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

The out-of-plane constraint factor, Tz, around I–II mixed-mode cracks in a thin elastic plate has been investigated systematically and a K–Tz 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 Tz factor for I–II mixed-mode cracks depends not only on TzI for the pure tensile mode and TzII 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. Tz 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 Tz, 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 Tz around the crack front for the pure tensile mode and pure shear mode, respectively. Next, the formula describing the 3D distribution of Tz around the I–II mixed-mode crack front was obtained. Two-parameter description of the 3D stress field (K–Tz) for I–II mixed-mode cracks was proposed.