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 phi from mode I (phi = 90 degrees) to mode II ((phi = 0 degrees). At the crack plane (theta = 0 degrees), 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. (c) 2006 Elsevier Ltd. All rights reserved.