Research on Matching of Variable Modulus Kinematic Hardening Constitutive Models and Decoupling Calibration Strategy for High-strength Steel

doi:10.3901/JME.2023.02.080

Abstract

Abstract: Higher strength of high-strength steel can be obtained by controlling microstructure, but the microscopic uneven deformation and micro-induced plasticity mechanism of different grades of high-strength steel are different, which makes the unloading and reverse loading behavior of high-strength steel more complicated and increases the difference between grades. For this reason, a systematic strategy of model adaptive matching and parameter decoupling matching to achieve accurate prediction of high-strength steel springback is given. Firstly, a hybrid hardening model of power function and exponential function is proposed.Based on the hybrid hardening model, the bending moment balance equation for free bending load and curvature constraint equation are raised. In view of the variable modulus model, the integral equation of the section elastic bending moment is established. A sub-optimization model is established to reversely identify the unloading parameters basing on the loading and unloading analytical models. The matching strategy including variable modulus linear and nonlinear kinematic hardening models and variable modulus kinematic hardening models with boundary surface is determined. Based on the experimental data of tension and compression, free bending and uniaxial tension, the optimization sequence of the corresponding constitutive sub-optimization model parameters is determined, and a systematic strategy of constitutive matching and its parameter decoupling calibration is formed finally, and calibration library is developed on the basis of the Fortran language. A prediction model for U-shaped bending parts and arc-shaped bending parts is established, and the recognition results and springback prediction results of DP980 and DH980 high-strength steels at different strain levels are compared and analyzed. The decoupling calibration strategy is verified. Not only the correlation of data of different grades of high-strength steel but also the accuracy and stability of the model under the same grade is greatly increased. It lays the foundation for the research on the unified self-identification method of material properties in view of data.

Key words: constitutive matching, bending springback, decoupling calibration, optimized recognition, high-strength steel

CLC Number:

TG156

DUAN Yongchuan, SUN Lili, ZHANG Fangfang, ZHENG Xuebin, DONG Rui, GUAN Yingping. Research on Matching of Variable Modulus Kinematic Hardening Constitutive Models and Decoupling Calibration Strategy for High-strength Steel[J]. Journal of Mechanical Engineering, 2023, 59(2): 80-95,103.

References

[1] 段永川, 乔海棣, 张芳芳, 等. 屈服强度在线识别的分散性分析与精度验证[J]. 中国机械工程, 2020, 31(23):2864-2873. DUAN Yongchuan, QIAO Haidi, ZHANG Fangfang, et al. Dispersive analysis and accaracy verification of yield strength online recognition[J]. China Mechanical Engineering, 2020, 31(23):2864-2873.
[2] DUAN Yongchuan, TIAN Le, ZHANG Fangfang, et al. A fast identification method of yield strength of materials based on bending experimental data[J]. Metals, 2020, 10(2):169.
[3] PIERRON F, AVRIL S, TRAN V T. Extension of the virtual fields method to elastic-plastic material identification with cyclic loads and kinematic hardening[J]. Int. J. Solids Struct., 2010, 47(22):2993-3010.
[4] KUWABARA T. Advances in experiments on metal sheets and tubes in support of constitutive modeling and forming simulations[J]. Int. J. Plast., 2007, 23(3):385-419.
[5] DUAN Yongchuan, ZHANG Fangfang, YAO Dan, et al. Numerical prediction of fatigue life of an A356-T6 alloy wheel considering the influence of casting defect and mean stress[J]. Engineering Failure Analysis, 2020, 118:104903.
[6] CHEN Jiang, CHEN Wenliang. The numerical simulation of multi-stage sheet metal forming based on modified Yoshida-Uemori hardening model[J]. Key Engineering Materials, 2017, 725:554-559.
[7] CHABOCHE J L. A review of some plasticity and viscoplasticity constitutive theories[J]. Int. J. Plast., 2008, 24(10):1642-1693.
[8] YOSHIDA F, UEMORI T. A model of large-strain cyclic plasticity describing the Bauschinger effect and work hardening stagnation[J]. Int. J. Plast., 2002, 18(5):661-686.
[9] LI Xuechun, YANG Yuying, WANG Yongzhi, et al. Effect of the material-hardening mode on the springback simulation accuracy of V-free bending[J]. J. Mater. Process. Technol., 2002, 123(2):209-211.
[10] SUN L, WAGONER R H. Complex unloading behavior:Nature of the deformation and its consistent constitutive Representation[J]. Int. J. Plast., 2011, 27(7):1126-1144.
[11] FINCATO R, TSUTSUMI S, ZILIO A, et al. Fully implicit numerical integration of the Yoshida-Uemori two-surface plasticity model with isotropic hardening stagnation[J]. Fracture and Structural Integrity, 2021, 15(57):114-126.
[12] EGGERTSEN P A, MATTIASSON K. On the identification of kinematic hardening material parameters for accurate springback predictions[J]. Int. J. Mater. Form., 2010, 4(2):103-120.
[13] GAU J, KINZEL G L. A new model for springback prediction in which the Bauschinger effect is considered[J]. International Journal of Mechanical Sciences, 2001, 43(8):1813-1832.
[14] DUAN Yongchuan, GUAN Yingping, WU Bin. Numerical prediction spring-back of high strength steel tailor welded blanks V-die bending process[J]. Chinese Journal of Mechanical Engineering, 2013, 49(23):76-83.
[15] LIN J, HOU Y, MIN J, et al. Effect of constitutive model on springback prediction of MP980 and AA6022-T4[J]. Int. J. Mater. Form., 2020, 13(5):1-13.
[16] MIN J, GUO N, HOU Y, et al. Effect of tension-compression testing strategy on kinematic model calibration and springback simulation of advanced high strength steels[J]. International Journal of Material Forming, 2021, 14:435-448.
[17] GHAEI A, GREEN D E, TAHERIZADEH A. Semi-implicit numerical integration of Yoshida-Uemori two-surface plasticity model[J]. International Journal of Mechanical Sciences, 2010, 52(4):531-540.
[18] 李健强. 材料本构模型的参数标定及其在高强度钢板材弯曲回弹预测中的应用[D]. 广州:华南理工大学, 2017. LI Jianqiang. Constitutive model parameter identification and its application to bending springback prediction of high strength sheet metal[D]. Guangzhou:South China University of Technology, 2017.
[19] JIHAD N, HASSAN M N, SIAMAK M. Effects of hardening model and variation of elastic modulus on springback prediction in roll forming[J]. Metals, 2019, 9(9):1005.
[20] ZHAO K M, LEE J K. Generation of cyclic stress-strain curves for sheet metals[J]. J. Eng. Mater. Technol., 2001, 123(4):391-397.
[21] CARBONNIERE J, THUILLIER S, SABOURIN F, et al. Comparison of the work hardening of metallic sheets in bending-unbending and simple shear[J]. Int. J. Mech. Sci., 2009, 51(2):122-130.
[22] ZHANG Zhiqiang, JIA Xiaofei, YUAN Qiuju. Springback analysis of trip high strength steel based on Yoshida-Uemori model[J]. Engineering and Technology Edition, 2015, 45(6):1852-1856.
[23] LEE J Y, LEE J W, LEE M G, et al. An application of homogeneous anisotropic hardening to springback prediction in pre-strained U-draw bending[J]. Int. J. Solids Struct., 2012, 49(25):3562-3572.
[24] CHUN B K, KIM H Y, LEE J K. Modeling the Bauschinger effect for sheet metals, part I:theory[J]. International Journal of Plasticity, 2002, 18(5-6):571-595.
[25] YOSHIDA F, UEMORI T. A model of large-strain cyclic plasticity and its application to springback simulation[J]. Key Engineering Materials, 2003, 457(233-236):47-58.
[26] CHUNG K, LEE M, KIM D, et al. Springback evaluation of automotive sheets based on isotropic-kinematic hardening laws and non quadratic anisotropic yield functions, part I:Theory and formulation[J]. International Journal of Plasticity, 2005, 21(5):861-882.
[27] CHOI Y, HAN C S, LEE J K, et al. Modeling multi-axial deformation of planar anisotropic elastic-plastic materials, part I:Theory[J]. International Journal of Plasticity, 2006, 22(9):1745-1764.
[28] LEE M, KIM D, KIM C, et al. A practical two surface plasticity model and its application to spring-back prediction[J]. International Journal of Plasticity, 2007, 23(7):1189-1212.