A MODEL FOR SHORT FATIGUE CRACK PROPAGATION WITH AN INTERPRETATION OF THE SHORT‐LONG CRACK TRANSITION

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Abstract
The behaviour of short cracks approaching growth barriers (e.g. grain boundaries) is considered. The crack model of Bilby, Cottrell and Swinden is applied to simulate the blocking of the plastic zone at the grain boundary and to obtain the stress concentration ahead of the crack as it approaches the barrier. The idea of the Hall‐Petch type relationship that the transmission of slip across grain boundaries needs the previous achievement of a critical stress has been used. By making the crack growth rate proportional to the plastic displacement at the root of the crack the deceleration behaviour of short cracks and the existence of non‐propagating cracks may be explained. The fatigue limit is related to the stress below which a crack growing in a single grain is unable to promote slip in the neighbouring grain. The different behaviour in the so‐called long crack period has been rationalized in terms of the plastic zone exceeding the grain size. For this case, and in the grain completely included within the plastic zone, the Hall‐Petch analysis must be applied. Hence the maximum back‐stress sustained by this grain cannot exceed the yield stress. After this point the Bilby et al. model is used with uy as a friction stress (i.e. the Dugdale model). Finally use is made of Fracture Mechanics to correlate the results in the long crack phase.

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