Abstract
Rotational degrees of freedom in Cosserat continua give rise to higher fracture modes. Three new fracture modes correspond to the cracks that are surfaces of discontinuities in the corresponding components of independent Cosserat rotations. We develop a generalisation of J- integral that includes these additional degrees of freedom. The obtained path-independent integrals are used to develop a criterion of crack propagation for a special type of failure in layered materials with sliding layers. This fracture propagates as a progressive bending failure of layers – a “bending crack that is, a crack that can be represented as a distribution of discontinuities in the layer bending. This situation is analysed using a 2D Cosserat continuum model. Semi-infinite bending crack normal to layering is considered. The moment stress concentrates along the line that is a continuation of the crack and has a singularity of the power − 1/4. A model of process zone is proposed for the case when the breakage of layers in the process of bending crack propagation is caused by a crack (microcrack in our description) growing across the layer adjacent to the crack tip. This growth is unstable (in the moment-controlled loading), which results in a typical descending branch of moment stress – rotation discontinuity relationship and hence in emergence of a Barenblatt-type process zone at the tip of the bending crack.
Highlights
This paper considers fracture of layered materials consisting of many layers that are thin compared to the characteristic size of the loading
The Cosserat continuum is characterized by the presence of three additional degrees of freedom corresponding to three components of independent Cosserat rotation
In Cosserat continuum modelling layered materials with freely sliding layers, the dislocations and disclinations create stresses that concentrate on an axis normal to the layering
Summary
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). Independent bending of layers introduces another degree of freedom associated with the field of rotations of central axes of the layers independent of macroscopic displacement field Such a material can macroscopically be modelled by an anisotropic Cosserat continuum, a 2D version of which was considered in [1,2,3]. 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. We provide highlights of the Fracture Mechanics of layered materials here
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