A unifying scaling for the Bauschinger effect in highly confined thin films: a discrete dislocation plasticity study

Abstract

In this study, sequential sputter deposition, diffusion bonding and focused ion beam milling are used to fabricate sapphire micropillars encapsulating a thin single crystal niobium film. A distinct Bauschinger effect is observed during the cyclic axial compression of the samples. Plain strain discrete dislocation plasticity is used to interpret the experimental results obtained for the encapsulated film-micropillar geometry. The simulations show that the experimental samples correspond to a saturated source density regime, producing the maximum Bauschinger effect for the chosen mean nucleation strength. Next, the source density and mean nucleation strength are shown to have a coupled effect on the size of the Bauschinger effect, understood in terms of the differing number of pile-ups occurring per source in the film. The coupled effect is found to be represented by the density of dislocations annihilated upon unloading: a consistent linear relationship is observed between the size of the Bauschinger effect and the annihilated dislocation density over the entire source density and nucleation strength parameter space investigated. It is found that different film orientations fulfil the same linear relationship, whereas changing the film thickness causes the slope of the linear trend to vary suggesting a length-scale dependence on reverse plasticity. Finally, all results are found to be unified by a power-law relationship quantifying the Bauschinger effect of the form ${{\rm{\Gamma }}}_{{\rm{B}}}\propto {\rm{\Delta }}{\rho }_{{\rm{ann}}}{l}^{n}$ where it is argued that the number of dislocations undergoing reverse glide in the confined film is represented by ${\rm{\Delta }}{\rho }_{{\rm{ann}}}$, the mean free path of dislocations by l and the effect of hardening processes by the exponent n. The net reverse glide is thus represented by ${\rm{\Delta }}{\rho }_{{\rm{ann}}}{l}^{n}$ which can be used as a measure of the Bauschinger effect.