The out-of-plane constraint of mixed-mode cracks in thin elastic plates

The out-of-plane constraint factor, T_z, around I-II mixed-mode cracks in a thin elastic plate has been investigated systematically and a K-T_z two-parameter description of the three-dimensional (3D) stress field near the crack front has been evaluated using the boundary layer model and the finite element method. The T_z factor for I-II mixed-mode cracks depends not only on T_zI for the pure tensile mode and T_zII for the pure shear mode loading but also on the ratio of the thickness functions for the local stress intensity factors of both loading modes. T_z increases gradually with decreasing crack angle φ from mode I (φ = 90°) to mode II (φ = 0°). At the crack plane (θ = 0°), the shear loading has no contribution to T_z, which equals the value for the pure mode I. By fitting the numerical results, two empirical formulae were obtained to describe the 3D distribution of T_z around the crack front for the pure tensile mode and pure shear mode, respectively. Next, the formula describing the 3D distribution of T_z around the I-II mixed-mode crack front was obtained. Two-parameter description of the 3D stress field (K-T_z) for I-II mixed-mode cracks was proposed.