Alexey Romanov

Abstract:

Disclinations play an important role in rotation-type motions of materials constitutive parts. Such internal motions contribute both to the irreversible change of the body shape (plasticity) and to the storage of internal energy in the body (elasticity). Disclinations, together with dislocations, represent a class of linear defects in solids with plastic distortion however localized at an internal surface. In this talk, we introduce the basis for mechanics of disclinations in solids and present an overview of recent applications of disclination concept to the mechanics of materials. The following themes of the disclination concept are discussed: (a) definitions and designations; (b) geometry of disclinations in structureless and structured continua; (c) elastic properties of screened low-energy screened disclination configurations; (d) applications of disclination approach to various problems of materials mechanics. The mathematical definitions of Volterra and Somigliana dislocations including Frank (rotation) vector of a disclination, types of disclinations: wedge or twist, are discussed. Perfect and partial disclinations are introduced for the continuum with internal structure. Screened disclination configurations are defined as those where the far-filed divergence of disclination elastic strains and mechanical stresses vanishes. The screened configurations include loops, dipoles, and defects at the vicinity of a free surface and in small elastic bodies. The mathematical methods and results of calculation of disclination elastic fields and energies are presented in details. A number of qualitative and quantitative models for rotational plastic deformation of conventional and low-dimensional solids is considered. As an example, disclination models of grain boundaries and their junctions in polycrystals and graphene are presented. The bands with misorientated crystal lattice in metals and other materials are described as a result of partial wedge disclination dipole motion. Finally, the role of disclinations in relaxation of mechanical stresses in lattice mismatched thin layers placed on the bulk substrate is examined.