A full three dimensional study of a fatigue crack in cast iron is presented. This analysis involves combining various tools, namely, Synchrotron X-ray microtomography Preprint submitted to Elsevier 4 October 2009of an in situ experiment, image acquisition and treatment, 3D volume correlation to measure 3D displacement fields, extraction of the crack geometry, extended digital image correlation to account for the crack displacement discontinuity, crack modeling in an elastic material exploiting the actual crack geometry, and finally estimation of stress intensity factors. All these different tasks are based on specific multiscale approaches.

A new multi-phase-field method is developed for modeling the fracture of polycrystals at the microstructural level. Inter and transgranular cracking, as well as anisotropic effects of both elasticity and preferential cleavage directions within each randomly oriented crystal are taken into account. For this purpose, the proposed phase field formulation includes: (a) a smeared description of grain boundaries as cohesive zones avoiding defining an additional phase for grains; (b) an anisotropic phase field model; (c) a multi-phase field formulation where each preferential cleavage direction is associated with a damage (phase field) variable. The obtained framework allows modeling interactions and competition between grains and grain boundary cracks, as well as their effects on the effective response of the material. The proposed model is illustrated through several numerical examples involving a full description of complex crack initiation and propagation within 2D and 3D models of polycrystals.