Photothermal Reliability Testing of a Multilayer Coating—Substrate Assembly: A Theoretical Approach

The paper presents the theoretical principles underlying the method for photothermal reliability testing of a multilayer coating-substrate assembly. In this method, the assembly is irradiated by the pump laser beam which causes heating and formation of thermal stresses in an assembly. The irradiated surface is monitored by a weak probe beam of another laser to detect the buckling of the coating. The two-dimensional distributions of temperature and thermal stresses in an assembly heated by the pump laser beam are obtained from the solution of the thermal elasticity problem. The developed mathematical procedure is based on the expansion of the Laplace and Hankel transforms of temperature and displacement distributions in series of a small parameter, which is of the order of the ratio of a coating thickness to a pump beam radius. The explicit expressions for the stress tensor components in the layers of a coating and the probe beam deflection angle are derived. Calculations show that the dependence of the deflection angle on a Fourier number is nonmonotone and attains a maximum at some value of the Fourier number. The latter property of the dependence of the deflection angle on the Fourier number can be used for detecting subsurface structural defects in an assembly.