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[1] Using analogue experiments on polymethylmethaacrylate (PMMA) models, we investigated the process of deformation localization at the tips of preexisting planar shear cracks. Experiments show that this can take place in any of the following four principal mechanisms. Mechanism A: Brittle deformation is the dominant process and forms a pair of long tensile fractures at the crack tips. The tensile fractures propagate along the compression direction and transgress the entire model thickness, causing model failure at a small bulk strain (3%). Mechanism B: It involves both brittle and ductile (plastic) strain localization, where the tensile fractures grow to a limited length and incipient ductile zones appear at the tips. Mechanism C: Deformation localization is characterized by an association of macroscale shear bands and short, opened-out tensile fissures (cf. wing fractures). Mechanism D: Ductile strain localizes in the form of a pair of shear bands at each tip. Fracture failure does not occur in this case. The transition from Mechanism A to Mechanism D is a continuous phenomenon in the experimental conditions, which we show as a function of initial crack angle (a angle between the crack and the far-field compression direction) and crack length (l). Mechanism A tends to be replaced by Mechanism D with decreasing a (60°to 20°) and/or l. Using a finite element method (FEM), we calculated the maximum principal tensile stress (s 1max ) and the maximum second stress invariant (I 2max ) of the stress field in the neighborhood of a sliding crack within a linearly elastic medium and analyzed the brittle-ductile transitions observed in physical experiments. The calculations show that s 1max is directly proportional to l and attains a peak value for a = 45°, promoting Mechanism A. On the other hand, I 2max occurs at a < 45°, favoring nucleation of ductile shear bands (Mechanism D). When a and l are increased simultaneously, s 1max takes its peak value at a = 60°. This analysis explains the dominance of Mechanism A for a > 45°in physical models with simultaneously varying crack length and orientation. We also demonstrate probable interactions between plastic strain localization and tensile fracturing at the crack tips. FEM results indicate that a plastic zone lowers the magnitude of tensile stress concentration at wing cracks and thereby dampen their growth when a < 45°. We finally complement our study with field examples.

[1] Employing analogue and numerical experiments, we investigated the process of plastic creep in the vicinity of stiff inclusions and its role in the formation of shear zones. Analogue experiments were performed on Polymethylmethacrylate (PMMA) models in pure shear (_ e % 10 À4 s À1 ), which produced shear zones at a bulk strain >0.05. The geometrical dispositions of the shear zones do not conform to the stress concentration map derived from the plane theory of elasticity. At the initial stage (e b < 0.03), PMMA models began to deform plastically in four discrete strain localizations, tracking the stress concentration map. These incipient plastic locations develop a new stress field, diverting the zone of plastic yield in the form of multiple shear zones. Finite element models were run to demonstrate the formation of shear zones in this mode. The pattern of shear zones varied with the inclusion geometry. Inclusions of low aspect ratio (<1.5) gave rise to multiple sets of shear zones in their neighborhood. The multiplicity of shear zones tends to progressively decrease toward a single set of conjugate zones when the inclusions have relatively high aspect ratio (>2) and are oriented at an angle (>20°) to the bulk compression direction. Inclusions with a large aspect ratio (>4) developed a single dominant shear zone. The experimental findings can be compared to inclusion-controlled shear zones from naturally deformed rocks.Citation: Misra, S., and N. Mandal (2007), Localization of plastic zones in rocks around rigid inclusions: Insights from experimental and theoretical models,

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