Competing damage mechanisms in a two-phase microstructure: how   microstructure and loading conditions determine the onset of fracture
  This paper studies the competition of fracture initiation in the ductile soft phase and in the comparatively brittle hard phase in the microstructure of a two-phase material. A simple microstructural model is used to predict macroscopic fracture initiation. The simplicity of the model ensures highly efficient computations, enabling an comprehensive study: a large range of hard phase volume fractions and yield stress ratios, for wide range of applied stress states. Each combination of these parameters is analyzed using a large set of (random) microstructures. It is observed that only one of the phases dominates macroscopic fracture initiation: at low stress triaxiality the soft phase is dominant, but above a critical triaxiality the hard phase takes over resulting in a strong decrease in ductility. This transition is strongly dependent on microstructural parameters. If the hard phase volume fraction is small, the fracture initiation is dominated by the soft phase even at high phase contrast. At higher hard phase volume fraction, the hard phase dominates already at low phase contrast. This simple model thereby reconciles experimental observations from the literature for a specific combination of parameters, which may have triggered contradictory statements in the past. A microscopic analysis reveals that the average phase distribution around fracture initiation sites is nearly the same for the two failure mechanisms. Along the tensile direction, regions of the hard phase are found directly next to the fracture initiation site. This `band' of hard phase is intersected through the fracture initiation site by `bands' of the soft phase aligned with shear. Clearly, the local mechanical incompatibility is dominant for the initiation of fracture, regardless whether fracture initiates in the soft or in the hard phase. 
T.W.J. de Geus, R.H.J. Peerlings, M.G.D. Geers
cond-mat.mtrl-sci