*5.1. Deformation Mechanisms Ultrafine Grains*

In this section, we consider grain sizes in the intermediate range, i.e., between 20 and 100 nm, where a departure from classical HP is first noticed. Even in nanoscale some features of pile-up characteristics are applicable, and can have a significant effect. These include the effect of a small number of dislocations, a continuum versus discrete crystal dislocation description and the influence of elastic anisotropy. For a detailed history of the first 60 years of HP relation, see the excellent review by Armstrong [43]. It is seen that, usually the pile-up of dislocations at GBs is envisioned as the key mechanism, which causes strength increase by grain refinement. However, several models predict the breakdown of the pile-up mechanism in NC metals. With even further grain refinement, some experiments evidence softening of the material (for a review see [9,44,45]). The HP effect is normally explained by appealing to dislocation pile-ups near the grain boundaries. Once the grain size drops below the equilibrium distance between dislocations in a pileup, pile-ups are no longer possible, and the HP relation should cease to be valid. For example, Pande, Masumura and Armstrong 1993 [46] following the dislocation pile-up model proposed by Pande et al. (see reference [9]), estimated that about ten dislocations can be stored in the approximately 100 nm Au or Cu grains. Such short dislocation pileups may not easily induce enough shear stress concentration to break through the grain, although it can accommodate a certain extent of plastic strain.

Using the dislocation pile-up model for the HP relation, Armstrong [47] examined ultrafine grain sizes when only a few dislocations were involved in the pile-up, which were formed at applied stress levels close to the theoretical limit. Each dislocation added to the pile-up contributes a step reduction in the HP stress. Consequently, differences in dislocation configurations and types of pile-ups are easily recognized in the limit of small dislocation numbers.

Even if the micro grains only have a few dislocations, the source of the dislocations are not established with certainty. FR sources in such small spaces seems unlikely. Could they come from the GB? We know that the GBs certainly play a role in determining properties of metallic materials. For example, dislocation-GB interactions, GB sliding grain rotation, GB diffusion, and GB migration all influence mechanical properties of polycrystalline materials. In this region they may also provide the small number of whole dislocations needed in the models discussed above.

Typically, the HP plot is divided into three regions: (1) where classical HP plot is fully valid, typically over 30 nm, (2) where a departure from HP is first noticed, typically below 30nm and (3) where HP plot starts to fall drastically, typically below 15 nm (for details see reference [9]). As the average grain size in nanomaterial is lowered say below 10nm, the dislocations inside most likely do not exist, and there are probably no FR or GB sources operating. Although GB can still be a source of partial dislocations. We will consider this in next section.
