Sample size dependence of flaw distributions for the prediction of brittle solids strength using additive Weibull bimodal distributions

A method to evaluate the mean strength of brittle solids at short gauge length from experiments performed at higher gauge length is proposed for bimodal fracture behavior. The method based on additive Weibull bimodal distributions takes the evolution of the relative proportion of flaws along the gauge length into account via a gauge length dependent mixing parameter. A linear dependence of this parameter vs. the gauge length is proposed. The approach is assessed using experimental results on carbon and E-glass fibers. The new method provides values for the average tensile strength of the fibers at 100 μm up to 27% higher than those calculated using the classical approach. The underestimation of the classical approach can be attributed to the weight of the severe category of flaws at short length that is considered to be the same as that determined at the experimental gauge length, which can be several orders higher. A simplified approach taking into account solely the more severe category of flaw is shown to be applicable for the prediction of the strength at short gauge length independently of the nature of the fiber.