Markov model of connection between the distribution of static strength and fatigue life of a fibrous composite

Within the framework of a unified mathematical model based on the Markov chain theory, an attempt is made to describe the distribution of static strength, the fatigue curve, and the accumulation of fatigue damages. It is assumed that the fatigue failure of a test specimen occurs after the destruction of some its critical microvolume consisting of two — elastic (brittle fibers) and plastic (matrix) — parts. In the second part, plastic strains accumulate as soon as the cyclic load exceeds some level. Numerical examples are presented.