Short and long fatigue crack growth: A unified model

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Abstract
In this model the growth of a crack is analysed in terms of the successive blocking of the plastic zone by slip barriers (e.g. grain boundaries) and the subsequent initiation of the slip in the next grain. The discontinuous character of the slip process (slip jumps) plays a fundamental role in the model. The factor governing the transfer of slip across a grain boundary is considered to be the stress concentration ahead of the plastic zone which, for a constant applied stress τ, is found to be dependent only on a parameter n = a/c defining the position of the crack tip relative to the grain boundary. The discrete behaviour of the slip has a strong influence in the short-crack period and hence cannot be neglected in the analysis of the crack growth rate. This period is characterized by large variations in the parameter n. In the long-crack period the slip jumps do not influence the overall description of the growth and the parameter n is almost constant. By making the crack extension per cycle proportional to the crack-tip plastic displacement, the intermittent pattern of decelerating and accelerating behaviour of short cracks and the existence of non-propagating cracks may be explained. For long cracks a linear relationship in log coordinates holds between the plastic displacement and the stress-intensity factor. The reasons why short cracks grow at rates higher than those predicted by the straightforward application of fracture mechanics long-crack data are explicit in the analysis. The fatigue limit is equated to the stress below which a crack is unable to transfer slip to the next grain. The application of this criterion leads to the representation of a Kitagawa-like plot. The deviations and the large scatter of data in the short-crack regime are explained and a model arises of the El Haddad type.

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