Abstract
We study the indentation problems of film-substrate composites. Axisymmetric indentation problem involving elastic film-substrate composites considered by Yu, et al. [1] is revisited. The results are extended to viscoelastic thin film on elastic substrate with flat-ended indenter. Instead of using surface displacement as one of the boundary conditions, the stress distribution is relative to that for a homogeneous half-space. First, the displacement and stress components are considered based on Navier's equation and Hankel transform. We solved linear algebraic equation with two different boundary conditions, perfectly bonded and freely sliding. Secondly, viscoelastic models are introduced, and elastic solutions are replased by two viscoelastic models, standard linear solid model and Burgers model, which come from inverse of Laplace transform. Finally, we find displacement and stress with different positions, thickness and material constants. The method is simpler and easier to use and also describe the load-penetration relationship. Compared with the previous method, our solutions match the elastic solutions at t = 0. We can change boundary condition using the same equations. Moreover, the method will be extended to n-layer thin films rested on substrate straightforwardly. For fitting experimental data, it will be a new and convenient solution to understand unknown material constants.