PARAMETER IDENTIFICATION OF NONLOCAL CRYSTAL PLASTIC MODEL BASED ON MACHINE LEARNING AND GENETIC ALGORITHM

Zhou Rui; Xiong Yukai; Chu Jielei; Kan Qianhua; Kang Guozheng; Zhang Xu

doi:10.6052/0459-1879-23-479

Volume 56 Issue 3

Mar. 2024

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Chinese Journal of Theoretical and Applied Mechanics > 2024 > 56(3): 751-762. > DOI: 10.6052/0459-1879-23-479 CSTR: 32045.14.0459-1879-23-479

Zhou Rui, Xiong Yukai, Chu Jielei, Kan Qianhua, Kang Guozheng, Zhang Xu. Parameter identification of nonlocal crystal plastic model based on machine learning and genetic algorithm. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(3): 751-762. DOI: 10.6052/0459-1879-23-479

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PARAMETER IDENTIFICATION OF NONLOCAL CRYSTAL PLASTIC MODEL BASED ON MACHINE LEARNING AND GENETIC ALGORITHM

*.
Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu 610031, China
†.
School of Computing and Artificial Intelligence, Southwest Jiaotong University, Chengdu 610031, China

Received Date: October 06, 2023
Accepted Date: December 04, 2023
Available Online: December 05, 2023
Published Date: December 05, 2023

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Abstract

Abstract

Nonlocal crystal plasticity models account for the spatial rearrangement of dislocations due to non-uniform deformation, resulting in complex constitutive models with many adjustable parameters. Hence, it is challenging to determine these parameters accurately using the conventional trial-and-error method. Although genetic algorithms can solve the parameter identification problem robustly by global optimization, their computational costs are relatively high for nonlocal crystal plasticity models. To address this issue, this paper proposes a genetic algorithm coupled with a machine learning model to effectively reduce the computational cost. Focusing on the tensile response of nickel-based superalloys with cooling holes, the uniaxial tensile stress-strain curve is the objective, and an evaluation formula is established based on the yield stress and the final stress, to make the optimization result as close as possible to the experiment. Through this method, the machine learning model can predict the corresponding stress values based on the parameters of the nonlocal crystal plasticity model, thus replacing the finite element calculation that was originally required in the genetic algorithm. To analyze the influence of the constitutive model parameters on the uniaxial tensile mechanical response, the SHAP framework is adopted and verified by the finite element results. The results show that the nonlocal crystal plasticity model parameters can be determined effectively by this method, and the stress-strain responses calculated by the parameters agree well with the experimental results. Moreover, the SHAP framework can offer insights into the significance of the constitutive model parameters, as well as their influence on the yield stress and the ultimate stress.
- crystal plasticity,
- machine learning,
- parameter identification,
- genetic algorithm

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References

[1]	Roters F, Eisenlohr P, Hantcherli L, et al. Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications. Acta Materialia, 2010, 58(4): 1152-1211 doi: 10.1016/j.actamat.2009.10.058
[2]	Arsenlis A, Parks D. Crystallographic aspects of geometrically-necessary and statistically-stored dislocation density. Acta Materialia, 1999, 47(5): 1597-1611 doi: 10.1016/S1359-6454(99)00020-8
[3]	章海明, 徐帅, 李倩等. 晶体塑性理论及模拟研究进展. 塑性工程学报, 2020, 27(5): 12-32 (Zhang Haiming, Xu Shuai, Li Qian, et al. Progress of crystal plasticity theory and simulations. Journal of Plasticity Engineering, 2020, 27(5): 12-32 (in Chinese) Zhang Haiming, Xu Shuai, Li Qian, et al. Progress of crystal plasticity theory and simulations. Journal of Plasticity Engineering, 2020, 27(5): 12-32 (in Chinese)
[4]	Zhang X, Zhao J, Kang G, et al. Geometrically necessary dislocations and related kinematic hardening in gradient grained materials: A nonlocal crystal plasticity study. International Journal of Plasticity, 2023, 163: 103553 doi: 10.1016/j.ijplas.2023.103553
[5]	Reuber C, Eisenlohr P, Roters F, et al. Dislocation density distribution around an indent in single-crystalline nickel: Comparing nonlocal crystal plasticity finite-element predictions with experiments. Acta Materialia, 2014, 71: 333-348 doi: 10.1016/j.actamat.2014.03.012
[6]	Khan AS, Lopez-Pamies O, Kazmi R. Thermo-mechanical large deformation response and constitutive modeling of viscoelastic polymers over a wide range of strain rates and temperatures. International Journal of Plasticity, 2006, 22(4): 581-601 doi: 10.1016/j.ijplas.2005.08.001
[7]	隋天校, 石多奇, 杨秦政等. 晶体塑性本构模型材料参数识别方法研究. 推进技术, 2023, 44(3): 200-209 (Sui Tianxiao, Shi Duoqi, Yang Qinzheng, et al. Material parameter identification method of crystal plastic constitutive models. Journal of Propulsion Technology, 2023, 44(3): 210593 (in Chinese) Sui Tianxiao, Shi Duoqi, Yang Qinzheng, et al. Material parameter identification method of crystal plastic constitutive models. Journal of Propulsion Technology, 2023, 44(3): 210593 (in Chinese)
[8]	Bruhns O, Anding D. On the simultaneous estimation of model parameters used in constitutive laws for inelastic material behaviour. International Journal of Plasticity, 1999, 15(12): 1311-1340 doi: 10.1016/S0749-6419(99)00046-7
[9]	Shahmardani M, Vajragupta N, Hartmaier A. Robust optimization scheme for inverse method for crystal plasticity model parametrization. Materials, 2020, 13(3): 735 doi: 10.3390/ma13030735
[10]	Mahnken R, Stein E. A unified approach for parameter identification of inelastic material models in the frame of the finite element method. Computer Methods in Applied Mechanics and Engineering, 1996, 136(3-4): 225-258 doi: 10.1016/0045-7825(96)00991-7
[11]	Qu J, Jin Q, Xu B. Parameter identification for improved viscoplastic model considering dynamic recrystallization. International Journal of Plasticity, 2005, 21(7): 1267-1302 doi: 10.1016/j.ijplas.2004.04.009
[12]	Lin J. Selection of material models for predicting necking in superplastic forming. International Journal of Plasticity, 2003, 19(4): 469-481 doi: 10.1016/S0749-6419(01)00059-6
[13]	Lin J, Yang J. GA-based multiple objective optimisation for determining viscoplastic constitutive equations for superplastic alloys. International Journal of Plasticity, 1999, 15(11): 1181-1196 doi: 10.1016/S0749-6419(99)00031-5
[14]	Savage DJ, Feng Z, Knezevic M. Identification of crystal plasticity model parameters by multi-objective optimization integrating microstructural evolution and mechanical data. Computer Methods in Applied Mechanics and Engineering, 2021, 379: 113747 doi: 10.1016/j.cma.2021.113747
[15]	Frydrych K, Papanikolaou S. Unambiguous identification of crystal plasticity parameters from spherical indentation. Crystals, 2022, 12(10): 1341 doi: 10.3390/cryst12101341
[16]	Andrade-Campos A, Thuillier S, Pilvin P, et al. On the determination of material parameters for internal variable thermoelastic–viscoplastic constitutive models. International Journal of Plasticity, 2007, 23(8): 1349-1379 doi: 10.1016/j.ijplas.2006.09.002
[17]	Furukawa T, Sugata T, Yoshimura S, et al. An automated system for simulation and parameter identification of inelastic constitutive models. Computer Methods in Applied Mechanics and Engineering, 2002, 191(21-22): 2235-2260 doi: 10.1016/S0045-7825(01)00375-9
[18]	Pandey A, Pokharel R. Machine learning based surrogate modeling approach for mapping crystal deformation in three dimensions. Scripta Materialia, 2021, 193: 1-5 doi: 10.1016/j.scriptamat.2020.10.028
[19]	Wen J, Zou Q, Wei Y. Physics-driven machine learning model on temperature and time-dependent deformation in lithium metal and its finite element implementation. Journal of the Mechanics and Physics of Solids, 2021, 153: 104481 doi: 10.1016/j.jmps.2021.104481
[20]	Heider Y, Wang K, Sun W. SO(3)-invariance of informed-graph-based deep neural network for anisotropic elastoplastic materials. Computer Methods in Applied Mechanics and Engineering, 2020, 363: 112875 doi: 10.1016/j.cma.2020.112875
[21]	Yuan M, Paradiso S, Meredig B, et al. Machine learning–based reduce order crystal plasticity modeling for ICME applications. Integrating Materials and Manufacturing Innovation, 2018, 7: 214-230 doi: 10.1007/s40192-018-0123-x
[22]	Veasna K, Feng Z, Zhang Q, et al. Machine learning-based multi-objective optimization for efficient identification of crystal plasticity model parameters. Computer Methods in Applied Mechanics and Engineering, 2023, 403: 115740 doi: 10.1016/j.cma.2022.115740
[23]	Roters F, Diehl M, Shanthraj P, et al. DAMASK – The düsseldorf advanced material simulation kit for modeling multi-physics crystal plasticity, thermal, and damage phenomena from the single crystal up to the component scale. Computational Materials Science, 2019, 158: 420-478 doi: 10.1016/j.commatsci.2018.04.030
[24]	Orowan E, Zur Kristallplastizitat I. Tieftemperaturplastizitat und Beckersche Formerl. Zeitschrift für Physik, 1934, 98: 605
[25]	Kords C. On the role of dislocation transport in the constitutive description of crystal plasticity. [PhD Thesis]. Epubli GmbH Berlin, 2013
[26]	Golberg DE. Genetic algorithms in search, optimization, and machine learning. Addion Wesley, 1989, 1989(102): 36
[27]	Harth T, Schwan S, Lehn J, et al. Identification of material parameters for inelastic constitutive models: Statistical analysis and design of experiments. International Journal of Plasticity, 2004, 20(8-9): 1403-1440 doi: 10.1016/j.ijplas.2003.11.001
[28]	Lundberg SM, Lee SI. A unified approach to interpreting model predictions. Advances in Neural Information Processing Systems, 2017, 30: 4768-4777
[29]	Feng D, Wang W, Mangalathu S, et al. Interpretable XGBoost-SHAP machine-learning model for shear strength prediction of squat RC walls. Journal of Structural Engineering, 2021, 147(11): 04021173 doi: 10.1061/(ASCE)ST.1943-541X.0003115
[30]	Štrumbelj E, Kononenko I. Explaining prediction models and individual predictions with feature contributions. Knowledge and Information Systems, 2013, 41(3): 647-665
[31]	熊宇凯, 赵建锋, 饶威等. 含冷却孔镍基合金次级取向效应的应变梯度晶体塑性有限元研究. 力学学报, 2023, 55(1): 120-133 (Xiong Yukai, Zhao Jianfeng, Rao Wei, et al. Secondary orientation effects of Ni-based alloys with cooling holes: A strain gradient crystal plasticity FEM study. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 120-133 (in Chinese) Xiong Yukai, Zhao Jianfeng, Rao Wei, et al. Secondary orientation effects of Ni-based alloys with cooling holes: A strain gradient crystal plasticity FEM study. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 120-133 (in Chinese)
[32]	Lu X, Zhao J, Wang Z, et al. Crystal plasticity finite element analysis of gradient nanostructured TWIP steel. International Journal of Plasticity, 2020, 130: 102703
[33]	Wong SL, Madivala M, Prahl U, et al. A crystal plasticity model for twinning- and transformation-induced plasticity. Acta Materialia, 2016, 118: 140-151 doi: 10.1016/j.actamat.2016.07.032
[34]	Kocks UF, Argon AS, Ashby MF. Thermodynamics and kinetics of slip. Progress in Materials Science, 1975, 19: 1-291 doi: 10.1016/0079-6425(75)90005-5
[35]	Zhou H, Zhang X, Wang P, et al. Crystal plasticity analysis of cylindrical holes and their effects on the deformation behavior of Ni-based single-crystal superalloys with different secondary orientations. International Journal of Plasticity, 2019, 119: 249-272 doi: 10.1016/j.ijplas.2019.04.009
[36]	Gupta S, Bronkhorst CA. Crystal plasticity model for single crystal Ni-based superalloys: Capturing orientation and temperature dependence of flow stress. International Journal of Plasticity, 2021, 137: 102896 doi: 10.1016/j.ijplas.2020.102896
[37]	Shang Y, Zhang H, Hou H, et al. High temperature tensile behavior of a thin-walled Ni based single-crystal superalloy with cooling hole: In-situ experiment and finite element calculation. Journal of Alloys and Compounds, 2019, 782: 619-631 doi: 10.1016/j.jallcom.2018.12.232

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PARAMETER IDENTIFICATION OF NONLOCAL CRYSTAL PLASTIC MODEL BASED ON MACHINE LEARNING AND GENETIC ALGORITHM

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