A modified 3D mean strain energy density criterion for predicting shale mixed-mode I/III fracture toughness

The fracture toughness of rocks is a critical fracturing parameter in geo-energy exploitation playing a signi ficant role in fracture mechanics and hydraulic fracturing. The edge-notched disk bending (ENDB) specimens are employed to measure the entire range of mixed-mode I/III fracture toughness of Longmaxi shale. To theoretically interpret the fracture mechanisms, this research first introduces the detailed derivations of three established fracture criteria. By distinguishing the volumetric and distortional strain energy densities, an improved three-dimensional mean strain energy density (MSED) criterion is proposed. As the critical volumetric to distortional MSED ratio decreases, the transition from tensiondominated fracture to shear-dominated fracture is observed. Our results indicate that both peak load and applied energy increase signi ficantly with the transition from pure mode I (i.e., tension) to pure mode III (i.e., torsion or tearing) since mode-III cracking happens in a twisted manner and mode-I cracking occurs in a coplanar manner. The macroscopic fracture signatures are consistent with those of triaxial hydraulic fracturing. The average ratio of pure mode-III fracture toughness to pure mode-I fracture toughness is 0.68, indicating that the obtained mode-III fracture resistance for a tensionbased loading system is apparent rather than true. Compared to the three mainstream fracture criteria, the present fracture criterion exhibits greater competitiveness and can successfully evaluate and predict mixed-mode I/III fracture toughness of distinct materials and loading methods. (c) 2024 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).