Stochastic Cumulative Models for Fatigue
This chapter is devoted to modelling of fatigue crack growth via cumulative jump stochastic processes. A wide class of such processes can be represented in the form of a stochastic integral with respect to counting Poisson measure in particular, such processes take a form of a random sum of random components. The cumulative jump processes are adopted as a model-process for fatigue crack growth in engineering materials subjected to random loading and other uncertainties. After brief presentation of the previous author’ results, the extension of the approach to a more general situation where elementary crack increments are mutually correlated is shown. The use of Morgenstern model for the joint probability distribution leads to approximate characterization of the crack size. The results quantify the effect of the correlation in crack’s increments on statistics of a crack size and show the features analogous to those in existing experimental data. In the last part of the chapter a stochastic cumulative jump model of fatigue crack growth with retardation is presented.
KeywordsFatigue Crack Fatigue Crack Growth Crack Size Crack Growth Retardation Dependent Random Variable
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