Interfaces within strain gradient plasticity: Theory and experiments

In this paper, it is shown that the occurrence of dislocation pileups across grain boundaries, as well as subsequent emission to the adjacent grains, is captured theoretically by gradient plasticity and confirmed experimentally by nanoindentation. From a theoretical point of view, this is accomplished (within a deformation theory framework applicable to continued loading) by accounting for a specific interfacial term in the overall potential of the material, in terms of which its response, taken to conform to strain gradient plasticity, is defined. The main features that result from the addition of this interfacial term are (i) significant size effects of Hall–Petch type in the overall stress–strain response of polycrystals and (ii) the determination of an analytical expression for the stress corresponding to the onset of dislocation transfer across interfaces. From an experimental point of view, the effective stress at which dislocation transfer takes place across an interface can be obtained from nanoindentations performed in close proximity to an Fe–2.2 wt.% Si grain boundary, since they exhibit a distinct strain burst that is related to the presence of the boundary. It is possible, therefore, to fit the theoretically determined analytical expression for the interfacial yield stress to the experimental data. From this fit, first estimates are obtained for key material parameters, namely the interfacial term and the internal length, that are required for the theoretical formulation. Dislocation mechanics are employed to provide physical insight of these parameters.