Size-dependent yield strength and surface energies of thin films

The strain gradient plasticity theory recently proposed by Gudmundson [P. Gudmundson, J. Mech. Phys. Solids 52 (2004) 1379–1406] is used to analyse the behaviour of a thin film on an elastic substrate. Boundary conditions for the film–substrate interface are introduced via a surface energy that depends on the plastic strain state at the interface. Finite element results show a strong dependence on the surface energy. If the surface energy is small, no size effects appear. On the other hand, if a stiff interface is simulated, corresponding to a large surface energy, a thickness dependence of the yield strength is found. The application of several alternative strain gradient models would predict a thickness dependent hardening, but strictly not a size dependence of the yield strength. The presently predicted thickness dependence on yield strength and hardening is supported by experimental results.