Green's function vs. shear-lag models of damage and failure in fiber composites

A Green's function method (GFM) for simulating fiber damage evolution and tensile strength in fiber-reinforced composites is compared in detail to the predictions of the standard shear-lag model (SLM) widely used in the literature. The GFM extracts the in-plane stress concentration factors describing how a broken fiber redistributes in-plane load to surrounding unbroken fibers from more-detailed micromechanical models, such as finite-element models, and uses this limited information to then calculate the propagation of fiber damage up to composite failure. The GFM only approximately includes the three-dimensional nature of the stress transfer and uses an approximate superposition method, but reduces the computational problem significantly. Here, elastic and elastic/plastic 3D SLM are used to provide the stress-transfer input to the GFM, and then predictions for composite behavior from the GFM are compared directly to those from the SLM. For exactly the same starting configuration of stochastic fibers, the GFM predicts (i) evolution of the fiber damage and the formation of critical clusters that are nearly identical to, (ii) composite tensile strengths within 2% of, (iii) a Weibull modulus for the composite strength essentially equal to, that of the SLM, all while requiring over an order of magnitude less computational time for modest-size composites. The approximations made in the GFM are found to have little effect on composite properties. These results support the use of the GFM approach with stress transfer input from accurate detailed finite element studies rather than from approximate SLM. Furthermore, the GFM is well-suited for tackling a wide range of problems that cannot easily be studied using the SLM; e.g. bending deformation and failure, matrix crack propagation, fatigue crack growth, and other situations in which the fiber stress distribution is nonuniform even in the absence of any fiber damage. (C) 2002 Elsevier Science Ltd. All rights reserved.