Elastic T-stress solutions for semi-elliptical surface cracks in finite thickness plates subject to non-uniform stress distributions

This paper deals with the T-stress calculation for surface cracks in plates. Three-dimensional finite element analyses have been conducted to calculate the elastic T-stress for semi-elliptical surface cracks in finite thickness plates. The T-stress solutions are presented along the crack front for cracks with a/t values of 0.2, 0.4, 0.6 or 0.8 and a/c values of 0.2, 0.4, 0.6 or 1.0. Four stress distributions: uniform, linear, parabolic and cubic were applied to the crack face. The superposition method for the calculation of T-stress for three-dimensional cracks is presented. Using the obtained solutions for the four polynomial stress distributions, the application of the superposition method to calculate the T-stress for other stress distributions is demonstrated. These current T-stress solutions together with the corresponding K or J values for surface cracks are suitable for the analysis of constraint effects for surface cracked components under non-uniform stress distributions.