Statistics of fracture for an elastic notched composite lamina containing Weibull fibers— Part I. Features from Monte-Carlo simulation

Abstract

Monte-Carlo simulation is used to study the effects of the statistics of fiber strength on the fracture process, the fracture resistance, and the overall strength distribution for an elastic composite lamina with an internal transverse notch of N contiguous, broken fibers (0 ≤ N ≤ 51). To isolate the effects of variability in fiber strength, we assign individual fiber strengths drawn from a Weibull distribution with shape parameter γ ≥ 3 typical of commercial fibers, and we consider a simple case where fiber strength does not vary along the fiber length. The latter forces fibers to fail in the notch plane, eliminating the need 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 concentrations 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 failure is performed by an efficient, shear-lag based, break influence superposition (BIS) technique. Results show that the mean strength relative to the deterministic value (y = ∞) and mean number of new fiber fractures up to crack instability all increase with N regardless of γ, whereas variability in strength decreases. For smaller γ, we identify mechanisms responsible for flaw intolerance in the short notch regime and for toughness in the long notch regime, and show that variability in fiber strength can manifest as a nonlinear mechanism in an otherwise elastically deforming composite. Indeed as N increases we observe R-curve behavior, which is most pronounced for the smallest γ values where fracture resistance increases markedly and where mean fracture strength scales inversely with the initial notch size slower than the usual power of 1 2 . Compared to simulation results, a weakest-link or first failure model and unique fiber strength model severely underestimate fracture strength, failing to capture the statistical aspects of composite fracture.