Mechanisms of deformation localization at the tips of shear fractures: findings from analogue experiments and field evidence

Abstract

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 α (60° to 20° ) and/or l. Using a finite element method (FEM), we calculated the maximum principal tensile stress (σ 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 σ _1max is directly proportional to l and attains a peak value for α = 45°, promoting Mechanism A. On the other hand, I 2max occurs at α< 45°, favoring nucleation of ductile shear bands (Mechanism D). When a and l are increased simultaneously, σ _1max takes its peak value at α = 60° . This analysis explains the dominance of Mechanism A for α > 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 α < 45° . We finally complement our study with field examples.