Inverse Determination Method of Johnson-Cook Model Parameters Based on the Stress State Test of Notched Specimens

doi:10.3901/JME.2021.22.060

Abstract

Abstract: Johnson-Cook model is one of the material models suitable for metals with high strain rate, large deformation and strong dynamic load. The determination of parameters corresponding to the material is the key to the application of the model. Since the influence of complex stress state on material properties is not considered, when the model determined by traditional method is used for simulation, there is a significant difference between the calculated results and the actual situation under different stress conditions. Aimed at reduction of such difference, the notched specimens of 6005A-T6 aluminum alloy are designed to characterize different stress states, and the quasi-static uniaxial tensile tests are carried out under the condition of strain rate 4×10^-4 s^-1. Then, an inverse determination method based on genetic algorithm is proposed, in which the test data under different stress states are included in the training set of genetic algorithm. Using Matlab programming, the data interaction and process integration of optimization algorithm and LS-DYNA simulation are realized. By running the program, the optimal solution of model parameters is obtained. The results show that the model parameters obtained by this method make up for the shortcomings of traditional methods. In the complex stress state, it has better applicability.

Key words: Johnson-Cook constitutive model, genetic algorithm, model parameters determination, 6005A-T6 aluminum alloy

CLC Number:

TG113

RU Yifan, ZHANG Lele, LIU Wen, CHEN Geng, DOU Weiyuan. Inverse Determination Method of Johnson-Cook Model Parameters Based on the Stress State Test of Notched Specimens[J]. Journal of Mechanical Engineering, 2021, 57(22): 60-70.

References

[1] JOHNSON G R, COOK W H. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures[J]. Engineering Fracture Mechanics, 1983(21):541-548.
[2] NING Jinqiang, NGUYEN V, HUANG Yong, et al. Inverse determination of Johnson-Cook model constants of ultra-fine-grained titanium based on chip formation model and iterative gradient search[J]. The International Journal of Advanced Manufacturing Technology, 2018, 99(5):1131-1140.
[3] CAI Jun, WANG Kuaishe, ZHAI Peng, et al. A modified Johnson-Cook constitutive equation to predict hot deformation behavior of Ti-6Al-4V alloy[J]. Journal of Materials Engineering&Performance, 2015, 24(1):32-44.
[4] ZHANG Yancheng, OUTEIRO J C, MABROUKI T. On the selection of Johnson-Cook constitutive model parameters for Ti-6Al-4V using three types of numerical models of orthogonal cutting[J]. Procedia Cirp, 2015(31):112-117.
[5] ZHANG Dingni, SHANGGUAN Qianqian, XIE Canjun, et al. A modified Johnson-Cook model of dynamic tensile behaviors for 7075-T6 aluminum alloy[J]. Journal of Alloys&Compounds, 2015(619):186-194.
[6] ZHANG Yiben, YAO Song, HONG Xiang, et al. Amodified Johnson-Cook model for 7N01 aluminum alloy under dynamic condition[J]. Journal of Central South University, 2017, 24(11):2550-2555.
[7] SPRINGMANN M, KUNA M. Identification of material parameters of the Gurson-Tvergaard-Needleman model by combined experimental and numerical techniques[J]. Computational Materials Science, 2005, 32(3-4):544-552.
[8] MILANI A S, DABBOUSSI W, NEMES J A, et al. An improved multi-objective identification of Johnson-Cook material parameters[J]. International Journal of Impact Engineering, 2009, 36(2):294-302.
[9] 董菲, GUENEL G, JEAN L L, 等. 有限元分析法确定Johnson-Cook本构方程材料参数[J]. 上海交通大学学报, 2011, 45(11):1657-1660, 1667. DONG Fei, GUENEL G, JEAN L L, et al. Identification of Johnson-Cook constitutive model by finite element analysis[J]. Journal of Shanghai Jiao Tong University, 2011, 45(11):1657-1660, 1667.
[10] 吕思雨, 钟睦, 葛凯. 7N01铝合金Johnson-Cook模型参数的反算方法[J]. 铁道建筑, 2020, 60(1):139-142. LÜSiyu, ZHONG Mu, GE Kai. Reverse calculation method for Johnson-Cook model parameters of 7N01aluminum alloy[J]. Railway Engineering, 2020, 60(1):139-142.
[11] SPITZIG W A, RICHMOND O. The effect of pressure on the flow stress of metals[J]. Acta Metallurgica, 1984, 32(3):457-463.
[12] BAI Yuanli. Effect of loading history in necking and fracture[D]. Cambridge:Massachusetts Institute of Technology, 2011.
[13] 彭一波, 王罡, 潘尚峰, 等. 考虑动态回复过程的6005A铝合金动态力学模型[J]. 机械工程学报, 2014, 50(10):32-39. PENG Yibo, WANG Gang, PAN Shangfeng, et al. 6005Aaluminum dynamic mechanical model considering the dynamic recovery process[J]. Journal of Mechanical Engineering, 2014, 50(10):32-39.
[14] PENG Yong, CHEN Xuanzhen, PENG Shan, et al. Strain rate-dependent constitutive and low stress triaxiality fracture behavior investigation of 6005 Al alloy[J]. Advances in Materials Science and Engineering, 2018:1-14.
[15] MOHR D, MARCADET S J. Micromechanicallymotivated phenomenological Hosford-Coulomb model for predicting ductile fracture initiation at low stress triaxialites[J]. International Journal of Solids&Structures, 2015(67-68):40-55.
[16] QIAN Lingyun, FANG Gang, PAN Zeng. Modeling of the ductile fracture during the sheet forming of aluminum alloy considering non-associated constitutive characteristic[J]. International Journal of Mechanical Sciences, 2017(126):55-66.
[17] 郭伟国, 田宏伟. 几种典型铝合金应变率敏感性及其塑性流动本构模型[J]. 中国有色金属学报, 2009, 19(1):56-61. GUO Weiguo, TIAN Hongwei. Strain rate sensitivity and constitutive models of several typical aluminum alloys[J]. The Chinese Journal of Nonferrous Metals, 2009, 19(1):56-61.
[18] 包卫平, 赵昱臻, 李春明, 等. 纯铁高温高应变率下的动态本构关系试验研究[J]. 机械工程学报, 2010, 46(4):74-79. BAO Weiping, ZHAO Yuzhen, LI Chunming, et al. Experimental research on the dynamic constitutive relation of pure iron at elevated temperatures and high strain rates[J]. Journal of Mechanical Engineering, 2010, 46(4):74-79.
[19] NOCEDAL J, WRIGHT S J. Numerical optimization[M]. 2nd ed. New York:Springer Science+Business Media, LLC, 2006.
[20] PAN Huanquan, MOTONAO L, MICHAEL C, et al. Solution of multiphase rachford-rice equations by trust region method in compositional and thermal simulations[J]. Journal of Petroleum Science and Engineering, 2020(200):108150.
[21] HOLLAND J B, HOLLAND J, HOLLAND J H, et al. Adaption in natural and artificial systems[J]. Ann Arbor, 1975, 6(2):126-137.