Conclusion

Abstract

We have considered theoretical models of plastic flow in NCMs, paying special attention to the abnormal Hall—Petch effect, localization of deformation, crossover to rotational modes of plasticity, amorphization and generation of micro- and nanocracks. On the basis of the results presented, one can draw the following general conclusions:

• Different theoretical models give different explanations of the abnormal Hall—Petch relationship, and most of them account well for the corresponding experimental data. However, it is extremely difficult to identify the deformation mechanism(s) in NCMs experimentally due to their very complicated nanoscale structure and the transformations it undergoes at various length scales during plastic deformation. In addition, the deformation mechanisms may be different in different NCMs or even in the saine material under different conditions of loading (e.g., temperature, strain rate). The main mechanisms, which determine the first stages of plastic deformation in NCMs, are gliding of partial or perfect lattice dislocations (for relatively coarse-grained NCMs, d ≥ 40 nm) and grain boundary sliding and diffusional plasticity (for relatively fine-grained NCMs, d ≤ 40 nm). Competition between these mechanisms, depending on structural and material properties of NCMs, as well as on conditions of external loading, leads to the abnormal Hall—Petch relationship.

• The regimes of homogeneous and inhomogeneous high-strain plastic deformation in NCMs are effectively described with the help of the concept of cooperative grain boundary sliding and the model of cellular dislocations whose elastic fields can be modelled by nonsingular solutions of gradient elasticity (both the nonlocal and gauge theories give the saine solutions), while their kinetics can be studied using the presented solution of the system of evolutionary equations. The degree of inhomogeneity of plastic deformation is determined by the intensity of the accommodation processes which accompany grain boundary sliding: low intensity results in the homogeneous regime of plastic flow and high intensity in the inhomogeneous regime.

• Rotational plastic deformation occurs in NCMs through generation and development of specific (rotational) structures of lattice and/or grain boundary dislocations which are effectively described as partial disclinations. The rotational structures are generated in NCMs at various imperfections of grain boundaries (kinks, double and triple junctions), where the misorientation angle changes sharply. The paths for the development of rotational plasticity depend on the dominant mechanisms of translational plasticity. Dominance of the lattice gliding mechanism can lead to the appearance of misorientation bands (or other disclination structures which are typical for conventional metals and alloys but have not been considered here) inside the grains or to motion of grain boundary disclinations by issuing lattice dislocations. Dominance of grain boundaries can result in the formation and motion of grain boundary disclinations through climb of grain boundary dislocations. In both these situations, the motion of grain boundary disclinations along their grain boundaries is accompanied by a change in the grain misorientations under external loading and is capable of producing the corresponding rotation of the grain crystalline lattice as a whole.

• In the late stages of plastic deformation in nano- and polycrystalline solids, local solid-state amorphization or generation of nano- and nucrocracks, respectively, can occur at triple junction and grain boundary disclinations. At low levels of plastic deformation, disclinations initiate microcrack generation. At high levels of plastic deformation, they initiate local amorphization of the triple junctions, which impedes microcrack generation. This means that such disclinations play a double role: they decrease plasticity at low plastic strains and increase plasticity at High plastic strains. Triple junctions of grain boundaries serve as effective obstacles for nanocrack growth along grain boundaries in NCMs. The larger the angle between grain boundaries adjacent to a triple junctioir, the larger the equilibrium length of the curved nanocrack and hence the smaller the probability of its generation.