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

Detailed full-field three-dimensional (3D) finite element analyses have been conducted to study the out-of-plane stress constraint factor Tz around a quarter-elliptical corner crack embedded in an isotropic elastic plate subjected to uniform tension loading. The distributions of Tz 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, Tz drops radially from Poisson’s ratio at the crack tip to zero beyond certain radial distances. Strong 3D zones (Tz > 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, Tz 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 Tz near the corner points are also discussed. Empirical formulae describing the 3D distributions of Tz 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 Tz 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.