Background on Stochastic Models for Cumulative Damage Process

Abstract

The chapter provides a short review of the stochastic models applied for cumulative fatigue damage in structural components. The empirical fatigue crack growth is given by Paris’s law, and it relates the increment of fatigue crack advance, da/dN, per stress cycle to range of the stress intensity factor ΔK in the framework of linear elastic fracture mechanics (LEFM). Investigation of the randomness of fatigue crack growth rate under service, loading conditions should consider the statistical characteristics of the crack growth law under constant amplitude loadings, and also the randomness of loadings that gives rise to fatigue under variable amplitude loads. Several probabilistic models for crack growth have suggested to “randomize” the deterministic crack propagation by a stochastic process. Few stochastic models of the cumulative fatigue damage process are nominated in this chapter. A method of calculating crack propagation by linear elastic fracture mechanics (LEFM) in the case of Gaussian temperature fluctuations has been proposed by Miller, and the principal steps are outlined. The main features of various structural assessment techniques for thermal striping and thermal fatigue crack growth but also some matters in respect of these methods are shortly reviewed.