SIF2004 Structural Integrity and Fracture. http://eprint.uq.edu.au/archive/00000836 A Theory Of Disclinations For Anisotropic Materials With Bending Stiffness E. Pasternak 1 , H.-B. Mühlhaus 2,1 and A.V. Dyskin 1 1 School of Civil and Resource Engineering, University of Western Australia, Australia 2 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. 1. INTRODUCTION This paper considers fracture of layered materials consisting of many layers that are thin compared to the characteristic size of the loading (eg, wave length). In this case the explicit modelling of fracturing of every layer becomes cumbersome. An alternative technique would be in representing the material as an equivalent continuum that provides a large-scale (average) description of the material response to loading. This is achieved by introducing volume elements that are much greater than the layer thickness and, at the same time, much smaller than the characteristic length of stress variations. It should be noted that in the framework of this approach no lengths smaller than the volume element size can be distinguished. Modelling materials with microstructure requires in some cases the introduction of continua with additional degrees of freedom, such as a Cosserat continuum. An example is a layered material in the case when slip between the layers is permitted. Then independent bending of layers introduces another degree of freedom associated with the field of rotations of central axes of the layers independent of the macroscopic displacement field. Such a material can macroscopically be modelled by an anisotropic Cosserat continuum, a 2D version of which was considered in [Zvolinskii and Shkhinek, 1984; Mühlhaus, 1993; 1995]. In this case the independent Cosserat rotation is represented by gradient of deflection, while the moment stress corresponds to the bending moment per unit area in the layer cross-section. Under this approximation the dislocations, disclination and fractures will be investigated representing different types of material failure. The Cosserat continuum is characterized by the presence of three additional degrees of freedom corresponding to three components of independent Cosserat rotation. Consequently, more crack modes can exist. These cracks can be envisaged as discontinuities in the corresponding components of the Cosserat rotation and modelled as distributions of disclinations (or disclination loops). The criteria of growth can then be formulated by generalizing the J-integral concept. Pasternak [2002] considered dislocations, disclinations and semi-infinite cracks in layered materials in the 2D Cosserat approximation. We provide highlights of the fracture mechanics of layered materials here. 2. MODEL OF LAYERED MATERIAL BASED ON COSSERAT CONTINUUM Let us consider a 2D approximation referred to a cross section normal to layers. Let the x-axis of the Cartesian co-ordinate set (x,y) be directed parallel to the layers. Then the behaviour of the