On influence of substrate compliance on delamination and buckling of coatings

摘要

Problems related to delamination of coatings from substrates and their buckling are widely investigated due to importance of the problem for application in industry, particularly in micro- and nano-electronics and biology. The problem was addressed by many authors by using both analytical and numerical approaches. Here 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 the coefficients of this matrix allows determining parameters of buckling such as the critical stress, energy release rate due to further delamination, amplitude of buckling. A few variants of analytical models to determine the coefficients of this 3×3 matrix were considered and discussed. Both the cases of isotropic and anisotropic coating and substrate are considered. The solution for some matrix coefficients was obtained with the help of Fourier transform and Wiener-Hopf technique. On the base of the obtained solution 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. The results correlate well with the results obtained using the FEM model.