M. Kleinhofs

Markov model of fatigue of a composite material with the poisson process of defect initiation

As a development of the model where only one weak microvolume (WMV) and only a pulsating cyclic loading are considered, in the current version of the model, we take into account the presence of several weak sites where fatigue damage can accumulate and a loading with an arbitrary (but positive) stress ratio. The Poisson process of initiation of WMVs is considered, whose rate depends on the size of a specimen. The cumulative distribution function (cdf) of the fatigue life of every individual WMV is calculated using the Markov model of fatigue. For the case where this function is approximated by a lognormal distribution, a formula for calculating the cdf of fatigue life of the specimen (modeled as a chain of WMVs) is obtained. Only a pulsating cyclic loading was considered in the previous version of the model. Now, using the modified energy method, a loading cycle with an arbitrary stress ratio is “transformed” into an equivalent cycle with some other stress ratio. In such a way, the entire probabilistic fatigue diagram for any stress ratio with a positive cycle stress can be obtained. Numerical examples are presented.

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.

Investigation of the reliability and longevity of parallel systems with defects using Daniels’ sequences

The Reliability and longevity of parallel systems is studied using the example of a fibrous composite material using Daniels sequences’ and the Markov chain theory. The connection between the strength distribution function of the separate longitudinal elements forming the parallel system and the longevity distribution function of this system under cyclic loads is analyzed. The obtained models do not give direct coincidence with the experimental data but can be used for their nonlinear regressive analysis. Numerical experimental data processing examples are given.

Modeling the Residual Strength of a Fibrous Composite Using the Residual Daniels Function

The concept of a residual Daniels function (RDF) is introduced. Together with the concept of Daniels sequence, the RDF is used for estimating the residual (after some preliminary fatigue loading) static strength of a unidirectional fibrous composite (UFC) and its S–N curve on the bases of test data. Usually, the residual strength is analyzed on the basis of a known S–N curve. In our work, an inverse approach is used: the S–N curve is derived from an analysis of the residual strength. This approach gives a good qualitive description of the process of decreasing residual strength and explanes the existence of the fatigue limit. The estimates of parameters of the corresponding regression model can be interpreted as estimates of parameters of the local strength of components of the UFC. In order to approach the quantitative experimental estimates of the fatigue life, some ideas based on the mathematics of the semiMarkovian process are employed. Satisfactory results in processing experimental data on the fatigue life and residual strength of glass/epoxy laminates are obtained.

Strength determination and prediction of destructive processes of composites

This paper is devoted to issues related to strength determination and prediction of destructive processes of composites; these issues enable determining the limits of safe use of a product and to recognize when limits are reached. The model that was developed and is presented in this paper enables to describe not only the predictable strength of unidirectional composites, but also the character of the destruction, taking into account the fiber stress and/ or ultimate strain distribution.