Analysis of Stress Intensity Factor of a Fibre Embedded in a Matrix

The analytical or numerical determination of the stress intensity factor (SIF) in cracked bodies usually assumes the body to be isolated. However, in fibre-reinforced composites, the fibre, which is the main load-carrying component, is embedded in a matrix. To clarify the effect the embedding matrix has on the SIF of the fibre, we propose a 3D computational model of an orthotropic fibre embedded in an isotropic matrix, and compute the SIF using the J-integral method. A parametric analysis based on dimensionless variables explores the effect of the fibre-matrix stiffness ratio as well as the effect of the degree of elastic orthotropy of the fibre. The results show that the SIF is strongly influenced by both factors, and that the matrix reduces the SIF by limiting the crack opening.