Ductile failure under plane stress conditions is analyzed at the meso-scale using periodic unit cell model simulations of void growth in a plastically deforming matrix. Equivalent strains to failure by the onset of plastic instability at the macro-scale are estimated using the loss of ellipticity criterion for the equilibrium equations. Failure loci obtained from the cell model simulations are compared with the predictions of an instability-based ductile failure model and the Hosford–Coulomb damage indicator model, under both proportional and non-proportional loading conditions. The instability-based model is shown to quantitatively predict the shape of the failure locus under proportional loading, including the presence of a cusp at uniaxial tension and a ductility minimum under plane strain tension, in the absence of heuristic adjustable parameters in the failure criterion. It is shown that the characteristic shape of the plane stress failure locus is primarily due to the Lode dependence of the failure criterion, and not the damage growth law as assumed in the damage indicator models. Under non-proportional loading involving a step change in loading direction at an intermediate strain, the instability-based model correctly predicts the non-linear variation of the failure strain as a function of the intermediate strain; unlike a linear variation predicted by the damage indicator models, which is not in agreement with the cell model simulations. Forming limit curves showing the strains to the onset of localized necking in thin sheets are also obtained from the cell model simulations using an appropriate modification of the macroscopic instability criterion.

使用周期性晶胞模型模拟塑性变形基质中的空隙增长，在中观尺度上分析平面应力条件下的延性失效。使用平衡方程的椭圆率损失准则估计宏观尺度上因塑性不稳定性开始而失效的等效应变。在比例和非比例加载条件下，将从单元模型模拟获得的失效轨迹与基于不稳定性的延性失效模型和 Hosford–Coulomb 损伤指示器模型的预测进行比较。基于不稳定性的模型显示在比例加载下定量预测失效轨迹的形状，包括在单轴拉伸下存在尖点和平面应变拉伸下的延展性最小值，在失效准则中没有启发式可调参数的情况下。结果表明，平面应力失效轨迹的特征形状主要是由于失效准则的 Lode 依赖性，而不是损伤指标模型中假设的损伤增长规律。在涉及中间应变加载方向阶跃变化的非比例加载下，基于不稳定性的模型正确预测了作为中间应变函数的失效应变的非线性变化；不像一个损伤指标模型预测的线性变化，这与细胞模型模拟不一致。显示应变到薄板中局部颈缩开始的形成极限曲线也通过使用宏观不稳定准则的适当修改从单元模型模拟获得。