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 u from mode I (u = 90°) to mode II (u = 0°). At the crack plane (h = 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.

Out-of-plane stress and displacement for through-the-thickness cracks in plates of finite thickness

“…The crack tip stress intensity factor for the case of a finite thickness plate is determined by Equation (9). The present results are identical to the through-the-thickness average of the values presented by She and Guo [2007b] and Nakamura and Parks [1988] for semiinfinite cracks. Figure 2.…”

“…Again a semiinfinite crack model has been used. The mid-thickness FE results by She and Guo [2007b] are given and they show a good agreement with the present results. Results for the ratio of the average crack tip stress intensity factor to the far-field stress intensity factor are shown in Figure 3 as a function of Poisson's ratio.…”

“…FE results by Nakamura and Parks [1988] and She and Guo [2007b] for semiinfinite cracks are also provided as a comparison. Both the mid-thickness (MT) and through-the-thickness average (AV) FE values are given.…”

“…Several researchers, including Nakamura and Parks [1988] and She and Guo [2007b], have provided detailed analyzes of the crack tip region for mode I and mixed mode (I-II) semiinfinite cracks, respectively. It was shown that the out-of-plane stress and displacement fields exhibit significant three-dimensional effects within a radial distance from the crack tip of about half the plate thickness and converge with the plane stress solutions at around 1.5 times the plate thickness.…”

3D thickness effects around notch and crack tip stress/strain fields

“…Fig. 5 shows how the ratios K Imax /K I,2D and K Imp /K I,2D vary with B/a, and compares them with the long crack SIF-dominated limit solution from She and Guo [20]. The maxima SIF tend to the long crack solution for cracks with very low B/a, and the middle plate SIF KImp tend to the limit 2D solution KI,2D as B/a becomes large and the cracks get shorter.…”