Three-dimensional finite element analyses have been conducted to calculate the stress intensity factors for high aspect ratio semi-elliptical cracks. The stress intensity factors are presented for the deepest and surface points on semi-elliptic cracks with aspect ratios of 1.5 and 2, 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 lower aspect ratio surface cracks to derive weight functions over the range 0.6 ≤ a/c ≤ 2.0 and 0.0 ≤ a/t ≤ 0.8. The weight functions were then verified against finite element data for parabolic or cubic stress distributions. Differences were less than 3% for the surface point and 6% for the deepest point. The present results complement weight functions for low aspect ratio cracks, 0.0 ≤ a/c ≤ 1.0, developed previously by the authors.

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Journal Engineering Fracture Mechanics
Wang, X, & Lambert, S.B. (S. B.). (1997). Stress intensity factors and weight functions for high aspect ratio semi-elliptical surface cracks in finite-thickness plates. Engineering Fracture Mechanics, 57(1), 13–24. doi:10.1016/S0013-7944(97)00018-0