Micromechanics theory of fatigue crack initiation and propagation

Abstract

This paper is concerned with the theoretical formulation of models describing the fatigue crack initiation and propagation processes in polycrystalline solids on the basis of their being nondeterministic. The crack initiation is established by using a technique based on the interference of Gaussian distribution functions, obtained from basic microstructural material information, to account for the residual stress effect, the work-hardening phenomenon and the microstructural damage accumulation that occurs prior to the initiation of a fatigue crack. The crack propagation process is developed in terms of a particular discontinuous Markovian stochastic process, namely, the general pure birth process which leads to a full description of the crack front in the form of its probability distribution. The propagation process is thus described as a fatigue-cycle-dependent evolution of such a distribution. The fategue crack initiation and propagation models are subsequently combined to give the overall stochastic fatigue characteristics of real polycrystalline solids. The validity of these combined models is then confirmed through an application to aluminium alloys and commercially pure titanium. The results of this application are described in detail and the distinction between the present theory and the continuum fatigue theories is discussed.