Shear forces, root rotations, phase angles and delamination of layered materials

In this paper, the concepts of root rotations and phase angles in laminated structures are reviewed, with particular reference to how the presence of a shear force affects the fracture mechanics of an interface. It is shown that it is possible to combine all the effects of shear into an effective root rotation, rather than the usual approach of invoking root rotation as a correction to a clamped Timoshenko beam. This simplifies the mechanics of the phenomenon, as root rotation is a general concept for interface cracks, and is not unique to shear loading. The root rotations enter into expressions for the energy-release rate associated with shear, and give rise to the crack-tip phase angles that provide a measure of how other modes of loading interact with shear loading. Additionally, the present analysis identifies the concept of a root displacement as an additional measure of the deformation at a crack tip. This is required to provide consistency with compliance-based approaches to the fracture mechanics of a double-cantilever beam, and allows one to make a direct connection to classical elastic-foundation models of that geometry.