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This paper studies a two-phase material with a microstructure composed of ahard brittle reinforcement phase embedded in a soft ductile matrix. Itaddresses the full three-dimensional nature of the microstructure andmacroscopic deformation. A large ensemble of periodic microstructures is used,whereby the individual grains of the two phases are modeled using equi-sizedcubes. A particular solution strategy relying on the Fast Fourier Transform isadopted, which has a high computational efficiency both in terms of speed andmemory footprint, thus enabling a statistically meaningful analysis. Thissolution method naturally accompanies the regular microstructural model, as theFast Fourier Transform relies on a regular grid.  Using the many considered microstructures as an ensemble, the averagearrangement of phases around fracture initiation sites is objectivelyidentified by the correlation between microstructure and fracture initiation --in three dimensions. The results show that fracture initiates where regions ofthe hard phase are interrupted by bands of the soft phase that are aligned withthe direction of maximum shear. In such regions, the hard phase is arrangedsuch that the area of the phase boundary perpendicular to the principal straindirection is maximum, leading to high hydrostatic tensile stresses, while notinterrupting the shear bands that form in the soft phase. The localincompatibility that is present around the shear bands is responsible for ahigh plastic strain. By comparing the response to a two-dimensionalmicrostructure it is observed that the response is qualitatively similar (bothmacroscopically and microscopically). One important difference is that thelocal strain partitioning between the two phases is over-predicted by thetwo-dimensional microstructure, leading to an overestimation of damage.

Fracture initiation in multi-phase materials: a systematic three-dimensional approach using a FFT-based solver