Thermoviscoelastic stresses in thin films/substrate system

This paper utilized the viscoelastic theorem to derive thermoviscoelastic stress in a thin film/substrate structure, and obtain a closed-form expression of the stress. In this viscoelastic analysis, the Maxwell model is assumed and the Laplace transformation is applied to the variables of time-space followed by the calculation of the viscoelastic stress of the thin film in the transformation domain. Finally, after the inverse Laplace transformation, the normalized stress at any depth and at any time was obtained analytically and expressed as a function of the relaxation times, the biaxial moduli ratio, and the ratio of thickness between the film and the substrate. The effects of the different thickness ratio values on the normalized viscoelastic stress were analyzed and the results showed that the effects were significant. In addition, the distribution of the viscoelastic stress varies with different depths of the film and the maximum stress induced on its surface.