In order to characterize the crack tip stress field in three-dimensional fatigue and fracture problems, stress intensity factor and T-stress solutions are usually necessary. In this paper, extensive three-dimensional (3D) finite element models are constructed for Compact-Tension-Shear (CTS) specimen, which is one of the most widely used specimens for fatigue and fracture tests under mixed-mode I&II loading. In-plane and out-of-plane geometric dimensions including varying crack depths ratios (a/W = 0.3, 0.5 and 0.7) and thicknesses ratios (B/W = 0.1, 0.3 and 0.5) are considered under different loading angles (β = 0°, 15°, 30°, 45°, 60°, 75° and 90°). The results of stress intensity factors ($K_{\mathrm{I}}$,$K_{\mathrm{II}}$ and $K_{\mathrm{III}}$) and T-stresses ($T_{11}$ and $T_{33}$) along the crack front are computed and analyzed. The combined effects of geometric dimensions and loading angles on these fracture parameters have been illustrated. The solutions of the parameters are then described using empirical formulae by fitting numerical results with the least-squares method. Solutions obtained have been used to predict the crack initiation angles for CTS specimens based on mixed-mode fracture criteria including the maximum tangential stress (MTS) criterion, the generalized MTS (GMTS) criterion, the strain energy density (SED) criterion and the generalized SED (GSED) criterion. Solutions are useful for fracture and fatigue problems of mixed-mode I&II, such as analysis of the constraint effects on fracture toughness and propagation path of fatigue crack.

为了表征三维疲劳和断裂问题中的裂纹尖端应力场，通常需要应力强度因子和T应力解。在本文中，为紧凑拉伸剪切 (CTS) 试样构建了广泛的三维 (3D) 有限元模型，该试样是在混合模式 I 和 II 载荷下进行疲劳和断裂试验最广泛使用的试样之一。在面内和面外几何尺寸包括改变裂纹深度比（一/ w ^  = 0.3，0.5和0.7）和厚度比（乙/ w ^  = 0.1，0.3和0.5）下不同的负载的角度被认为是（β = 0°、15°、30°、45°、60°、75° 和 90°）。应力强度因子的结果（${钾}_{\mathrm{一世}}$,${钾}_{二}$ 和 ${钾}_{三}$) 和T应力 (${吨}_{11}$ 和 ${吨}_{33}$) 沿裂纹前沿进行计算和分析。已经说明了几何尺寸和加载角度对这些断裂参数的综合影响。然后使用经验公式通过最小二乘法拟合数值结果来描述参数的解。所获得的解已用于基于混合模式断裂准则预测 CTS 试样的裂纹起始角，包括最大切向应力 (MTS) 准则、广义 MTS (GMTS) 准则、应变能密度 (SED) 准则和广义SED (GSED) 标准。解决方案对于混合模式 I&II 的断裂和疲劳问题很有用，例如分析对疲劳裂纹的断裂韧性和扩展路径的约束影响。