Interfaces in crystalline materials

As the scale of consideration in materials decreases to the micron and sub-micron scales, the effect of internal surfaces on the plastic flow becomes dominating. To explicitly account for interfaces and grain boundaries a gradient plasticity framework, enhanced with a separate interface energy term, has been developed. This interface energy depends on the plastic strain at the interface and defines an interface yield-like criterion which indicates the stress at which the interface begins to deform plastically. Experimentally this interfacial yielding is captured through nanoindentation experiments near the grain boundary of crystalline materials, namely Nb. Fitting the theoretical analytical expression to the experimental data allows the determination of the key material parameters; for Nb it gives the internal length to be approximately 1.4|im, and in fact for pure (single phase) materials the dislocation source distance is approximated as 1.5|im. In order to further render the interface-dislocation interactions, discrete dislocation dynamics simulations are performed for a micron-scale tri-crystal with rigid/non-deforming grain boundaries. The resulting strain distribution profile from the simulation coincides with the predicted plastic strain of the gradient plasticity framework, while the best fit results when the internal length in the analytical expression is chosen to be the same as the value of the dislocation source distance used in the simulation. Hence, the gradient plasticity model that considers an interface energy term has been validated using experimental and numerical investigations.