M. Yu. Gutkin

Crossover from grain boundary sliding to rotational deformation in nanocrystalline materials

A theoretical model is suggested which describes cooperative action of grain boundary (GB) sliding and rotational deformation in mechanically loaded nanocrystalline materials. Focuses are placed on the crossover from GB sliding to rotational deformation occurring at triple junctions of GBs. In the framework of the model, gliding GB dislocations at triple junctions of GBs split into dislocations that climb along the adjacent boundaries. The splitting processes repeatedly occurring at triple junctions give rise to climb of GB dislocation walls that carry rotational deformation accompanied by crystal lattice rotation in grains of nanocrystalline materials. The role of GB sliding, rotational deformation and conventional dislocation slip in high-strain-rate superplastic flow in nanocrystalline materials is discussed.

Edge dislocation in gradient elasticity

The present paper is a natural continuation of the authors` previous work where they have considered the screw dislocation in gradient elasticity. They consider two dislocation configurations: a separate edge dislocation and a dipole of edge dislocations. The gradient solutions presented have been obtained by two different ways, i.e., in total displacements and in elastic strains with both leading to equivalent results. The authors show that the elastic dilatation takes a zero value at the dislocation line in contrast to the classical solution which is singular there. Other components of the elastic strain remain singular within an extremely small region r {le} r*{sub 0} {approx} 10{sup {minus}3}{radical}c ({approx}10{sup {minus}3} {angstrom} for an atomic lattice) around the dislocation line. Beyond this region, all strain components are finite approaching a zero value as r {yields} r*{sub 0} and achieving maximum values (3--14)% within the dislocation core (r {le} 4{radical}c). Also, the gradient solution eliminates the classical singularity of the total displacement at the dislocation line. The existence of the aforementioned two characteristic distances for the screw dislocation has also been confirmed in the present case of edge dislocation.

Transformations of grain boundary dislocation pile-ups in nano- and polycrystalline materials

A theoretical model is suggested which describes several types of transformations of grain boundary dislocation pile-ups at triple junctions of grain boundaries in (super) plastically deformed nanocrystalline and polycrystalline materials. Ranges of parameters of defect configurations are revealed at which the transformations considered are energetically favourable. The role of transformations of grain boundary dislocation pile-ups at triple junctions of grain boundaries in plastic deformation processes in nanocrystalline and polycrystalline materials is discussed with special attention being paid to the influence of such transformations on competition between different deformation mechanisms in nanocrystalline materials.

Grain boundary migration as rotational deformation mode in nanocrystalline materials

Stress-induced grain boundary migration is theoretically described as a new mode of rotational plastic deformation in nanocrystalline materials. We have calculated the strain energy change due to migration of a grain boundary that carries rotational plastic flow. It is shown that, depending on the stress level, the grain boundary can either be immobile or mobile, and in the latter case it can migrate in either a stable or unstable regime. The critical stress values, which correspond to the transitions between these migration regimes, are estimated and discussed.

Triple junction diffusion and plastic flow in fine-grained materials

Abstract A theoretical model is suggested which describes the yield stress dependence on grain size in fine-grained materials, based upon competition between conventional dislocation slip, grain boundary diffusional creep (Coble creep) and triple junction diffusional creep. In the framework of the model, the contribution of diffusional creep mechanisms to plastic deformation increases with reduction of grain size, causing the abnormal Hall–Petch dependence in the range of small grains. A grain size distribution is incorporated into the consideration to account for a distribution of grain sizes occurring in real specimens. The results of the model are compared with experimental data from Cu and shown to be in good agreement.

Misfit dislocations in wire composite solids

A theoretical model is suggested, which describes generation of misfit dislocations in film/substrate composites of wire form. In the framework of the model, the ranges of the geometric parameters (wire radius, film thickness, misfit parameter) of a wire composite are calculated at which the generation of misfit dislocations is energetically favourable. The specific features of generation of misfit dislocations in wire composites are discussed and compared with those in conventional platelike composites.

On the yield stress of nanocrystals

A generalization of the Hall-Petch relationship is proposed. The generalized relationship takes account of the contributions from intergrain sliding, generation of lattice dislocations, and influence of disclination-like defects. From this approach, a critical size corresponding to a maximum of the Hall-Petch size dependence is obtained. The value of the critical size essentially depends on the state of boundaries and it explains contradictory results for the microhardness of nanocrystals (NCs), since grain-boundary sliding is facilitated in unrelaxed nanocrystals and constrained in aged ones.

Disclinations, amorphization and microcrack generation at grain boundary junctions in polycrystalline solids

Abstract Splitting of disclinations (decay of disclinations into small-power disclinations) at grain boundary junctions in polycrystalline solids is examined theoretically, and related to local amorphization. Energetic characteristics of the splitting process are revealed. It is shown that such a process competes effectively with microcrack generation at triple junctions of grain boundaries, causing a plastification of deformed polycrystalline materials.

Dislocations and Disclinations in Gradient Elasticity

A special gradient theory of clasticity is employed to consider dislocations and disclinations with emphasis on the elimination of strain singularities appearing in the classical theory of elasticity. For dislocations, we give a briel summary of our earlier results pertaining to non-singular expressions for the elastic strains, as well as new results for non-singular expressions for the strain energies. For disclinations, we derive non-singular expressions for the elastic strains demonstrating that dipoles of straight disclinations of general type give zero or finite values for the strain components at the disclination line. The finite values depend strongly on the dipole arm d and exhibit a regular monotonous (wedge disclinations) or non-monotonous (twist disclinations) behavior for short-range (d < 10 √c) interactions. At annihilation distances (d → 0), the elastic strains tend smoothly to zero. Far from the disclination line (r » 10 √c), gradient and classical solutions coincide. When the dipole arm d is much smaller than the scale unit √c. the clastic fields of a dipole of wedge disclinations transform into the elastic fields of an edge dislocation, as is the case in classical elasticity.

Misfit dislocations in composites with nanowires

A theoretical model is suggested which describes the generation and evolution of misfit dislocations in composite solids containing nanowires with rectangular cross-section. In the framework of the model, the ranges of the geometric parameters (nanowire sizes, misfit parameter, interspacing between the nanowire and the free surface of the composite) are calculated at which the generation of various misfit dislocation configurations (loops, semi-loops and dipoles) is energetically favourable. Transformations of these dislocation configurations and their specific features are discussed.