Size effects in single crystal thin films: nonlocal crystal plasticity simulations

Stress relaxation in single crystalline thin films on substrates subjected to thermal loading is studied using a recently proposed nonlocal continuum crystal plasticity theory. The theory is founded on a statistical-mechanics description of the collective behaviour of dislocations in multiple slip, which is coupled to a small-strain continuum crystal plasticity description. The theory is inherently nonlocal with the length scale being determined by the evolving dislocation density. Symmetric double slip is considered with the film being in plane strain. The predicted stress versus temperature response and the evolution of the dislocation structure are analyzed for different orientations and film thicknesses. The effect of film size is associated with the formation of a boundary layer of dislocations at the film-substrate interface which does not scale with the film thickness. The width of the boundary layer itself is shown to be dependent on the slip system orientation. The results are consistent with those of recent discrete dislocation simulations.