Approximate upper and lower bounds for the strength of unidirectional composites

This paper addresses the problem of determining the probabilistic strength of unidirectional composites. We first calculated the stress-concentration factors (SCFs) around broken fibers in a three-dimensional, hexagonal-array model. Two approaches were tried to calculate the SCFs. One is a shear-lag analysis originated by Hedgepeth and Van Dyke and the other is close to a local load-sharing rule (LLS). These two sets of SCFs provide the upper and lower bounds of the strength. With these SCFs, we next carried out a Monte Carlo simulation to evaluate the strength of unidirectional composites in which a chain-of-bundles probability model and a Weibull distribution were used. Parametric studies were first conducted and a comparison with experiments and other existing theories was next done. Our `approximate' upper bound was lower than Rosen's prediction and lower bound, higher than Zweben's value. The value from the simulation was also close to the experimental results.