Periodic cracking of elastic coatings

Abstract

In this study the periodic cracking of an elastic coating bonded to a homogeneous substrate is considered. The problem is assumed to simulate the segmentation or “mud-flat” cracking of ceramic layers used as thermal barrier coatings in stationary and aircraft gas turbine engines. By expressing the displacements in terms of a combination of finite and infinite Fourier transforms, the corresponding mixed boundary value problem is reduced to an integral equation with the crack surface displacement as the unknown function. The main objective of the study is the examination of the influence of the length parameters c/b and b/h and the stiffness ratio μ2/μ1 on the crack tip stress intensity factors, the crack opening displacement, the strain energy released as a result of periodic cracking, and the in-plane tensile stress on the coating surface, where c, b, h, μ1 and μ2, respectively, are crack spacing, crack depth, coating thickness, shear modulus of the coating, and shear modulus of the substrate. The case of a periodically cracked strip is investigated separately and the stress intensity factors under fixed-load and fixed-grip conditions are compared. Also, the validity of the assumption made in simple energy balance calculations to the effect that the entire strain energy contained within the volume of the cell is released during periodic cracking is studied. It is shown that such an assumption is valid only for very small values of relative crack spacing c/b.