Influence of a neighbour fibre on the onset and growth of a fibre-matrix debond under biaxial loading. A study by Finite Fracture Mechanics at linear elastic interfaces

Abstract

The aim of the present paper is to study the interaction between two aligned fibres embedded in a large matrix. Special attention is taken to the influence of the presence of a second fibre on the fibre-matrix interface failure. The Linear Elastic Brittle Interface Model (LEBIM) is used to model the fibre-matrix interface behaviour. In LEBIM, an undamaged point of the interface behaves as a linear-elastic spring with a linear relation between tractions and relative displacements. In order to model an interface point failure, the LEBIM follows a law which takes into account the variation of the fracture toughness with the fracture mode mixity. The failure criterion used in this study is based on a Finite Fracture Mechanics (FFM) approach, where the stress and energy criteria are appropriately coupled. The FFM approach applied to the LEBIM is able to make the values of interface strength and fracture toughness to be independent. In the original LEBIM these values are restrictively tied. The present methodology uses a 2D Boundary Element Method (BEM) code to carry out the analysis of interfaces failure. The numerical results show that the distance between the fibres affects the position where the debond (interface crack) onset occurs. It also influences the subsequent debond growth along the interfaces. As could be expected, for increasing distances the results tend to the single-fibre problem solution.