A probabilistic approach to the fracture toughness of composites

Abstract

Abstract Fatigue cracks in polyester reinforced with short Kevlar fibres and glass beads propagate with no detectable damage along random trajectories, reflecting severe heterogeneities in the composite. An order of magnitude scatter of the critical energy release rate, or fracture toughness, has been observed. A statistical approach is introduced to evaluate the cumulative probability of the critical energy release rate as a function of fracture stress, critical crack length, and the angles of crack trajectory inclination, which are random variables. An assemblage of crack trajectories possesses features of Brownian particle motion. With crack propagation considered as a diffusive process, a ‘crack diffusion coefficient’ is introduced which reflects the ability of the composite to deviate the crack trajectory from the energetically most efficient path and thus links the material toughness to its structure. Assuming that the crack propagates through the ‘weakest’ points, the strength field γ is formulated on the basis of the Wiebull distribution. Thus, the γ-field is characterized by scale and shape parameters and a radius of correlation which are found to be 3·70 kJ m−2, 2·88 and 1·0 mm, respectively.