Fracture in plates of finite thickness

Application of the plane theory of elasticity to planar crack or angular corner geometries leads to the concept of stress singularity and stress intensity factor, which are the cornerstone of contemporary fracture mechanics. However, the stress state near an actual crack tip or corner vertex is always three-dimensional, and the meaning of the results obtained within the plane theory of elasticity and their relation to the actual 3D problems is still not fully understood. In particular, it is not clear whether the same stress field as found from the well-known 2D solutions of the theory of elasticity do describe the corresponding stress components in a plate made of a sufficiently brittle material and subjected to in-plane loading, and what effect the plate thickness has. In the present study we adopt, so called, first order plate theory to attempt to answer these questions. New features of the elastic solutions obtained within this theory are discussed and compared with 2D analytical results and experimental studies as well as with 3D numerical simulations.