Modelling interfacial cracking and matrix cracking in particle reinforced composites using the extended Voronoi cell finite element method

Abstract

In this paper, a new extended Voronoi cell finite element method (X-VCFEM), in which two new elements in the crack propagation process are proposed and a remeshing algorithm is constructed, is proposed to model the initiation and propagation of the interface crack and the matrix crack in particulate reinforced composites. In order to accurately capture crack-tip stress concentrations, some singular stress terms of Williams expansion in the vicinity of crack tips are introduced in the stress functions in X-VCFEM. The direction of the crack propagation in matrix is determined by the maximum energy release rate and the interface crack propagation along the interface or into the matrix is assessed on the base of a series of criteria relating to the critical normal stress and the critical hoop stress. Then several numerical examples are used to demonstrate the effectiveness of X-VCFEM by comparing with results obtained by the commercial software ABAQUS. At last, a numerical example is given for a complex structure with 20 randomly distributing inclusions to model the interfacial cracking and matrix cracking. It is certain that this method is a powerful way to model the interfacial and matrix damage of composites containing a great deal of inclusions and cracks.