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Randomness in the void distribution within a ductile metal complicatesquantitative modeling of damage following the void growth to coalescencefailure process. Though the sequence of micro-mechanisms leading to ductilefailure is known from unit cell models, often based on assumptions of a regulardistribution of voids, the effect of randomness remains a challenge. In thepresent work, mesoscale unit cell models, each containing an ensemble of fourvoids of equal size that are randomly distributed, are used to find statisticaleffects on the yield surface of the homogenized material. A yield locus isfound based on a mean yield surface and a standard deviation of yield pointsobtained from 15 realizations of the four-void unit cells. It is found that theclassical GTN model very closely agrees with the mean of the yield pointsextracted from the unit cell calculations with random void distributions, whilethe standard deviation $\textbf{S}$ varies with the imposed stress state. It isshown 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 $T \approx4$. At even higher triaxialities it decreases slightly. The results indicatethat the dependence of the standard deviation on the stress state follows fromvariations in the deformation mechanism since a well-correlated variation isfound for the volume fraction of the unit cell that deforms plastically atyield. Thus, the random void distribution activates different complexlocalization mechanisms at high stress triaxialities that differ from theligament thinning mechanism forming the basis for the classical GTN model. Amethod for introducing the effect of randomness into the GTN continuum model ispresented, and an excellent comparison to the unit cell yield locus isachieved.

A micro-mechanics based extension of the GTN continuum model accounting for random void distributions