A new model family for the strength distribution of fibers in relation to their length

Based on the weakest-link model, a family of fiber strength distributions is investigated assuming a two-stage failure process. At the first stage, a weakest link is formed (instantly or gradually), but at the second one the fracture of this link takes place. The gradual accumulation of flaws is described with the aid of Markov chain theory. The adequacy of the models considered is verified by checking them against experimental strength data for E-glass and flax fibers of various lengths. It is found that the models are not less accurate, but are even better, in a number of cases, than the model based on the known modified Weibull model with a power-law relation between the fiber length and the scale parameter.