The fiber-matrix interface crack — A numerical analysis using Boundary Elements

Abstract

The calculation of the energy release rate of a debonding interface crack between fiber and matrix in plane strain requires a knowledge of the stress state and displacements at the neighbourhood of the crack tip. Analytical solutions which involve interpenetrations of the free boundaries of the fiber and matrix have classically been used to predict the variation of the energy release rate with the debonding angle. In this paper a numerical study of this problem as a contact problem, using Boundary Elements, is carried out. The singular stress components are modelled by means of singular discontinuous elements, a particular contact algorithm, which is very appropriate for cases like that under consideration where the fiber is much stiffer than the matrix, having been proposed. The numerical procedure shows the appearance of a contact zone with physical meaning starting at a certain value of the debonding angle, which implies the presence of a pure mode II of fracture. The values of G found by BEM are compared with those predicted by the use of an analytical solution showing clear discrepancies when the contact zone starts to develop, BEM always predicting smaller values of the energy release rate, in accordance with the absence of mode I in the presence of a contact zone.