Shear-lag model for failure simulations of unidirectional fiber composites including matrix stiffness

Abstract

In this paper, we develop a shear-lag model and an influence superposition technique to quickly compute the stresses and displacements in 2D unidirectional fiber composites in response to multiple fiber and matrix breaks. Unlike previous techniques, both the fiber and matrix are able to sustain axial load, and the governing shear-lag equations are derived based on the principle of virtual work and the finite element method. The main advantages of influence superposition techniques are that computation is tied to the amount of damage, rather than the entire volume considered and discretization is not needed, removing any uncertainties associated with meshing. For illustration, we consider a row of N (up to 301) contiguous fiber breaks and highlight important influences that N and the matrix-to-fiber stiffness ratio, ρ= E m A m/ E f A f, have on stress redistribution. Comparisons with the Mode I plane orthotropic linear elasticity solution are favorable for both shear and axial tensile stresses. The best applications for such techniques are as numerical micromechanics tools in large-scale simulation codes of failure in fibrous composites. The present study is an important prerequisite for simulations and modeling of random fracture patterns, as would naturally develop in a real composite. Arbitrarily misaligned breaks are no more complicated to compute, and we reserve analyses of such cases to future simulation work involving random fiber strengths.