Cohesive element approach to grain level modelling of intergranular cracking

Abstract

A cohesive element approach to modelling the intergranular cracking on the grain level is presented. The cohesive elements with zero physical thickness are directly inserted between the adjacent grains. These are obtained using 3D Voronoi tessellation. The grain boundary with the highest normal stress has on average 50% higher normal stress compared to the applied external load, which in this work is equal to half yield stress. Setting the maximum traction of a cohesive element equal to yield stress therefore results in limited grain boundary damage. Most of the early damage initiates at intersections of grain boundaries with the external surfaces of the model. A smaller fraction of damage develops inside the model, mostly at the triple lines where several grain boundaries come together.A novelty in this work is the developed analytical expression for assessing the cohesive element response when using viscous regularization for alleviating the convergence issues. It shows that the viscous regularization should not be higher than 10% of the step time. Otherwise the delay in the damage evolution and the area underneath the traction-separation response of a cohesive element increase considerably. This is also demonstrated on a model with 500 grains where the time-evolution of the displacements in the cohesive elements is significantly more complicated compared to the linear assumption in the theoretical expression. Also, the fraction of the elastic displacements compared to the total displacements at complete failure plays a role, with a higher elastic part resulting in smaller increase of the maximum traction in the cohesive element.