On propagation of interface cracks in bi-layered strip in relation to delamination of coatings from substrates of final thickness

Abstract

The problem of a coatings delamination from a substrate is considered. Both the delaminated part of the coating and substrate are modelled as plates with a special attention to the boundary conditions, which are considered as generalized elastic clamping. For this type of boundary conditions the angle of rotation and components of the displacement vector at the clamping point are related to the acting bending moment and components of the resulting force vector at that point by means of 3x3 matrix of elastic compliance. Such type of boundary conditions appeared from the solution of the problem of a bilayered strip with the semi-infinite interface crack loaded at infinity. The analytical solution of this problem for the particular relation between the elastic constants of the layers (zero second Dundurs’ parameter) is obtained by reducing it to the homogeneous matrix Riemann boundary value problem solved by matrix factorization for two particular cases: (1) equal thickness of both layers; (2) thickness of one of the layers (corresponding to the substrate) being much more than the thickness of the other, so that this layer may be considered as a half-plane. For the general case of the arbitrary elastic constants and layers thicknesses the approximate solution has been obtained. The approximation involves neglecting the influence of the normal to interface stresses to the shear displacements and shear stresses to the normal displacements. According to the obtained solutions the asymptotics for the relative displacements of the separated layers for the points, remote from the crack tip, correspond to the deflection of plate (beam) with the described above boundary conditions. The fracture parameters (stress intensity factors and energy release rates) have also been obtained. Using the obtained solution the problem on buckling of the delaminated coatings is addressed. It has been shown that for a wide range of parameters the ratio of the critical stress, corresponding to buckling of the delaminated parts of coatings and the critical stress of a rigidly clamped plate is determined by a single nondimensional parameter, which is a combination of the elastic constants of the coating and substrate, and a combination of the geometrical parameters of the model.