On influence of substrate compliance on delamination and buckling of coatings

• Components of matrix of elastic clamping for a plate modeling a coating were found.
• Expanded matrix of elastic clamping was introduced.
• Dimensionless complex controls ratio of buckling stress of coating and clamped plate.

The aim of the paper consists in obtaining simple formulae to describe processes related to delamination and buckling of coatings.The model is developed that treats the delaminated part of the coating as a plate with a special attention given to the boundary conditions, which are supposed in the form of the generalized elastic clamping, i.e. it is supposed that components of displacements and angle of rotation at the point of clamping are related to the acting total force and total moment by means of 3 × 3 matrix of elastic coefficients. Knowing this matrix allows determining parameters of buckling such as the critical stress, energy release rate due to further delamination, amplitude of buckling. Explicit expressions for the matrix components were obtained by various techniques. Both the cases of isotropic and anisotropic coating and substrate are considered.On the base of the obtained solution it is shown that for a wide range of parameters the ratio of the obtained critical stress and the critical stress of a rigidly clamped plate is determined by a single dimensionless parameter, which is a combination of the elastic constants of the coating and substrate, and the ratio of delamination length to coating thickness.