Modeling of interface cracks in ®ber-reinforced composites with the presence of interphases using the boundary element method

An advanced boundary element method (BEM) with thin-body capabilities was developed recently for the study of interphases in ®ber-reinforced composite materials (Y.J. Liu, N. Xu and J.F. Luo, Modeling of interphases in ®berreinforced composites under transverse loading using the boundary element method, ASME J. Appl. Mech. 67 (2000) 41±49). In this BEM approach, the interphases are modeled as thin elastic layers based on the elasticity theory, as opposed to spring-like models in the previous BEM and some FEM work. In the present paper, this advanced BEM is extended to study the interface cracks at the interphases in the ®ber-reinforced composites. These interface cracks are curved cracks between the ®ber and matrix, with the presence of the interphases. Stress intensity factors (SIFs) for these interface cracks are evaluated based on the developed models. The BEM approach is validated ®rst using available analytical and other numerical results for curved cracks in a single material and straight interface cracks between two materials. Then, the interface cracks at the interphases of ®ber-reinforced composites are studied and the e€ects of the interphases (such as the thickness and materials) on the SIFs are investigated. As a special case, results of the SIFs for sub-interface cracks are also presented. It is shown that the developed BEM is very accurate and ecient for the interface crack analyses, and that the properties of the interphases have signi®cant in ̄uences on the SIFs for interface cracks in ®ber-reinforced composites. Ó 2000 Elsevier Science Ltd. All rights reserved.