A microstructural approach to flaw size dependence of strength in engineering ceramics

In this work, microstructural effects on the flaw size dependence of ceramic strength were investigated from aspects of stress analysis in the grain just ahead of the crack tip and also R-curve behaviour. In the analysis, it was assumed that the stress averaged in one grain just ahead of the crack tip, in ceramics, might control the fracture from a flaw. A microstructurally modified fracture criterion using the averaged stress was established by introducing the R-curve due to the grain bridging effect for longer cracks. A new R-curve of an exponential type was proposed for the fracture criterion. The criterion could adequately express the central trend in the dispersal of experimental results in the strength versus flaw size relation. To explain the scatter of results, the size distribution and the crystallographic anisotropy of the grain ahead of the crack tip were examined as dominant factors. The lower bound of strength scatter was estimated from the largest grain size, and the strength dispersion was reduced by decreasing the range of grain size variation. In FEM simulations, each element was regarded as one grain with a different crystallographic orientation, which was randomly selected by using a series of quasi-uniform random numbers. It was revealed that the scatter of strength due to crystallographic variations was smaller than the strength dispersion caused by a distributed grain size.