13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Mechanism of in-plane fracture growth in particulate materials based on relative particle rotations Arcady V. Dyskin 1,*, Elena Pasternak 2 1 Deep Exploration Technologies Cooperative Research Centre, School of Civil and Resource Engineering, University of Western Australia, 6009, Australia 2 Deep Exploration Technologies Cooperative Research Centre, School of Mechanical and Chemical Engineering, University of Western Australia, 6009, Australia * Corresponding author: arcady@civil.uwa.edu.au Abstract In-plane fracture propagation in particulate materials (rock, concrete) under high tri-axial compression is observed in both Mode I tensile cracks (opened by additional load), Mode II shear cracks and in Mode I anti-cracks (compaction bands). This commonality suggests that when the conventional fracture mechanisms are supressed by high compression, a new universal mechanism takes over. We propose a fracture growth mechanism based on mutual rotations of the particles leading to breakage of inter-particle bonds followed by particle detachment and re-compaction. The Cosserat characteristic lengths are found to be of the order of the particle size. This allows expressing the stress concentrations as an intermediate asymptotics (between the Cosserat continuum characteristic length and the crack length). For Mode I crack and anti-crack and for Mode II crack the stress singularities are the same as for the cracks in a classical continuum, while the moment stress has a stronger singularity (3/2 power). This stress singularity leads to relative particle rotations and bending of interparticle bonds. The tensile microstress induced by the bending is an order of magnitude higher than the stress associated with conventional stress singularities. Keywords Fracture Criterion, Grain rotation, Moment stress, Small-scale Cosserat continuum, Compaction band 1. Introduction Fracture mechanics recognises 3 main fracture modes, one tensile (Mode I) and two shear (Modes II and III). Numerous experiments show that in brittle and quasi-brittle materials without pronounced planes of weakness, Mode I cracks are capable of in-plane growth, that is growing in their own plane, while Mode II cracks kink. In rock fracturing in compression however two more phenomena are observed. Firstly, it is in-plane propagation of shear bands; they start at near the peak load and propagate at an angle to the load direction throughout the rock sample separating it into two parts. This zone looks like shear (Mode II) crack (e.g. [1-3]) and is usually treated as such, but contrary to the behaviour of genuine Mode II crack it does not kink. Secondly, it is the existence and in-plane propagation of Mode I anti-cracks, which are the cracks that propagate under compressive load applied normally to their surface. In this case the load has the sign reverse to the conventional Mode I cracks giving the name to this type of cracks. They are observed in rocks and rock masses as compaction bands (e.g. [4-8]) and in laboratory experiments on rock samples in uniaxial compression as anti-wing cracks generated at the locations of compressive stress concentration created by pre-existing cracks [9, 10]. In-plane propagation of shear bands is usually associated with the formation of en-echelons of tensile (micro) cracks (e.g. [11-14]), however the process by which these cracks eventually merge and form the continuation of the shear band is not clear. Indeed, the tensile cracks grow parallel in the direction of maximum compressive stress. In order to merge the cracks should either start growing in a lateral direction, which is not possible, as they will be closed by the largest principal compressive stress, or to initiate shear microcracks by yet unknown mechanism. Thus even in the simple 2D case the mechanism of coalescence of en-echelon cracks is not clear. Even less clear is the mechanism of crack coalescence in 3D, when the orientation of the cracks forming en-echelon is
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