Thermal stress analysis of a trilayer film/substrate system with weak interfaces

Trilayer film/substrate systems with weak interfaces are investigated in this article, and the closed-form analytical solution is presented, which can be readily used to evaluate the thermal residual stresses induced by temperature change. A fourth-order differential equation governing the curvature is derived and its solution is obtained. The present analytical results can be degenerated to the ones for a system with perfect interfaces, as well as those for a bilayer system with weak interface as reported previously. A quite different feature from our previous work is that certain force equilibrium conditions in the longitudinal direction must be used for trilayer systems, while they are satisfied automatically in the analysis of bilayer systems.