Three-parameter description of the stress field near the border of an embedded elliptical crack

The elastic T-stress and stress intensity factor K for embedded elliptical 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, 0.4, 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 ν. For ν=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 T _z , the three-parameter K-T-T _z approach has been provided, which can accurately describe the stress field around the crack front.