A model for predicting grain boundary cracking in polycrystalline viscoplastic materials including scale effects

A model is developed herein for predicting the mechanical response of inela stic crystalline solids. Particular emphasis is given to the development of microstructural damage along grain boundaries, and the interaction of this damage with intragranular inelasticity caused by dislocation dissipation m echanisms. The model is developed within the concepts of continuum mechanic s, with special emphasis on the development of internal boundaries in the c ontinuum by utilizing a cohesive zone model based on fracture mechanics. In addition, the crystalline grains are assumed to be characterized by nonlin ear viscoplastic mechanical material behavior in order to account for dislo cation generation and migration. Due to the nonlinearities introduced by th e crack growth and viscoplastic constitution, a numerical algorithm is util ized to solve representative problems. Implementation of the model to a fin ite element computational algorithm is therefore briefly described. Finally , sample calculations are presented for a polycrystalline titanium alloy wi th particular focus on effects of scale on the predicted response.