Micromechanical Bases for the Prediction of Failure of the Matrix in Fibrous Composites

Abstract

Prediction of the failure of the matrix (also called inter-fiber failure) has been assigned in many proposals to a certain interaction (typically quadratic) between the components of the stress vector associated to the plane of failure. In this paper, a numerical micromechanical study is conducted considering, based on failure observations, that the mechanism of failure is first of all produced by a crack running between the fiber and the matrix, and secondly by the kinking of these interface cracks whose coalescence produces a crack of macromechanical relevance associated to the inter-fiber failure. The study is carried out by means of several micromechanical models, whose numerical analysis is performed using the Boundary Element Method, allowing contact between the lips of the cracks under consideration. With reference to the first step, which is considered the one determinant of the inter-fiber failure, the objective of the micromechanical analysis is to elucidate the adequacy of the assumption that the stress vector associated to a plane controls the failure of the plane. The results obtained prove numerically that stresses not associated to the macromechanical plane of failure play an important role in the micromechanism of failure of fibrous composites. This conclusion is based on the influence that normal stresses not associated to the plane of failure have in the energy release rate of the interfacial crack between fiber and matrix, this having been considered to be the parameter that characterizes the damage at this first step. With reference to the second step, i.e. the coalescence of the interfacial cracks to generate a crack of macromechanical meaning, it has been found that the most significant phenomena appear for debonding angles between fiber and matrix in the interval between 60 and 70 degrees. First, it has been found that the growth of the crack along the interface is plausibly unstable in mixed mode until it reaches the interval and unconditionally stable in mode II for greater debondings. Second, it is at this interval that the direction of maximum circumferential stress at the neighbourhood of the crack tip is approximately normal to the applied load. Third, if a crack corresponding to a debonding in this interval leaves the interface and penetrates into the matrix: the growth through the matrix is unstable, the value of the energy release rate reaches a maximum (in comparison with other debonding angles), and the energy released is greater than that released for the crack continuing to grow along the interface. All this suggests that it is in this interval of debondings that conditions are most appropriate for a crack to kink. All the aforementioned facts create a micromechanical basis to generate proposals of inter-fiber failure of fibrous composites.