Influence of substrate compliance on stresses generating stability loss of a delaminated coating

The problem of stability loss of a coating delaminated from the substrate due to the presence of intrinsic compressive deformations caused, for example, by heating is considered. Analytical and numerical (finite-element) solutions are obtained. The analytical solution is found within the framework of a classical thin plate theory. The two-dimensional problem of stability loss of a plate compressed in its own plane, which simulates a covering, is studied. The plate is bonded to an elastic substrate treated as an infinite elastic body almost everywhere except over a certain delaminated zone. An expression for the critical compressive stress is derived. It is shown that the difference between the obtained critical stress and the critical stress of a rigidly clamped plate can be defined by a single nondimensional parameter, which is a combination of the elastic constants of the coating and substrate, and the ratio of delamination length to coating thickness. Alternative boundary conditions and coating-substrate contact conditions are considered. These results correlate well with the results obtained using the FEM model.