Binomial version of Markov model of fatigue life of composite with two reasons for failure

Abstract

A model of fatigue damage accumulation in laminate with two reasons for fatigue failure (the distortion of rigid items and the excessive yielding of the plastic part of the composite (matrix)) is offered. The model is based on the use of the Markov chains theory. It is shown how the corresponding transition probability matrix can be filled and how to calculate the mean time to failure, the variance of this time, and the probability distribution function. This model can be used as a nonlinear regression model for fatigue curve approximation and for fatigue damage accumulation description in program fatigue test. Processing of experimental data (fatigue test of carbon‐fiber reinforced laminate for fatigue curve building and for residual fatigue‐life investigation in program test with two levels of stress) shows that the model can be used for satisfactory description of the results of these tests. The specific feature of the model considered in this paper is the use of binomial distribution of failure of rigid items and the number of acts of yielding in the plastic part of the laminate.

First Published Online: 14 Oct 2010

Keyword : strength, yielding, fatigue life, composite, fatigue curve