An approach to the elastic field of a hybrid dislocation

ABSTRACT

The transfer of plastic sliding through a crystalline interface involves at least a dislocation having a branch in each crystal. The elastic field associated with this elemental configuration has been processed in the past by Belov et al. (1983 A.Y.Belov, A.Chamrov, V.L.Indenbom and J.Lothe , Elastic fields of dislocations piercing the interface of an anisotropic bicrystal , Phys. Stat. Sol. (B) 119 (1983), pp. 565–578. Available at https://doi.org/10.1002/pssb.2221190216 .[Crossref] , [Google Scholar], 1992) but has never been verified or used, to the author’s knowledge. With typographical corrections and various verifications, the results obtained in this work confirm the validity of the theory for isotropic and/or anisotropic crystals. A general explicit solution to the elastic field is derived in the case of two different isotropic crystals. The theory fails when one branch is along the interface while the other lies in a crystal (hybrid dislocation). On the other hand, if a branch is very little inclined relative to the interface (quasi-hybrid dislocation), the theory applies fully. In this context, the combination of two quasi-hybrid dislocations solves in practice the problem of the triple node anchored to the interface.     

Interaction between phase transformations and dislocations at the nanoscale. Part 1. General phase field approach

Thermodynamically consistent, three-dimensional (3D) phase field approach (PFA) for coupled multivariant martensitic transformations (PTs), including cyclic PTs, variant–variant transformations (i.e., twinning), and dislocation evolution is developed at large strains. One of our key points is in the justification of the multiplicative decomposition of the deformation gradient into elastic, transformational, and plastic parts. The plastic part includes four mechanisms: dislocation motion in martensite along slip systems of martensite and slip systems of austenite inherited during PT and dislocation motion in austenite along slip systems of austenite and slip systems of martensite inherited during reverse PT. The plastic part of the velocity gradient for all these mechanisms is defined in the crystal lattice of the austenite utilizing just slip systems of austenite and inherited slip systems of martensite, and just two corresponding types of order parameters. The explicit expressions for the Helmholtz free energy and the transformation and plastic deformation gradients are presented to satisfy the formulated conditions related to homogeneous thermodynamic equilibrium states of crystal lattice and their instabilities. In particular, they result in a constant (i.e., stress- and temperature-independent) transformation deformation gradient and Burgers vectors. Thermodynamic treatment resulted in the determination of the driving forces for change of the order parameters for PTs and dislocations. It also determined the boundary conditions for the order parameters that include a variation of the surface energy during PT and exit of dislocations. Ginzburg–Landau equations for dislocations include variation of properties during PTs, which in turn produces additional contributions from dislocations to the Ginzburg–Landau equations for PTs. A complete system of coupled PFA and mechanics equations is presented. A similar theory can be developed for PFA to dislocations and other PTs, like reconstructive PTs and diffusive PTs described by the Cahn–Hilliard equation, as well as twinning and grain boundaries evolution.     

Investigation of activities of grain boundaries in nanocrystalline Al under an indenter by a multiscale method

Activities of grain boundaries in nanocrystalline Al under an indenter are studied by a multiscale method. It is found that grain boundaries and twin boundaries can be transformed into each other by emitting and absorbing dislocations. The transition processes might result in grain coarsening and refinement events. Dislocation reflection generated by a piece of stable grain boundary is also observed, because of the complex local atomic structure within the nanocrystalline Al. This implies that nanocrystalline metals might improve their internal structural stability with the help of some special local grain boundaries.     

Compliant interfaces: A mechanism for relaxation of dislocation pile-ups in a sheared single crystal

Discrete dislocation plasticity models and strain-gradient plasticity theories are used to investigate the role of interfaces in the elastic–plastic response of a sheared single crystal. The upper and lower faces of a single crystal are bonded to rigid adherends via interfaces of finite thickness. The sandwich system is subjected to simple shear, and the effect of thickness of crystal layer and of interfaces upon the overall response are explored. When the interface has a modulus less than that of the bulk material, both the predicted plastic size effect and the Bauschinger effect are considerably reduced. This is due to the relaxation of the dislocation stress field by the relatively compliant surface layer. On the other hand, when the interface has a modulus equal to that of the bulk material a strong size effect in hardening as well as a significant reverse plasticity are observed in small specimens. These effects are attributed to the energy stored in the elastic fields of the geometrically necessary dislocations (GNDs).     

Strain accommodation and interfacial structure of AlN interlayers in GaN

The strain accommodation mechanisms at AlN interlayers in GaN, grown by radio‐frequency plasma assisted molecular beam epitaxy, are studied using transmission electron microscopy techniques and atomistic modelling. Interlayers of various thicknesses grown within GaN epilayers deposited on both sapphire and silicon substrates have been employed. Interlayers of thickness below 6 nm do not exhibit line defects although local roughness of the upper interlayer interface is observed as a result of the Al adatom kinetics and higher interfacial energy compared to the lower interface. Above 6 nm, introduction of a ‐type misfit and threading dislocations constitutes the principal relaxation mechanism. Due to strain partitioning between AlN and GaN, threading dislocations adopt inclined zig‐zag lines thus contributing to the relief of alternating compressive‐tensile elastic strain across the AlN/GaN heterostructure. The observed dislocation configurations are consistent with a model of independent motion by climb or ancillary glide in response to their localized three‐dimensional strain environment. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Interdiffusion in two-layer Pd/Ag films III. TEM investigation of diffusion-induced grain boundary migration

Diffusion-induced grain boundary migration (DIGM) is studied by the transmission electron microscopy method in polycrystalline two-layer Pd/Ag thin films with a grain size (100–2000 nm). In addition to the typical features of DIGM known for coarse-grained bulk objects and foils, new features are found which are caused by a quite dense network of triple junctions and by misfit dislocations: fast increase of grain boundary curvature and inclination; back motion of grain boundaries owing to recrystallization forces and termination of DIGM. Homogenization resulted from diffusion-induced migration of misfit dislocations is observed in addition to DIGM.     

Microdisks on (100) cleavages and (110) fractured faces of NaCl crystals

Some elevated microdisks are reported on (100) cleavages and (110) fractured faces of NaCl, produced by the etchant reported by Davidge and Whitworth (1961). It is observed that the structure of the disks is similar on both the faces, but does not coincide with the matched faces. It is shown that these disks are not formed due to the protective action of microbubbles during the etching process but formed at the sites of localized impurities.     

Non-uniform, axisymmetric misfit strain： in thin films bonded on plate substrates/substrate systems： the relation between non-uniform film stresses and system curvatures

Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. By considering a circular thin film/substrate system subject to non-uniform, but axisymmetric misfit strain distributions in the thin film, we derived relations between the film stresses and the misfit strain, and between the plate system’s curvatures and the misfit strain. These relations feature a ‘‘local’’ part which involves a direct dependence of the stress or curvature components on the misfit strain at the same point, and a ‘‘non-local’’ part which reflects the effect of misfit strain of other points on the location of scrutiny. Most notably, we also derived relations between the polar components of the film stress and those of system curvatures which allow for the experimental inference of such stresses from full-field curvature measurements in the presence of arbitrary radial non-uniformities. These relations also feature a ‘‘non-local’’ dependence on curvatures making a full-field measurement a necessity. Finally, it is shown that the interfacial shear tractions between the film and the substrate are proportional to the radial gradients of the first curvature invariant and can also be inferred experimentally.