An isotropic multi-surface model of porous material plasticity is derived and employed to investigate the effects of the third stress invariant in ductile failure. The constitutive relation accounts for both homogeneous and inhomogeneous yielding of a material containing a random distribution of voids. Individual voids are modeled as spheroidal but the aggregate has no net texture. Ensemble averaging is invoked to operate a scale transition from the inherently anisotropic meso-scale process of single-void growth and coalescence to some macroscopic volume that contains many voids. Correspondingly, expressions for effective yield and associated evolution equations are derived from first principles, under the constraint of persistent isotropy. It is found that the well-known vertex on the hydrostatic axis either disappears for sufficiently flat voids or develops into a lower-order singularity for elongated ones. When failure is viewed as the onset of an instability, it invariably occurs after the transition to inhomogeneous yielding with the delay between the two depending strongly upon the Lode parameter. The strain to failure is found to be weakly dependent on the Lode parameter for shear-dominated loadings, but strongly dependent on it near states of so-called generalized tension or compression. Experimentally determined fracture loci for near plane stress states are discussed in light of the new findings.

导出了多孔材料可塑性的各向同性多表面模型，并将其用于研究第三应力不变性对延性破坏的影响。本构关系解释了包含空隙随机分布的材料的均匀和不均匀屈服。单个空隙被建模为球形，但聚集体没有净纹理。调用集合平均来进行从单孔生长和合并的固有各向异性介观尺度过程到包含许多空隙的某些宏观体积的尺度转换。相应地，在持续各向同性的约束下，有效收益率的表达式和相关的演化方程式是从第一原理导出的。发现静液压轴上的众所周知的顶点对于足够平坦的空隙会消失，或者对于细长的空隙会发展为较低阶的奇点。当故障被视为不稳定的开始时，它总是在过渡到非均匀屈服后发生，两者之间的延迟很大程度上取决于Lode参数。发现破坏应变与剪切支配载荷的Lode参数关系不大，而在所谓的广义拉力或压缩状态附近则强烈依赖于Lode参数。根据新发现，讨论了针对近平面应力状态的实验确定的断裂位点。