The effects of transverse shear on the delamination of edge-notch flexure and 3-point bend geometries

A general approach to develop complete and rigorous analytical expressions for the energy-release rates and phase angles for delamination of isotropic beam-like geometries is summarized. The analysis allows the effects of transverse shear to be correctly incorporated within the resulting expressions. The approach requires four effective crack-tip loads to be determined from the applied loads: a moment, an axial force, a double transverse shear force and a single transverse shear force. Each of these effective loads provides an energy-release rate and an associated phase angle; expressions for these quantities can be found in the literature. These fundamental expressions can be combined algebraically to generate analytical expressions for the total energy-release rate and phase angle for any geometry and loading configuration of interest. The approach is illustrated by general analyses of edge-notched flexure (ENF), end-loaded split (ELS) and 3-point bending specimens. In particular, it is shown that the equation for the energy-release rate for the ENF geometry reduces to a very simple form that has previously been proposed from numerical studies, when the geometry is perfectly anti-symmetrical.