Probabilistic failure criteria for individual microstructural elements: an application to hydrogen-assisted crack initiation in alloy 725

Abstract

Mechanical failure of polycrystalline metals is often difficult to predict, in part because of the wide range of conditions under which individual elements of the material’s microstructure fail. We describe an efficient method for posing, assessing, and optimizing failure criteria for individual microstructural elements, such as grains, grain boundaries, precipitates, or precipitate–matrix interfaces. Such criteria may lead to improved failure predictions for polycrystalline metals. Our method constructs a failure probability function from a database of individual failure events obtained from experiments on polycrystalline samples. It then uses the Kullback–Leibler (K–L) divergence to compare it to probability densities corresponding to specific hypothesized failure mechanisms. The likeliest failure mechanism is the one that minimizes the K–L divergence with respect to a suitably chosen null hypothesis. As a demonstration, we apply this approach to hydrogen-assisted crack initiation at coherent twin boundaries in Ni-based alloy 725 and deduce a best-fit failure criterion for them.