•The applicability of two mixed-mode I + III fracture specimen are compared.•The effect of loading type on mixed-mode I + III fracture toughness is assessed.•The fracture parameters of both specimens are numerically and experimentally obtained.•The influence of stress triaxiality constraints on mixed-mode I + III fracture toughness is studied. Towards measuring the mixed-mode I + III fracture toughness independent of geometry and loading type, two test specimens were numerically and experimentally compared. The capabilities of edge-notched disc bend (ENDB) and edge-notched diametrically compressed disc (ENDC) fracture test specimens were compared in producing the full range of mixed-mode I + III. Although the geometry of both specimens was similar, the difference of their loading type (i.e., bending and compression) noticeably affected the mixed-mode I + III fracture parameters. The existence of mixed-mode I + III fracture in the crack front of the ENDC specimen was more stable than the ENDB specimen. However, the variation of mode mixities ratio in the ENDC specimen was more sensitive to the rotation of the crack inclination angle than the ENDB specimen. The map of T-stress as the function of mixed-mode I + III geometry factors plotted for both specimens. There was an optimal crack length in the ENDB specimen by which the full range of mixed-mode I + III fracture toughness can be measured independent of geometry and loading type effects. While for the ENDC specimen, the optimum crack length only existed for pure mode III. The full range of mixed-mode I + III fracture toughness tests were performed using both test specimens. The corresponding fracture loads and fracture initiation angles were also obtained for both ENDB and ENDC specimens made of granite rock. The magnitude of pure mode I fracture toughness measured by the ENDB specimen was greater than the ENDC specimen. Conversely, the pure mode III fracture toughness measured by the ENDC specimen was greater than the ENDB specimen. These discrepancies were also predicted by the computed T-stress map. In addition to the T-stress, Tz, process zone size, and the stress triaxiality constraints, which governed the crack propagation path were other effective parameters on the difference between mixed-mode I + III fracture toughness values measured via both specimens.