Analysis of residual stresses in a single fibre–matrix composite

Abstract

Thermal stresses are induced in fibre/matrix composites due to the difference in coefficients of thermal expansion of the constituent materials. The present theoretical method is developed for the analysis of thermal stresses in fibres of finite length embedded in a matrix. Based on the complementary energy approach and minimization of the total complementary energy, the method yields closed-form solutions for the thermal residual stresses, which satisfy the requirements of a free surface around the fibre/matrix composite. The analysis shows that a radial-tensile stress concentration appears at both ends of the composite, subjecting the interface in the vicinity to tension. The interfacial shear stress peaks at some distance into the interface from the fibre ends. A parametric study further shows that thermal stresses are dependent upon the material and geometric properties of the constituents. Stress concentrations shift nearer to the ends of the composite with increase in fibre length while reduction in matrix radius will further accentuate the stress concentrations. A softer matrix tends to reduce the peak interfacial shear and radial-tensile stresses. A small mismatch in the coefficient of thermal expansion between fibre and matrix induces very low thermal stresses in the constituents. The stress concentrations, existing very close to the fibre ends tend to augment the fibre debonding stresses due to mechanical loading and will influence the analysis of interfacial properties in fibre pull- and push-out tests.