Stress-driven evolution of waviness in an elastic layer

The effect of a far-field tensile stress on surface evolution of an elastic layer deposited on a rigid cylindrical substrate is analyzed by using the linear perturbation theory and frictionless contact condition between the elastic layer and the substrate. The driving force controlling the surface evolution is the gradient of chemical potential associated with surface energy and the stored strain energy in the elastic layer. A new expression of dispersion relation is derived, which depends on geometrical configuration and elastic properties of the material. It is found that the tensile stress has a significant effect on destabilizing surface evolution. Closed-form solution of the critical spatial frequency of surface perturbations for the zero growth rate is obtained. The critical frequency is proportional to the tensile stress and inversely proportional to the square root of the film thickness for elastic thin films deposited on planar rigid substrate.