Modified Stoney's Formulas for Small-Scaled Bilayer Systems

Abstract

The mechanics of a small-scaled bilayer film-substrate system subject to temperature variation is studied. The modified couple stress theory is employed to take account of the size effects that are usually observed in small-scaled structures. In addition, the effect of weak bonding between the film and substrate is examined by using a linear slip-type model. Exact solutions are derived and the closed-form expressions for residual thermal stress and curvature of the system are given. Modified Stoney’s formulas are also presented for the bilayer system with perfect interface or imperfect interface between the film and the substrate.