Statistics of fragmentation in a single-fiber composite under matrix yielding and debonding with application to the strength of multi-fiber composites

We study the statistics of fiber fragmentation in a single-fiber composite (SFC) when matrix yielding followed by interface debonding and fiber slip o ccur near fiber breaks as the applied strain is increased. Fiber strength i s governed by flaws that follow Weibull/Poisson statistics. The model assum es that, under increasing applied strain on the SFC, fiber breaks occur ran domly along the fiber from which matrix yield zones grow. At a critical str ain, debond zones also initiate and grow from these breaks, resulting in fi ber sliding with friction at the interface. This results in a two-step, she ar traction profile producing bi-linear fiber stress recovery from breaks u p to a plateau stress. These zones of yielding and debonding form growing e xclusion zones around breaks within which further fiber fractures cannot oc cur. Eventually such zones cover the fiber, a condition called saturation. We model the fragmentation process by using a newly developed statistical t heory that embodies the exclusion zone concept. Key parameters are the debo nd stress and the friction-yield stress ratio. These parameters are varied to determine the effects of debonding on the average fiber fragmentation le ngth versus applied strain. We also obtain accurate estimates of the mean a nd variance in the stress along a fiber versus applied strain, and mention complications involved in obtaining the true values. These quantities are u sed to study the strength distribution and toughness of a long multi-fiber composite undergoing global load-sharing among fibers. Finally, we suggest how to estimate the model parameters from SFC test data. (C) 2000 Elsevier Science Ltd. All rights reserved.