Geol Soc Lond Spec Publ 360(1):17510.1144/SP360.10 ↗
36. Bunge HJ (2013) Texture analysis in materials science: mathematical methods. Elsevier, Amsterdam
37. Adams BL, Henrie A, Henrie B, Lyon M, Kalidindi S, Garmestani H (2001) Microstructure-sensitive design of a compliant beam. J Mech Phys Solids 49(8):163910.1016/S0022-5096(01)00016-3 ↗
38. Adams BL, Gao XC, Kalidindi SR (2005) Finite approximations to the second-order properties closure in single phase polycrystals. Acta Mater 53(13):356310.1016/j.actamat.2005.03.052 ↗
39. Sundararaghavan V, Zabaras N (2005) Classification and reconstruction of three-dimensional microstructures using support vector machines. Comput Mater Sci 32(2):22310.1016/j.commatsci.2004.07.004 ↗
40. Sundararaghavan V, Zabaras N (2004) A dynamic material library for the representation of single-phase polyhedral microstructures. Acta Mater 52(14):411110.1016/j.actamat.2004.05.024 ↗
41. Sundararaghavan V, Zabaras N (2008) A multi-length scale sensitivity analysis for the control of texture-dependent properties in deformation processing. Int J Plast 24(9):158110.1016/j.ijplas.2007.12.005 ↗
42. Fullwood DT, Niezgoda SR, Adams BL, Kalidindi SR (2010) Microstructure sensitive design for performance optimization. Prog Mater Sci 55(6):47710.1016/j.pmatsci.2009.08.002 ↗
43. Kalidindi SR, Houskamp JR, Lyons M, Adams BL (2004) Microstructure sensitive design of an orthotropic plate subjected to tensile load. Int J Plast 20(8):156110.1016/j.ijplas.2003.11.007 ↗
44. Niezgoda SR, Yabansu YC, Kalidindi SR (2011) Understanding and visualizing microstructure and microstructure variance as a stochastic process. Acta Mater 59(16):638710.1016/j.actamat.2011.06.051 ↗
45. Niezgoda SR, Kanjarla AK, Kalidindi SR (2013) Novel microstructure quantification framework for databasing, visualization, and analysis of microstructure data. Integr Mater Manuf Innov 2(1):110.1186/2193-9772-2-3 ↗
46. Galbincea ND, Yuan M, Niezgoda SR (2017) Computational design tools for quantifying uncertainty due to material variability. In: 19th AIAA non-deterministic approaches conference, p 0816
47. Fukunaga K (2013) Introduction to statistical pattern recognition. Academic Press, Cambridge
48. Johnson RA, Wichern D (2002) Multivariate analysis. Wiley Online Library, New York
49. Ghodsi A (2006) Dimensionality reduction a short tutorial. In: Department of Statistics and Actuarial Science, Univ of Waterloo, Ontario, Canada, vol 37, p 38
50. Maaten Lvd, Hinton G (2008) Visualizing data using t-sne. J Mach Learn Res 9:2579
51. Wattenberg M, Viégas F, Johnson I (2016) How to use t-sne effectively. Distill 1(10):e210.23915/distill.00002 ↗
52. Schölkopf B, Smola A, Müller KR (1998) Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput 10(5):129910.1162/089976698300017467 ↗
53. Ma X, Zabaras N (2011) Kernel principal component analysis for stochastic input model generation. J Comput Phys 230(19):731110.1016/j.jcp.2011.05.037 ↗
54. Ringnér M (2008) What is principal component analysis?. Nat Biotechnol 26(3):30310.1038/nbt0308-303 ↗
55. Abdi H, Williams LJ (2010) Principal component analysis. Wiley Interdiscip Rev Comput Stat 2(4):43310.1002/wics.101 ↗
56. Shlens J (2014) A tutorial on principal component analysis. arXiv:1404.1100
57. Kalidindi SR, Niezgoda SR, Salem AA (2011) Microstructure informatics using higher-order statistics and efficient data-mining protocols. JOM 63(4):3410.1007/s11837-011-0057-7 ↗
58. Sundararaghavan V, Zabaras N (2009) A statistical learning approach for the design of polycrystalline materials. Statistical Analysis and Data Mining 1(5):30610.1002/sam.10017 ↗
59. Pilania G, Wang C, Jiang X, Rajasekaran S, Ramprasad R (2013) Accelerating materials property predictions using machine learning. Sci Rep 3:281010.1038/srep02810 ↗
60. Meredig B, Agrawal A, Kirklin S, Saal JE, Doak J, Thompson A, Zhang K, Choudhary A, Wolverton C (2014) Combinatorial screening for new materials in unconstrained composition space with machine learning. Phys Rev B 89(9):09410410.1103/PhysRevB.89.094104 ↗
61. Schütt K, Glawe H, Brockherde F, Sanna A, Müller K, Gross E (2014) How to represent crystal structures for machine learning: towards fast prediction of electronic properties. Phys Rev B 89(20):20511810.1103/PhysRevB.89.205118 ↗
62. Robert C (2014) Machine learning a probabilistic perspective10.1080/09332480.2014.914768 ↗
63. Nasrabadi NM (2007) Pattern recognition and machine learning. J Electron Imaging 16(4):04990110.1117/1.2819119 ↗
64. Goldberg DE, Holland JH (1988) Genetic algorithms and machine learning. Mach Learn 3(2):9510.1023/A:1022602019183 ↗
65. Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, Blondel M, Prettenhofer P, Weiss R, Dubourg V et al (2011) Scikit-learn: machine learning in python. J Mach Learn Res 12(Oct):2825
66. Demuth H, Beale M (1993) Neural network toolbox for use with matlab – user’s guide verion 3.0
67. Hill J, Mannodi-Kanakkithodi A, Ramprasad R, Meredig B (2018) Materials science with large-scale data and informatics: unlocking new opportunities. In: Computational materials system design. Springer, pp 193–22510.1007/978-3-319-68280-8_9 ↗
68. Ling J, Hutchinson M, Antono E, Paradiso S, Meredig B (2017) High-dimensional materials and process optimization using data-driven experimental design with well-calibrated uncertainty estimates. Integr Mater Manuf Innov 6(3):20710.1007/s40192-017-0098-z ↗
69. Breiman L (2001) Random forests. Mach Learn 45(1):510.1023/A:1010933404324 ↗
70. Liaw A, Wiener M, et al (2002) Classification and regression by randomforest. R news 2(3):18
71. Hutchinson M, Paradiso S lolo https://githubcom/CitrineInformatics/lolo
72. Citrine informatics https://citrinationcom Accessed: 2018-11-01