The in-plane and out-of-plane stress constraint factors and K − T − Tz description of stress field near the border of a semi-elliptical surface crack

The elastic T-stress and stress intensity factor K for semi-elliptical surface 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 font with aspect ratios (a/c) of 0.2, 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 increasing a/c. When ϕ rises to 90°, the K values tend to maximum for various a/c. The normalized T-stress increases in the beginning and then decreases with the increase of ϕ except for a/c = 1.0. 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 Tz, the three-parameter K − T − Tz approach has been provided, which can accurately describe the stress field around the crack front.