Application of Markov chains to the critical element model for determining the fatigue life of composites

A stochastic model for predicting the lifetime of composite laminates subjected to multiaxial fatigue loading is proposed. The model is based on the application of Markov chains to the well known "critical element" model for the fatigue of composite laminates. The model considers the accumulation of fatigue damage as an evolutionary random process characterized by changes in the global compliance of a laminate. These changes are modeled as nonstationary, discrete time, discrete state Markov processes (Markov chains) utilizing stationary Markov chains and polynomial transformations of their indexing parameters. The stationary Markov chains are developed on the assumption of "equivalent damage". Their parameters are determined from experimental data. The Markov chain models yield full cycle dependent probability distributions for the changes in laminate compliance. These changes and their respective distributions are used as input into a mechanical analysis to determine the stresses on the life controlling critical elements of a laminate. The stresses on the critical elements and their derived probability distributions are used in turn to predict the lifetime of a laminate based on Markov chain models of the fatigue behavior of the critical elements. The predictive capability of the proposed model is demonstrated by comparison with experimental results.