Deformation localization at the tips of shear fractures: An analytical approach

Mechanical heterogeneities are important features in rocks which trigger deformation localization in brittle, ductile or brittle–ductile modes during deformation. In a recent study Misra et al. (2009) have investigated these different processes of deformation localization at the tips of pre-existing planar shear fractures. The authors identified four mechanisms of deformation, ranging from brittle to ductile, operating at the crack tips. Mechanism A: brittle deformation is the dominant process that forms a pair of long tensile fractures at the two crack tips. Mechanism B: nature of deformation is mixed where the tensile fractures grow to a finite length with incipient plastic deformation at the tips. Mechanism C: mixed mode deformation characterized by dominating macro-scale shear bands, and short, opened-out tensile fissures. Mechanism D: localization of plastic bands in the form of a pair of shear bands at each tip without any discernible brittle fracturing. The transition of the mechanisms is a function of orientation (α) of the crack with respect to the bulk compression direction and the finite length (l) of the crack. The aim of this study is to present a theoretical analysis to account for the variability of deformation localization in the vicinity of pre-existing shear cracks considering an elastic-plastic rheological model. The analysis calculates the principal tensile stress (σ1) and the second stress invariant (I2) of the stress field at the fracture tip to explain the transition from Mechanism A (tensile fracturing) to Mechanism D (ductile strain). The results show that σ1 at the fracture tip increases non-linearly with increasing α and Ar (aspect ratio of the shear crack), and assumes a large value when α > 50o, promoting tensile fractures. On the other hand, I2 is a maximum at α < 45°, resulting in nucleation of ductile shear bands.

Research Highlights►Brittle-ductile transition can be observed at tips of pre-existing shear fractures. ►The transition depends on the initial orientation and geometry of fractures. ►Ductile deformation dominates at low angle (α>30°) crack tips. ►Brittle deformation dominates at high angle (α <55°) crack tips. ►The brittle-ductile transition occurs between α = 30 to 55°.