两种塑性失稳理论下的分散性颈缩极限预测

Diffused necking limit predicted by two different plastic instability theories

使用考虑金属材料各向异性及内部微损伤的弹塑性本构模型结合Hill一般性分叉理论及Swift最大拉力失稳理论,进行了金属材料的成形极限曲线的理论计算。基于Hill一般性分叉理论的计算使用有限元软件Abaqus进行;对于Swift最大拉力失稳理论,推导了4种各向同性硬化模型下的长轴、短轴极限应变解析表达式。计算结果表明:在平面应力大变形条件下,使用Hill一般性分叉失稳理论与Swift最大拉力理论预测得到的金属的分散性颈缩发生时对应的极限应变之间的差异小于2%,在实际应用中当难以使用Swift最大拉力理论对复杂材料进行分散性颈缩极限应变的解析计算时,可以使用一般性分叉理论进行替代计算。

The theoretical calculation of forming limit curve of metals was carried out by a damaged elastic-plastic constitutive model according to its anisotropy and tiny microdamage combining with the Hill＇s general bifurcation theory and Swift＇s maximum force theory. Calculation with Hill＇s theory was realized by Abaqus,while analytical formulas of major and minor limit strain under four different hardening laws were found by Swift＇s theory. Results show that under the condition of plane stress and large deformation,the difference of ultimate strains corresponding to diffused necking predicted by Hill＇s theory and Swift＇s theory respectively is less than 2%. In practice,when it is difficult to calculate by Swift＇s theory,it can be replaced by Hill＇s theory.