Weight functions for T-stress for semi-elliptical surface cracks in finite-thickness plates

This paper presents the application of the weight function method for the calculation of elastic T-stress for semi-elliptical surface cracks. First, the weight function method for the calculation of T-stress previously developed for two-dimensional crack problems was extended for the T-stress calculation for three-dimensional crack problems. Then, the T-stress weight functions for the deepest point (corresponding to the parametric angle phi = 90 degrees) and for any general point (5 degrees <= phi < 90 degrees) along the crack front of semi-elliptical surface cracks in finite-thickness plates for wide ranges of crack aspect ratios a/c and relative depths a/t were derived. The resulting weight functions were validated using available finite element results for non-linear stress fields and remote tension and bending cases, and very good agreement was achieved. The weight functions are suitable for the calculation of the T-stress under complex loading conditions for any general point (5 degrees <= phi <= 90 degrees) of surface cracks with wide ranges of aspect ratios, 0 <= a/c <= 1, and relative depths, 0 <= a/t <= 0.8.