基于细观损伤理论的刚塑性有限元方程

Rigid Plastic FEM Equations Based on Void Damage Theory

有限元软件一般将变形体当作致密体进行分析，很少考虑金属空穴损伤对成形极限的影响．基于Ｇｕｒｓｏｎ－Ｔｖｅｒｇａａｒｄ空穴型材料塑性势方程，利用正交法则在刚塑性材料的Ｌｅｖｙ－Ｍｉｓｅｓ流动规则中引入了空穴损伤对应力－应变率场的影响，给出了空穴增长率计算方法，推证了含空穴材料的刚塑性变分原理与含有空穴体积分数的有限元列式，考虑了空穴体积扩张对成形过程的影响．为研究体积成形时材料损伤、裂纹起裂及扩展奠定了基础．

FEM softwares available today carry out numerical analysis of a sound forming body as if it were undamaged. The void effects on the formability limits in the process are seldom taken into account . In this article, based on Gurson Tvergaard void damage plastic potential equations and by using orthogonal flow rules of plastic materials, the influence of void volume fraction on stress and strain rate field is introduced in the Levy Mises flow rules. The variation principle of rigid plastic material with void degradation is demonstrated and the void volume fraction formula is listed. The FEM equations coupled with damage factor are also presented to study the voids growing effects on the volume change. The theory makes it possible to simulate the crack initiation and propagation in metal formation processes.