Three-dimensional analysis of an edge crack in a plate of finite thickness with the first-order plate theory

In this paper, plasticity effects at the tip of an edge through-the-thickness crack are investigated by invoking the strip-yield model and the first order plate theory. The latter theory is the simplest extension of the classical plane theories of elasticity, which is capable of accounting for three-dimensional effects and, in particular, the plate thickness effect. By utilising the distributed dislocation technique, new results are obtained on the interaction of the free boundaries (free edge and free plate planes) with the crack tip plasticity region. Numerical results for the crack tip opening displacement and global constraint factor are first presented at various crack length to plate thickness and applied stress to yield stress ratios. The results are validated against past 3D solutions for an embedded crack as well as analytical solutions obtained under the plane stress or plane strain assumption. The new model and results can be utilised in advanced fracture and fatigue analyses of cracks emanating from a free surface.