各向异性本构关系在板料成形数值模拟中的应用

Application of anisotropic constitutive equations to numerical simulation of sheet forming

对几种能表达面内各向异性的屈服准则Hill、Barlat-Lian、Barlat进行了比较。在弹性变形服从各向同性广义虎克定律的情况下,给出了基于张量算法推导的弹塑性本构关系的一般表达式,并由此导出了相应屈服准则的弹塑性本构关系的显式表达。借助ABAQUS软件本构模块用户子程序接口,分别实现了这些屈服准则在ABAQUS的嵌入。以模拟方形盒的拉延过程为例,分析了不同的屈服准则在板料成形过程数值模拟中的应用。模拟结果表明,基于弹塑性本构关系一般表达所列出的相应屈服准则的显式表达式是正确的;在采用壳元来模拟板料成形时,采用Barlat准则的模拟结果和采用Barlat-Lian准则的结果差别不大。

Three yield criteria including Hill, Barlat-Lian and Barlat are reviewed which characterize the planar anisotropy for the metal sheet forming process. Under the condition that the elastic deformation obeys the generalized Hooke's Law, a general expression of elastoplastic constitutive equations applicable to various yield criteria is derived based on the tensor algorithms. The explicit expressions of elastoplastic constitutive equations related to each yield criterion are presented and implemented to ABAQUS software as the user subroutines. Through simulating the drawing process of a square box, the application of anisotropic constitutive equations to the numerical simulation of sheet forming is studied. The results show that the presented explicit expressions, which are derived from the general expression, are correct, and there are no more differences between the applications of Barlat and Barlat-Lian to shell elements.