Three-dimensional finite element analyses have been conducted to calculate the stress intensity factors for low aspect ratio semi-elliptic cracks. The stress intensity factors are presented for the deepest and surface points on semi-elliptic cracks with low aspect ratios of 0.05 and 0.1, and a/t values of 0.2, 0.4, 0.6 and 0.8. Uniform, linear, parabolic or cubic stress distributions were applied to the crack face. The results for uniform and linear stress distributions were combined with corresponding results for higher aspect ratio surface cracks and edge cracks to derive the weight function over the entire range of 0 ≤ a/c ≤ 1 and 0 ≤ a/t ≤ 0.8. The weight function is then verified against finite element data for the parabolic or cubic stress distributions. Differences were less than 3% for the surface point and 5% for the deepest point.

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Journal Engineering Fracture Mechanics
Wang, X, & Lambert, S.B. (S. B.). (1995). Stress intensity factors for low aspect ratio semi-elliptical surface cracks in finite-thickness plates subjected to nonuniform stresses. Engineering Fracture Mechanics, 51(4), 517–532. doi:10.1016/0013-7944(94)00311-5