The in-plane and out-of-plane stress constraint factors and K-T-T_z description of stress fields near the border of a quarter-elliptical corner crack

The elastic T-stress and stress intensity factor K for quarter-elliptical corner cracks have been investigated in elastic plates by detailed three-dimensional finite-element calculations. The distributions of normalized K and T-stress have been obtained along the crack front with aspect ratios (a/c) of 0.2, 0.3, 0.4, 0.5, 0.6, 0.8 and 1.0, and far-field tension and the effect of Poisson's ratio have also been considered. The normalized K increases and the normalized T -stress decreases with the increase of Poisson's ratio v. For v = 0.3, the normalized K gradually increases in the range of crack-face angle φ ≥ 22.5° and decreases in the range of φ ≤ 22.5° with the increase of a/c. The normalized T-stress increases in the beginning and then decreases with increasing φ except for a/c = 0.2 and a/c = 0.3. By fitting the numerical results with the least squares method, empirical formulae have been given for the convenience of engineering applications. Combining with the corresponding out-of-plane constraint factor T_z, the three-parameter K-T-T_z approach has been provided, which can accurately describe the stress field around the crack front.