Statistics of fracture of composite materials under multiaxial loading

A brittle fracture model is developed for composite structures with continuous aligned fiber reinforcement. Statistical data from the fracture of uniaxial coupons and information from a stress analysis are used to predict the fracture statistics of a brittle composite structure. The structure is divided into physically plausible subvolumes: these subvolumes must be large enough to contain the typical fracture-inducing flaw, thus minimizing element interactions, and small enough to have an approximately constant stress state within the volume. Probabilistic forms of various macroscopic fracture theories are applied to compute the subvolume reliabilities; the reliability for a subvolume is scaled according to its volume using a weak link model. These subvolume reliabilities are then combined to yield the structure reliability in a process analogous to numerical integration. The macroscopic fracture theories considered include the maximum stress, which leads to the principle of independent action, and the interactive maximum distortion energy criterion. The developed model is used to predict fracture statistics for a short off-axis specimen which experiences substantial stress concentrations because of its end constraints. Using data for a glass-epoxy system, the convergence of the method is illustrated by a progressive refinement of the maximum element size. The strength degradation induced by the geometric constraint is determined to be essentially constant. Results of the interactive and non-interactive criteria are compared for a graphite-epoxy system, demonstrating the conservatism of interactive criteria. The short off-axis specimen results show the potential effect of an improper test design on an anisotropic material.