A comparison of classical and consistent shear lag models for failure analysis of unidirectional composites

Abstract

Classical shear lag models have been widely employed for analyzing fiber dominant unidirectional composites with and without damage and are based on the assumptions that all of the axial load is carried by the fibers whereas the matrix carries only shear. With these assumptions the longitudinal equilibrium equation gets decoupled from the transverse equilibrium equation and the analysis becomes simple and, in most cases, presentable in closed form. With the advent of high-temperature composites such as those of ceramic and metal matrix, in which the matrix and fiber moduli are comparable, the axial and transverse load carrying capacity of the matrix cannot be neglected. This necessitated the development of an improved shear lag model, the “Consistent shear lag model”. Comparison of the above two models shows that the classical shear lag model predicts acceptable results if the ratio of the Young's modulus of the fiber to the Young's modulus of the matrix is large. However, for composites in which the fiber and matrix moduli are comparable, a consistent shear lag formulation yields better results, especially in predicting some of the matrix-dominant failure modes.