Delaunay-Network Modelling of Creep Failure in Regular Polycrystalline Aggregates by Grain Boundary Cavitation

In polycrystalline materials at elevated temperatures subjected to stationary loading, creep fracture occurs as a result of failure mechanisms on the size scale of grains, namely the nucleation and diffusive growth of cavities until coalescence leads to microcracks. In this paper, a polycrystalline aggregate is modelled by so-called Delaunay elements associated with individual grain boundary facets, whose constitutive behaviour represents dislocation creep inside the grains as well as the cavitation processes on the associated grain facet. Free grain boundary sliding and the elastic deformation of the grain material are also taken into account. Unit cells of polycrystalline aggregates containing many grains are investigated, assuming regular hexagonal grains and allowing for cavitation on all facets, possibly at different rates. The development of creep damage is simulated numerically, starting from nearly no initial damage until an excessive number of microcracked grain boundaries cause disintegration of the polycrystal. It is demonstrated that continuous stress redistributions take place during the failure process, and that nonuniformities in the nucleation activity can cause the formation of "zones" of stress attenuation, where the grain boundaries damage and microcrack relatively quickly, separated by "shielded" regions. As a result of this, it is found that the orientation of the first microcracks is perpendicular to the macroscopic largest principal tensile stress, as expected, but that the orientation of the microcrack pattern is not necessarily in the same direction