Effect of a thin surface coating layer on thermal stresses within an elastic half-plane

Summary The paper studies the dilatational eigenstrain problem of a thermal inclusion of any shape within an elastic half-plane coated with a thin stiff surface layer. The emphasis is on the effect of the surface coating layer on internal stresses within the inclusion and interfacial shear stress between the coating layer and the surface of the elastic half-plane. The mixed boundary value problem is reduced to a first-order differential equation for an analytic function in the elastic half-plane, and the exact solution is obtained explicitly in terms of an auxiliary function constructed from the polynomial conformal mapping which maps the exterior of the inclusion onto the exterior of the unit circle. The exact solution is used to study the conditions under which the surface coating layer can be negligible or treated as an inextensible coating layer. In particular, when the surface coating is inextensible, the exact solution shows that the mean stress is exactly uniform inside the thermal inclusion of any shape and vanishes outside the thermal inclusion in the whole elastic half-plane. Detailed results are shown for the mean stress and the interfacial shear stress caused by a circular or elliptical thermal inclusion. The results show that the surface coating layer could have a significant effect on the internal stress field within the thermal inclusion and the interfacial shear stress between the coating layer and the elastic half-plane especially when the inclusion is close to the surface coating layer.