Randomness in the void distribution within a ductile metal complicates quantitative modeling of damage following the void growth to coalescence failure process. Though the sequence of micro-mechanisms leading to ductile failure is known from unit cell models, often based on assumptions of a regular distribution of voids, the effect of randomness remains a challenge. In the present work, mesoscale unit cell models, each containing an ensemble of four voids of equal size that are randomly distributed, are used to find statistical effects on the yield surface of the homogenized material. A yield locus is found based on a mean yield surface and a standard deviation of yield points obtained from 15 realizations of the four-void unit cells. It is found that the classical GTN model very closely agrees with the mean of the yield points extracted from the unit cell calculations with random void distributions, while the standard deviation $\textbf{S}$ varies with the imposed stress state. It is shown that the standard deviation is nearly zero for stress triaxialities $T\leq1/3$, while it rapidly increases for triaxialities above $T\approx 1$, reaching maximum values of about $\textbf{S}/\sigma_0\approx0.1$ at $T \approx 4$. At even higher triaxialities it decreases slightly. The results indicate that the dependence of the standard deviation on the stress state follows from variations in the deformation mechanism since a well-correlated variation is found for the volume fraction of the unit cell that deforms plastically at yield. Thus, the random void distribution activates different complex localization mechanisms at high stress triaxialities that differ from the ligament thinning mechanism forming the basis for the classical GTN model. A method for introducing the effect of randomness into the GTN continuum model is presented, and an excellent comparison to the unit cell yield locus is achieved.

翻译：韧性金属中空隙分布的随机性使得从空隙生长到聚结失效过程的损伤定量建模变得复杂。尽管导致韧性失效的微观机制序列已通过单胞模型（通常基于规则空隙分布的假设）得到明确，但随机性的影响仍然是一个挑战。本研究使用介观尺度单胞模型（每个模型包含四个随机分布、尺寸相等的空隙集合）来探究统计效应对均质化材料屈服面的影响。基于从15个四空隙单胞模型实现中获得的平均屈服面与屈服点标准差，确定了屈服轨迹。研究发现，经典GTN模型与随机空隙分布下单胞计算提取的屈服点均值非常吻合，而标准差$\textbf{S}$随所施加应力状态而变化。结果表明，当应力三轴度$T\leq1/3$时标准差接近于零，而当三轴度高于$T\approx 1$时标准差迅速增大，在$T \approx 4$时达到最大值约$\textbf{S}/\sigma_0\approx0.1$，在更高三轴度下又略有降低。这一结果揭示：标准差对应力状态的依赖性源于变形机制的变化，因为在屈服时发生塑性变形的单胞体积分数呈现出高度相关的变异。因此，随机空隙分布在高应力三轴度下激活了不同于构成经典GTN模型基础的韧带减薄机制的其他复杂局部化机制。本文提出了一种将随机性效应引入GTN连续介质模型的方法，并与单胞屈服轨迹取得了极佳的吻合度。