Stress and failure localization associated with sliding in layered materials

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Delamination in layered materials makes the layers susceptible to bending and, if the load is sufficiently high, to fracture. The fracture may develop as a progressive breakage of layers forming a narrow zone propagating as a “bending crack”. This situation is analysed using a 2-D Cosserat continuum model of the layered material. Edge dislocations (displacement discontinuities) and a disclination (the discontinuity in the derivative of layer deflection) are considered for the case of free layer sliding. The solutions show that the stresses and the moment stress generated by the dislocations and disclination get localized along a line passing through the dislocation/disclination kernel perpendicular to the layering. This can be interpreted in the way that layered materials are prone to localizations associated with the layer sliding. Fundamental solutions of the Lame equations also show the weakest decay in the direction normal to layering in the smooth layer limit. The dislocation-generated stress localization can serve as a mechanism of failure localization in tabular excavations driven in layered rock masses. This is demonstrated by considering a model in which the tabular stope is modelled as an edge dislocation. The disclination-generated moment stress decays as inverse square root of the distance, r, while other stresses from the disclination and the stresses from dislocation decay more strongly, as 1/r. This enables one to consider a “pure bending crack”, i.e. the crack consisting of disclinations only. The moment stress concentration at the crack tip has a singularity of the power −1/4. Such a crack can only propagate in the direction perpendicular to the layering owing to the stress localization. A problem for a semi-infinite bending crack normal to layering was considered. The problem was reduced to a problem of linear relationship that was solved in closed form. The result was used to model fracture propagation in layered materials in compression.