Mixed mode conditions, characterized by either tension-shear or compression-shear loading, occur in numerous geomechanical applications. Several investigators (Erdogan and Sih 1963; Palaniswamy 1972; Sih 1973; Hussain, Pu, and Underwood 1974; Chang 1981; Nemat-Nasser and Horri 1982) have developed theories for various mixed mode fracture problems. However, the development of a more unifying criterion is warranted. Various researchers (Cotterell 1969 and 1972; Hoek and Bteniawski 1965) have emphasized that essential differences in behavior under tension and compression exist. For cracks subjected to tension, the crack extension force increases with crack growth. For cracks subjected to compression, the crack driving force reaches a maximum, then, for further crack extension, it decreases. Erdogan and Sih (1963) advanced the maximum tensile hoop stress fracture criterion in plane problems for brittle materials such as rock. Sih (1973, 1974(a), and 1974(b)) advanced the minimum strain energy density criterion for mixed mode fracture characterization. Chiang (1977) obtained the energy release rate for two-dimensional crack problems under combined tension and shear stresses. Hellen and Blackburn (1975) also used complex variables to determine the energy release rate for crack extensions and the orientation for the maximum energy release rate. The available experimental evidence (Erdogan and Sih 1963) does not confirm such a theory where a crack in shear extends in its plane.
Nemat-Nasser and Horii (1982) studied angled cracks under far field compression. They showed that relative frictional sliding of the faces of the pre-existing cracks may produce, at their tips, stable tension crack extension at sharp angles from the sliding plane, curving toward an orientation parallel to the direction of axial compression. For a wide range of pre-existing crack orientations, the outof-plane crack extension initiates at an angle close to 70° from the direction of the pre-existing crack.
The problem considered herein entails the development of a fracture criterion which is both simple to implement and is applicable to both tension-shear and compression-shear mixed mode conditions. This criterion has wider applicability to geomechanical problems. The results obtained are compared with selected studies reported in the literature.