It was found that the crack surface broke suddenly in mixed-mode I/III fractures by using a three-point bending specimen with a large thickness and an inclination angle less than \(10^{\circ}\), and a relationship between the scale of the fragmentation and the mixed mode was established [41]. In another investigation of mixed-mode I/III fractures, the crack deflection angles of the specimen achieved larger inclination angles, but only four groups of inclination angles were considered, and the crack depth was fixed and low [42], so the persuasiveness of the research results was inadequate. In order to study the initiation and propagation of cracks, some fracture criteria, such as the maximum tangential stress (MTS) criterion [43], the maximum tangential strain (MTSN) criterion [44] and the maximum tangential strain energy density (MTSED) criterion [45] were proposed and frequently used to analyze the fracture characteristics. These criteria only considered the singular term of the stress field at the crack tip and ignored the non-singular term (T-stress). However, a large number of experiments have proven that the fracture criterion considering the non-singular term can predict the experimental results more effectively [16; 17; 18; 19; 20; 26; 28; 30; 31; 37; 38; 39; 40]. It was found that the generalized maximum tangential stress (GMTS) or generalized maximum tangential strain (GMTSN) criteria, both considering T-stress, can better predict the central cracked disc experimental results of mixed-mode I/II fractures compared with the MTS criterion [16; 17; 18; 19; 20]. The GMTS criterion was also used to predict and verify the experimental results of three-point bending specimens in mixed-mode I/II fracture studies, whether SCB or ETC specimens [26; 28; 30; 31]. The mixed-mode I/III fracture experimental results for various materials such as marble [37], asphalt concrete [39] and graphite [40] using ENBD specimens were in good agreement with the theoretical predicted value of the MTSED criterion without considering T-stress. The experimental results of pure mode III fracture toughness were also in good agreement with the theoretical predictions of the MTSED criterion [38]. However, an extended MTSED criterion considering T-stress was proposed, which was considered to better predict the testing results of ENDB specimens, especially for the pure mode III case [46]. Most of the existing studies on mixed-mode fractures involve I/II and I/III fractures. The mixed-mode I/II/III fracture is rare, and the applicability of the existing criteria to mixed-mode I/II/III fractures still needs more study. Therefore, based on the previous investigations, a mixed-mode fracture test configuration, called the three-point bending specimen with inclined crack (TPB-IC), was proposed in this study. By changing the deflection angles of the crack in two directions, it can cover most ranges of mode I/II/III mixed fractures. The influences of the deflection angles and crack length on fracture parameters (i.e., SIFs and T-stress) and the experiments of the TPB-IC specimen made of sandstone for mixed-mode I/II/III fracture were carried out. Through the extended analysis of the MTSED criterion, the generalized maximum tangential strain energy density (GMTSED) criterion considering T-stress was obtained, and a unified and complete three-dimensional expression under the conditions of plane stress and plane strain was derived. The experimental results and the predicted values of the GMTSED criterion considering the three-dimensional T-stress were comparatively analyzed.