Establishment and Application of an Anisotropic Nonlinear Kinematic Hardening Constitutive Model

doi:10.3901/JME.2017.14.159

Abstract

Abstract: Based on the assumption of plane stress, an anisotropic nonlinear kinematic hardening constitutive model has been established according to HILL48 anisotropic yield criterion, non-linear kinematic hardening theory of ARMSTRONG-FREDERICK and plastic flow theory. The corresponding UMAT subroutine of ABAQUS for this constitutive model is compiled by Fortran, in which the backward Euler return mapping algorithm is adopted. A process of sheet metal being pulled through drawbead are simulated using the developed constitutive model and two constitutive models in ABAQUS with isotropic yield criterion and kinematic hardening theory respectively, then corresponding tangential stress-strain cycle curves are received. On comparison, the result of applying the developed constitutive model is closer to the experimental result. The developed elasto-plastic constitutive model is credible, which could be applied to research about the reverse load deformation behavior of sheet metal.

Key words: anisotropic yield, cyclic loading, drawbead, non-linear kinematic hardening, UMAT subroutine

CLC Number:

TG381

LI Qun, XIN Ce, JIN Miao, ZHANG Qing. Establishment and Application of an Anisotropic Nonlinear Kinematic Hardening Constitutive Model[J]. Journal of Mechanical Engineering, 2017, 53(14): 159-164.

References

[1] 李光耀,王琥,杨旭静,等. 板料冲压成形工艺与模具设计制造中的若干前沿技术[J]. 机械工程学报,2010,46(10):31-39. LI Guangyao,WANG Hu,YANG Xujing,et al. Some cutting-edge technology in sheet metal forming process and die design[J]. Journal of Mechanical Engineering,2010,46(10):31-39.
[2] 张飞飞,陈劼实,陈军,等. 各向异性屈服准则的发展及实验验证综述[J]. 力学进展,2012,42(1):68-80. ZHANG Feifei,CHEN Jieshi,CHEN Jun,et al. Development and experimental verification of anisotropic yield criteria[J]. Advances in Mechanics. 2012,42(1):68-80.
[3] HILL R. A theory of the yielding and plastic flow of anisotropic metals[J]. Proceedings of the Royal Society A,1948,193(1033):281-297.
[4] HILL R. 塑性数学理论[M]. 北京:科学出版社,1966. HILL R. Mathematical theory of plasticity[M]. Beijing:Science Press,1966.
[5] BARLAT F. Plastic behavior and stretch ability of sheet metals. Part I:A yield function for orthotropic sheets under plane stress conditions[J]. International Journal of Plasticity,1989,5(1):51-66.
[6] BARLAT F,LEGE D J,BREM J C. A six-component yield function for anisotropic materials[J]. International Journal of Plasticity,1991,7(7):693-712.
[7] HU W. An orthotropic yield criterion in a 3-D general stress state[J]. International Journal of Plasticity,2005,21(9):1771-1796.
[8] VERMA R K,KUWABARA T,CHUNG K,et al. Experimental evaluation and constitutive modeling of non-proportional deformation for asymmetric steels[J]. International Journal of Plasticity,2011,27(1):81-101.
[9] 柳玉起,徐丹,许江平. 改进的5参数BARLAT-LIAN屈服准则[J]. 华中科技大学学报,2008,36(1):129-132. LIU Yuqi,XU Dan,XU Jiangping. BARLAT-LIAN 5 parameter yield criterion for improvement[J]. Journal of Huazhong University of Science:Science,2008,36(1):129-132.
[10] CAZACU O,PLUNKETT B,BARLAT F. Orthotropic yield criterion for hexagonal closed packed metals[J]. International Journal of Plasticity,2006,22(7):1171-1194.
[11] PLUNKETT B,CACAZU O,BARLAT F. Orthotropic yield criteria for description of the anisotropy in tension and compression of sheet metals[J]. International Journal of Plasticity,2008,24(5):847-866.
[12] 马鸣图,段祝平,友田阳. 金属合金中的包辛格效应及其在工业生产中的应用[M]. 北京:机械工业出版社,1994. MA Mingtu,DUAN Zhuping,YOU Tianyang. Bauschinger effect for metal alloys and its application in the industrial production[M]. Beijing:China Machine Press,1994.
[13] ZIEGLER H. A modification of Prager's hardening rule[J]. Quart. Appl. Math.,1959,17:55-65.
[14] 余海燕. 金属薄板应变硬化模型比较分析[J]. 锻压技术,2012,37(5):1-6. YU Haiyan. Comparative study on strain hardening models of thin metal sheet[J]. Forging & Stamping Technology,2012,37(5):1-6.
[15] MROZ Z. An attempt to describe the behavior of metal under cyclic loads using a more general work hardening model[J]. Acta Mech.,1969,7:199-212.
[16] ARMSTRONG P J,FREDERICK C O. A mathematical representation of the ulti-axial bauschinger effect[R]. Report RD/B/N 731,Central Electricity Generating Board,1966.
[17] CHABOCHE J. Constitutive equations for cyclic plasticity and cyclic viscoplasticity[J]. International Journal of Plasticity,1989,5(3):247-302.
[18] CHUN B K,JINN J T,LEE J K. Modeling the bauschinger effect for sheet metals,Part I:Theory[J]. International Journal of Plasticity,2002,18(5):571-595.
[19] 蒋成钢,陈章华,臧勇. 镁合金板材温热冲压过程的各向异性损伤与失效分析[J]. 机械工程学报,2013,49(16):62-69. JIANG Chenggang,CHEN Zhanghua,ZANG Yong. Analysis of anisotropic damage and failure in hot stamping process of magnesium alloy sheet[J]. Journal of Mechanical Engineering,2013,49(16):62-69.
[20] 王海波,万敏,阎昱,等. 屈服准则在有限元软件中实现的正确性验证[J]. 固体力学学报,2010,31(2):173-180. WANG Haibo,WAN Min,YAN Yu,et al. Correctness verification of yield criterion implemented in a finite element software[J]. Acta Mechanica Solida Sinica,2010,31(2):173-180.