MinMaxDM distributions for an analysis of the tensile strength of a unidirectional composite

An analysis of the tensile strength of some fiber or fiber bundle specimens is presented. The specimens are modeled as chains of links consisting of longitudinal elements (LEs) with different cumulative distribution functions of strength, corresponding to the presence and absence of defects. Each link is considered as a system of parallel LEs a part of which can have defects. In the simplest case, the strength of defective elements is assumed equal to zero. The strength of a link is determined by the maximum average stress the link can sustain under a growing load. To calculate the stress, the randomized Daniels model or the theory of Markov chains is used. The strength of specimens is determined by the minimum strength of links. The concept of MinMaxDM family of distribution functions is introduced. A numerical example of processing experimental results for a monolayer of carbon bundles is presented.