Void size, shape, and orientation effects in shear-dominated void coalescence across scales

Abstract

In a stress state dominated by shear, pre-existing voids rotate, elongate, and close up to form micro-cracks, which interact through void coalescence and eventually may cause a complete loss of load-carrying capacity. The mechanism sets apart void coalescence in shear from that under tensile-dominated stress states, and the present work demonstrates that gradient strengthening affects the macroscopic strain at the onset of plastic flow localization leading to coalescence. Despite that zero or limited void growth develop in shear, a severe heterogeneous plastic straining develops near the void, which generates large plastic strain gradients accompanied by densities of Geometrically Necessary Dislocations (GNDs) in addition to the Statistically Stored Dislocations (SSDs) that controls conventional strain hardening. The GNDs lead to additional micron scale strengthening, and the present work investigates their effect on the plastic flow localization leading to void coalescence in shear by modeling voids embedded in a gradient-enhanced matrix material, thus revisiting the early work by Tvergaard (2008), which was carried out in a conventional scale independent setting. The Fleck–Willis gradient theory is assumed to govern the matrix surrounding the voids such that a material length parameter enters the analysis. Increasing the length parameters while keeping the void volume fraction and intervoid distance constant corresponds to diminishing the material microstructure. The results show that (i) voids with the minor axis in the direction of the shear (denoted “prolate”), give the highest ductility mainly due to the larger intervoid ligament; (ii) both the initial relative void size and the initial void orientation have strong effects on material ductility across the scales; (iii) the initial void orientation plays a fundamental part in the void deformation mechanism and the plastic field that develops prior to coalescence; (iv) the ductility increases substantially when down-scaling the microstructure where the gradient strengthening intensifies (corresponding to increasing the material length parameter). Throughout, fitting functions for the average shear angle at the onset of plastic flow localization are suggested, with respect to the relative void size, the initial void orientation, and the intrinsic material length parameter, to bring out the dependencies and facilitate using the unit cell results in continuum models.