STATISTICS OF FRACTURE FOR AN ELASTIC NOTCHED COMPOSITE LAMINA CONTAINING WEIBULL FIBERS .1. FEATURES FROM MONTE-CARLO SIMULATION

Monte-Carlo simulation is used to study the effects of the statistics of fiber strength on the fracture process, the fracture resistance, an d the overall strength distribution for an elastic composite lamina wi th an internal transverse notch of N contiguous, broken fibers (0 less than or equal to N less than or equal to 51). To isolate the effects of variability in fiber strength, we assign individual fiber strengths drawn from a Weibull distribution with shape parameter gamma greater than or equal to 3 typical of commercial fibers, and we consider a sim ple case where fiber strength does not vary along the fiber length. Th e latter forces fibers to fail in the notch plane, eliminating the nee d to consider staggered breaks, debonding and fiber pullout. So under an increasing tensile load, failure develops through a progression of random fiber fractures governed by an interplay of stress concentratio ns and variations in fiber strength along the notch plane. Calculation of the fiber stresses for every configuration of surviving and broken fibers that occurs as the load is increased up to catastrophic failur e is performed by an efficient, shear-lag based, break influence super position (BIS) technique. Results show that the mean strength relative to the deterministic value (gamma = infinity) and mean number of new fiber fractures up to crack instability all increase with N regardless of gamma, whereas variability in strength decreases. For smaller gamm a, we identify mechanisms responsible for flaw intolerance in the shor t notch regime and for toughness in the long notch regime, and show th at variability in fiber strength can manifest as a nonlinear mechanism in an otherwise elastically deforming composite. Indeed as N increase s we observe R-curve behavior, which is most pronounced for the smalle st gamma values where fracture resistance increases markedly and where mean fracture strength scales inversely with the initial notch size s lower than the usual power of 1/2. Compared to simulation results, a w eakest-link or first failure model and unique fiber strength model sev erely underestimate fracture strength, failing to capture the statisti cal aspects of composite fracture. (C) 1997 Elsevier Science Ltd.