An investigation of T-stresses in a plate with an inclined crack under biaxial loadings

For plates with an inclined crack of wide-range aspect ratios under biaxial loadings, T-stress values are calculated with three-dimensional finite element method. The results show that the normalized T-stress is crack length and orientation dependent. A linear equation for the relationship between normalized T-stresses and biaxility factors is proposed to describe the normalized T-stresses for different crack lengths and crack angles under different biaxial loadings, which is more convenient and involves wider biaxility ratios compared with the existing solutions. The plate thickness effect and the trend of normalized T-stresses along the crack front thickness are also studied for mode I and I–II mixed-mode cracks. Based on the analyses and comparisons, it is necessary to take the thickness effect into consideration when the crack length is long enough (a/W = 7/10). When the component of mode II is significant (β > 45°), and the biaxility ratios are negative, T-stresses near the free surface are lower than those at other positions, which are the opposite of mode I crack and most of I–II mixed-mode crack.