On some approaches to the stress-state determination in layered cracked plates

A survey of approaches to determination of the stress-state in layered plates with the cracks located symmetrically about their thickness is presented. The plate is subject to a complex biaxial loading; i.e., tension – shear or bending – torsion, while the crack of length 2a is unloaded. The plate layers can be homogeneous or non-homogeneous, rigid to shear or yielding due to shear. To study such plates the following mathematical models are employed: the plates rigid to shear are considered within the framework of classical plate theory, while those yielding due to shear are within the scope
of Timoshenko's theory.

The asymptotic formulae for stress distribution near the crack tip in each layer of the plate are obtained; the limiting equilibrium of layered plate having a transverse crack is studied.

The results presented can be applied to strength evaluation of layered plates within the framework of fracture mechanics. The paper presents the results obtained by the authors recently and proposes some generalisation.