A three-dimensional penny-shaped crack under combined tensile and shear loadings is analyzed. The assumptions of Dugdale are applied to estimate the effects of plasticity around the edge of the crack. The solution for mode I tensile loading is well established within the context of the Dugdale assumptions, and for the case of shear loading, approximate results are derived for the yield ring width and crack sliding displacements, with the assumptions similar in form to the mode I case. By superposing the results of the tensile and shear loading, the solutions for a penny-shaped Dugdale crack under mixed mode static loading and modified for the analysis of fatigue crack growth. Based on the mixed mode Dugdale model and the accumulated plastic displacement criterion for crack growth, a fatigue crack growth equation with four-power effective stress intensity factor dependence is developed for a penny-shaped crack under conditions of mixed mode loading and small-scale yielding.

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