Three-dimensional stress state around quarter-elliptical corner cracks in elastic plates subjected to uniform tension loading

Abstract

Detailed full-field three-dimensional (3D) finite element analyses have been conducted to study the out-of-plane stress constraint factor T z around a quarter-elliptical corner crack embedded in an isotropic elastic plate subjected to uniform tension loading. The distributions of T z are studied in the forward section (0° ⩽ θ ⩽ 90°) of the corner cracks with aspect ratios a/ c of 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0. In the normal plane of the crack front line, T z drops radially from Poisson’s ratio at the crack tip to zero beyond certain radial distances. Strong 3D zones ( T z > 0) exist within a radial distance r/ a of about 4.6–0.7 for a/ c = 0.2–1.0 along the crack front, despite the stress-free boundary conditions far away. At the same radial distance along the crack front in the 3D zones, T z increases from zero on one free surface to a peak value in the interior, and then decreases to zero on another free surface. The distributions of T z near the corner points are also discussed. Empirical formulae describing the 3D distributions of T z are obtained by fitting the numerical results, which prevail with a sufficient accuracy in the valid range of 0.2 ⩽ a/ c ⩽ 1.0 and 0° ⩽ θ ⩽ 90° except very near the free surfaces where T z is extremely low. Combined with the K– T solution, the transition of approximate plane-stress state near the surfaces to plane-strain state in the interior can be characterized more accurately.