Two-scale porosity effects on cohesive crack growth in a ductile media

Abstract

Microstructures with two distinct size-scales of voids are commonplace in additively-manufactured metals. The smaller-scale voids nucleate from inclusions within the metal, while the larger-scale voids originate from unsintered powder particles. In this work, we study the interaction between these two size-scales of voids ahead of a crack, and the influence on the ductile fracture process. We adopt a finite element model of a centerline crack subjected to small-scale yielding conditions. The diffuse process zone ahead of the crack is modeled by several rows of void-containing cell elements governed by a Gurson porous material relation. Results show that the larger-scale voids near the initial crack tip generally reduces the fracture toughness by facilitating void coalescence with the crack-tip to form a single contiguous damage zone. However, strategic placements of these larger-scale voids within the active plastic zone of the crack-tip can promote crack-tip shielding, leading to diffused damage in the form of multiple unconnected damage zones, and ultimately, a several-fold improvement in toughness. We quantify the fracture behavior, as a function of the relative size and proportion of larger-scale voids in the diffuse process zone, by reconstructing the equivalent crack-tip cohesive zone laws in an elasto-plastic medium via nonlinear field projection. We demonstrate that the cohesive strength, cohesive energy, as well as the functional form of the cohesive zone law, are strongly dependent on the dual void size-scales, which introduces a size-effect into the homogenized traction-separation relationship.