A unit cell model for brittle fracture of particles embedded in a ductile matrix

A finite element based approach for modeling the successive failure of brittle particulates embedded in a ductile matrix is presented. Three-dimensional unit cells describing specific arrangements of spherical particles are employed, which are meshed so that an appropriate fracture surface is predefined for each of the inhomogeneities. Activation of brittle cleavage at these surfaces is controlled deterministically on the basis of Weibull-type fracture probabilities, which are evaluated from the current stress distributions within the particles. irst step uniaxial tensile loading of a particle reinforced metal matrix composite is considered for which damage due to particle fracture is modeled while the other damage modes, interfacial decohesion and ductile failure of the matrix, are not active. Results covering the consecutive cleavage of a number of particles are presented and discussed in terms of the macroscopic response and of the evolution of the fracture probabilities of the particulates.