Modelling the effects of texture on the statistics of stage I fatigue crack growth

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Abstract
A physically based model for the growth of short fatigue cracks through a local grain structure is presented. The growth rate is taken to be proportional to the cyclic plastic displacement at the crack tip, which is evaluated using an existing solution for the continuous distribution of dislocations ahead of the crack in a slip band that is blocked by a grain boundary. The effect of the local microstructure and texture are incorporated using orientation factors relating the applied far field stress to the shear stress which causes a grain to grain variation in the mode II loading of the crack tip. The orientation factor for each grain is established by assigning the crystallographic orientation of the grain using a probabilistic description of the overall texture of the polycrystal. The effects of idealized fibre (〈111〉 and 〈100〉), double fibre and random textures are examined. The growth rates of many individual cracks through different local microtextures were calculated within a Monte Carlo framework. This allows the influence of texture on not only the average behaviour of the short cracks but also the statistical variation in the behaviour to be examined. Curves showing the probability of propagating cracks reaching a given crack length in a given number of cycles are shown.

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