Stress gradient interpretation of boundary layers in passivated thin films

• Continuum stress gradient plasticity predicts the size effects associated with passivation layers in thin metal films.
• A single length scale parameter, representing the length of dislocation pileups against passivation layers, is utilized for all films.
• The boundary layer of film, having constant size but higher stress levels, leads to the size-dependent response of the film.

A continuum implementation of stress gradient plasticity is established to analyze passivated thin films under tension. It is verified and evaluated by investigation of the tensile response of passivated Cu films with different thicknesses and grain sizes. The material parameters are fitted to the stress–strain experimental data, while the length scale parameter is directly characterized from the corresponding available discrete dislocation predictions. The numerical solutions give rise to boundary layers near the interface between film and passivation. This prediction is consistent with the formation of dislocation pileups at the film-passivation interface and also is responsible for the thickness-dependent hardening observed in passivated thin films. The numerical results are in good agreement with the experimental data and discrete dislocation predictions.