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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。
Based on the elastoplastic constitutive model considering the anisotropy of metal material and internal micro-damage, combined with Hill general bifurcation theory and Swift maximum tension instability theory, the theoretical calculation of metal forming limit curve is carried out. The calculation based on the Hill general bifurcation theory is carried out by the finite element software Abaqus. For the maximum Swift failure theory of Swift, the analytical expressions of the long axis and short axis ultimate strain under four kinds of isotropic hardening models are deduced. The calculated results show that the difference between the corresponding ultimate strain of metal dispersed necking occurs predicted by Hill general buckling theory and Swift maximum tension theory is less than 2% under the condition of large deformation, In practical applications, when it is difficult to use Swift maximal pull theory to analyze the dispersion and constriction limit strain of complex materials, we can use the general bifurcation theory to make the substitution calculation.