Cohesive traction–separation relations for tearing of ductile plates with randomly distributed void nucleation sites

Cohesive zone traction-separation relations, and the related phenomenological parameters, for steady-state ductile plate tearing, are strongly tied to the micro-mechanics governing the void nucleation and growth process leading to localized deformation and micro-crack formation. The effects of such local variations on the damage evolution and cohesive zone parameters, respectively, are brought out in this study. A 2D plane strain model setup, first considered in Nielsen and Hutchinson (Int J Impact Eng 48:15–23 (2012)], is adopted, but here by discretely modeling a finite number of finite-size void nucleation sites distributed randomly in the plate material. It is found that the heterogeneous material conditions, resulting from the nucleation process, strongly affect the localization of damage and fracture, which influence the cohesive energy. By considering a number of realizations of the random distribution for each material configuration, it is concluded that: (i) the peak force in the cohesive traction-separation relation is, essentially, unaffected by the heterogeneity coming into play through the damage-related microstructure, while (ii) the cohesive energy decreases when either increasing the number or the size of the nucleation sites. The cohesive energy is found to be in the range of those previously reported for homogeneous materials, but a direct comparison should be made with caution. The results imply that care should be taken if the actual material configuration diverges from a homogeneous microstructure such as when considering very thin plates and for plates with a few void nucleation sites.