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

In this paper, we develop a shear-lag model and an influence superposition technique to quickly compute the stresses and displacements in 2D unidirect ional fiber composites in response to multiple fiber and matrix breaks. Unl ike previous techniques, both the fiber and matrix are able to sustain axia l load, and the governing shear-lag equations are derived based on the prin ciple of virtual work and the finite element method. The main advantages of influence superposition techniques are that computation is tied to the amo unt of damage, rather than the entire volume considered and discretization is not needed, removing any uncertainties associated with meshing. For illu stration, we consider a row of N (up to 301) contiguous fiber breaks and hi ghlight important influences that N and the matrix-to-fiber stiffness ratio , rho = 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 b oth shear and axial tensile stresses. The best applications for such techni ques are as numerical micromechanics tools in large-scale simulation codes of failure in fibrous composites. The present study is an important prerequ isite for simulations and modeling of random fracture patterns, as would na turally develop in a real composite. Arbitrarily misaligned breaks are no m ore complicated to compute, and we reserve analyses of such cases to future simulation work involving random fiber strengths. (C) 1999 Elsevier Scienc e Ltd. All rights reserved.