Modelling the Strength and Fatigue Life of a Unidirectional Fibrous Composite by Using Daniels’ Sequence and Markov Chains

A review of the previous works of the authors dedicated to the use of Daniels’ sequence (DS) for analyzing the relation between the distribution of the static strength of components of a unidirectional fibrous composite (UFC) and the distribution of its fatigue life is presented. A generalization of the DS which can be used to analyze the association of distribution of the static strength of composite components with distribution of the static strength of the UFC itself is given. In analyzing the fatigue life of a UFC, unlike in Daniels’ model, the loading rate and randomness of the number of still workable components in the weak microvolume in which the destruction process takes place are taken into account. By analyzing the fatigue life, it is possible to explain the existence of the random fatigue strength and to calculate the maximum load at which the probability of absence of fatigue failure is great enough when the number of cycles of fatigue loading tends to infinity. Numerical examples of processing of experimental data are presented, and estimates for parameters of the corresponding nonlinear regression model, which can be interpreted as the strength parameters of UFC, are obtained.