The extrinsic indentation size effect (ISE) is utilized to analyze the depth-dependent hardness for Berkovich indentation of non-uniform dislocation distributions with one and two dimensional deformation gradients and is then extended to indentation results at grain boundaries. The role of the Berkovich pyramid orientation and placement relative to the grain boundary on extrinsic ISE is considered in terms of slip transmission at yield and plastic incompatibility during post-yield deformation. The results are interpreted using a local dislocation hardening mechanism originally proposed by Ashby, combined with the Hall–Petch equation. The Hall–Petch coefficient determined from the extrinsic ISE of the grain boundary is found to be consistent with the published values for pure Fe and mild steel. A simple, linear continuum strain gradient plasticity model is used to further analyze the results to include contributions from a non-uniform distribution in plastic strain and dislocation density.

Instrumented indentation of a high purity Fe surface with unresolved surface deformation due to mechanical polishing is compared to the same grain surface annealed at increasing time and temperature. The differences in indentation size effect behavior with annealing are correlated with hardness and electron backscatter diffraction measurements as independent measures of surface layer deformation. It is found that the Nix Gao plot evolves from non-linear (bilinear) towards the predicted linear relationship as the surface deformation is removed. The experimental observations are rationalized by inclusion of a depth dependent, polishing induced forest dislocation density within the Nix-Gao model.

Gradient plasticity provides an effective theoretical framework to interpretheterogeneous and irreversible deformation processes on micron and submicronscales. By incorporating internal length scales into a plasticity framework,gradient plasticity gives access to size effects, strain heterogeneities atinterfaces, and characteristic lengths of strain localization. To relate themagnitude of the internal length scale to parameters of the dislocationmicrostructure of the material, 3D discrete dislocation dynamics (DDD)simulations were performed for tricrystals of different dislocation sourcelengths (100, 200, and 300 nm). Comparing the strain profiles deduced from DDDwith gradient plasticity predictions demonstrated that the internal length scaledepends on the flow-stress-controlling mechanism. Different dislocationmechanisms produce different internal lengths. Furthermore, by comparing agradient plasticity framework with interfacial yielding to the simulations itwas found that, even though in the DDD simulations grain boundaries (GBs) werephysically impenetrable to dislocations, on the continuum scale the assumptionof plastically deformable GBs produces a better match of the DDD data than theassumption of rigid GBs. The associated effective GB strength again depends onthe dislocation microstructure in the grain interior.

Constitutive models that describe crystal microplasticity in a continuum framework can be envisaged as average representations of the dynamics of dislocation systems. Thus, their performance needs to be assessed not only by their ability to correctly represent stress–strain characteristics on the specimen scale but also by their ability to correctly represent the evolution of internal stress and strain patterns. Three-dimensional discrete dislocation dynamics (3D DDD) simulations provide complete knowledge of this evolution, and averages over ensembles of statistically equivalent simulations can therefore be used to assess the performance of continuum models. In this study, we consider the bending of a free-standing thin film. From a continuum mechanics point of view, this is a one-dimensional (1D) problem as stress and strain fields vary only in one dimension. From a dislocation plasticity point of view, on the other hand, the spatial degrees of freedom associated with the bending and piling up of dislocations are essential. We compare the results of 3D DDD simulations with those obtained from a simple 1D gradient plasticity model and a more complex dislocation-based continuum model. Both models correctly reproduce the nontrivial strain patterns predicted by 3D DDD for the microbending problem.

Experimental and simulation studies have shown that decreasing the grain size below a critical value results in softening rather than hardening in both the yield stress and flow stress of nanomaterials. In this work, a gradient plasticity framework is presented that can capture this softening behavior by treating grain boundaries as a separate phase with a finite thickness. The theoretical expression obtained for the yield stress as a function of the grain size can capture numerous experimental data that exhibit this “normal” to “abnormal” Hall–Petch transition, and an analytical equation is obtained that can predict the grain size at which this transition occurs. Furthermore, analytical expressions are obtained for the flow stress in nanomaterials, and they are in precise agreement with atomistic simulations on nanocrystalline Cu, which predict that below a critical grain size the flow stress decreases proportional to it.