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 occur near fiber breaks as the applied strain is increased. Fiber strength is governed by flaws that follow Weibull/Poisson statistics. The model assumes that, under increasing applied strain on the SFC, fiber breaks occur randomly along the fiber from which matrix yield zones grow. At a critical strain, debond zones also initiate and grow from these breaks, resulting in fiber sliding with friction at the interface. This results in a two-step, shear traction profile producing bi-linear fiber stress recovery from breaks up to a plateau stress. These zones of yielding and debonding form growing exclusion zones around breaks within which further fiber fractures cannot occur. Eventually such zones cover the fiber, a condition called saturation. We model the fragmentation process by using a newly developed statistical theory that embodies the exclusion zone concept. Key parameters are the debond stress and the friction-yield stress ratio. These parameters are varied to determine the effects of debonding on the average fiber fragmentation length versus applied strain. We also obtain accurate estimates of the mean and variance in the stress along a fiber versus applied strain, and mention complications involved in obtaining the true values. These quantities are used 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.