A theory of disclination for anisotropic materials with bending stiffness

Department of Earth Sciences, University of Queensland, Australia & CSIRO Division of Exploration and Mining, Australian Resource Research Centre, Australia ABSTRACT: The paper considers a special type of failure in layered materials with sliding layers that develops as a progressive breakage of layers forming a narrow zone. This zone propagates as a “bending crack”, ie a crack that can be represented as a distribution of disclinations. This situation is analysed using a 2D Cosserat continuum model. Edge dislocations (displacement discontinuities) and a disclination (the discontinuity in the derivative of layer deflection) are considered. The disclination does not create shear stresses along the axis perpendicular to the direction of layering, while the dislocation does not create a moment stress along the same axis. Semi-infinite and finite bending cracks normal to layering are considered. The moment stress concentration at the crack tip has a singularity of the power -1/4. The possibility to derive equilibrium conditions for cracks and disclinations from J-type path independent integrals is also pointed out.