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

Publication Date
DOI: 10.1016/j.tecto.2010.09.030
  • Strain Localization
  • Brittle–Ductile Transition
  • Elastic-Plastic Rheology
  • Tensile Fractures
  • Shear Bands


Abstract 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 ( σ 1) and the second stress invariant ( I 2) 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 σ 1 at the fracture tip increases non-linearly with increasing α and A r (aspect ratio of the shear crack), and assumes a large value when α > 50 o, promoting tensile fractures. On the other hand, I 2 is a maximum at α < 45°, resulting in nucleation of ductile shear bands.

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