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

Abstract

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.