Elastic thermal stresses in a circular overlay/rigid substrate system

When an overlay/substrate system is subjected to a temperature change, thermal stress is induced due to the difference of thermal expansion coefficients between the overlay and substrate. This paper studies elastic thermal stress distribution of a circular overlay bonded to a rigid substrate due to temperature variation. Under the plane assumption, the radial displacement in the overlay is obtained in a series form. Using a weak form boundary condition, one can obtain an approximate solution in closed form for the thermoelastic field. This approximate solution gives a description of displacement along both radial and thickness directions. Elastic thermal stress distributions are demonstrated and compared with the finite element results. An asymptotic analysis of the solution is given when the thickness of a thin film is much less than its radius. The closed-form solution is useful for stress-strain analyses and design of circular layered systems such as protective coatings and microelectromechanical components. Application of this solution in modeling spiral cracking of circular thin film/substrate is underway.