Dynamic dislocation–defect analysis

The dynamic internal variables which control plastic flow can only be assessed by dynamic materials testing at any given instance. The testing method championned by our studies has been precision strain rate sensitivity (PSRS) whereby the change in flow stress due to a set change in strain rate is taken to be an operational measure of the activation volume and its product with the flow stress gives rise to the operational activation work. Also, from the work hardening slope, a modelled parameter proportional to the mean slip distance (λ) is simultaneously determined. The deviation from the linear Cottrell–Stokes relation as determined with the Haasen plot indicates the evolution of secondary defects other than monopole dislocations. Hence PSRS can assess the theoretical predictions of the activation distance (d) and work as a function of temperature, resulting in quantitative values that are in accord with dislocation theory at temperatures below that where point defects become mobile. A method to calibrate λ using Stage II slope θ_II shows that λ/?, where ? is the mean forest dislocation spacing, is inversely proportional to θ, the work hardening coefficient. This analysis has led to a new plot of θ_II/θ versus b ²λ/ν where b is the Burgers vector and its slope is directly proportional to d. An example using an alumina-dispersed high conductivity copper shows that geometrically necessary punched out loops are continuously generated. The role of point defect mobility is dramatically illustrated by load drops in [001] aluminium crystals with the formation of slip clusters.     

Can vacancies lubricate dislocation motion in aluminum?

The interaction of vacancy with dislocations in Al is studied using the semidiscrete variational Peierls-Nabarro model with ab initio determined gamma surface. For the first time, we confirm theoretically the so-called vacancy lubrication effect on dislocation motion in Al, a discovery that can settle a long-standing controversy in dislocation theory for fcc metals. We provide insights into the lubrication effect by exploring the connection between dislocation mobility and its core width. We predict an increased dislocation splitting in the presence of vacancy. We find that on average there is a weak repulsion between vacancies and dislocations which is independent of dislocation character.     

Modification of the Peierls–Nabarro model for misfit dislocation

For a misfit dislocation, the balance equations satisfied by the displacement fields are modified, and an extra term proportional to the second-order derivative appears in the resulting misfit equation compared with the equation derived by Yao et al. This second-order derivative describes the lattice discreteness effect that arises from the surface effect. The core structure of a misfit dislocation and the change in interfacial spacing that it induces are investigated theoretically in the framework of an improved Peierls–Nabarro equation in which the effect of discreteness is fully taken into account. As an application, the structure of the misfit dislocation for a honeycomb structure in a two-dimensional heterostructure is presented.     

Atomistic simulation of kink structure on edge dislocation in bcc iron

Based on the general theory of dislocation and kink, we have constructed the three kink models corresponding to the 1/2 （111）{011} and 1/2 （111）{112} edge dislocations （EDs） in bcc Fe using the molecular dynamics method. We found that the geometric structure of a kink depends on the type of ED and the structural energies of the atom sites in the dislocation core region, as well as the geometric symmetry of the dislocation core and the characteristic of the stacking sequence of atomic plane along the dislocation line. The formation energies and widths of the kinks on the 1/2 （111）{011} and 1/2 （111）{112} EDs are calculated, the formation energies are 0.05eV and 0.04eV, and widths are 6.02b and 6.51b, respectively （b is the magnitude of the Burgers vector）. The small formation energies indicate that the formation of kink in the edge dislocation is very easy in bcc Fe.     

Universal probes of two-dimensional topological insulators: dislocation and π flux

We show that the π flux and the dislocation represent topological observables that probe two-dimensional topological order through binding of the zero-energy modes. We analytically demonstrate that π flux hosts a Kramers pair of zero modes in the topological Γ (Berry phase Skyrmion at the zero momentum) and M (Berry phase Skyrmion at a finite momentum) phases of the M-B model introduced for the HgTe quantum spin Hall insulator. Furthermore, we analytically show that the dislocation acts as a π flux, but only so in the M phase. Our numerical analysis confirms this through a Kramers pair of zero modes bound to a dislocation appearing in the M phase only, and further demonstrates the robustness of the modes to disorder and the Rashba coupling. Finally, we conjecture that by studying the zero modes bound to dislocations all translationally distinguishable two-dimensional topological band insulators can be classified.     

Solute-diffusion-controlled dislocation creep in pure aluminium containing 0.026 at.% Fe

Pure aluminium containing about 200?at.ppm Fe in solution is shown to creep about 10⁶ times slower at 200°C than the same aluminium containing a negligible amount of iron in solution. The high creep resistance of the Al–200?at.ppm?Fe alloy is attributed to the presence of subgrain boundaries containing iron solute atoms. It is proposed that the opposing stress fields from subgrain boundaries and from the piled-up dislocations during creep are cyclically relaxed, by iron solute diffusion, to allow climb of the lead dislocation in the pile-up. The mechanism is a form of mechanical ratcheting. The model is applied to Al–Fe alloys and correctly predicts that the creep rate is controlled by the rate of iron solute diffusion and by a temperature dependence equal to the activation energy for iron diffusion, namely Q _c?=?221?kJ?mol^?1. Basic creep studies on solid-solution alloying with solute atoms that diffuse slowly in the lattice of aluminium (e.g. manganese, chromium, titanium and vanadium) appear worthy of study as a way of enhancing creep strength and of understanding creep mechanisms involving solute-atom-containing subgrain boundaries.     

An improvement of the lattice theory of dislocation for a two-dimensional triangular crystal

The structure of dislocation in a two-dimensional triangular crystal has been studied theoretically on the basis of atomic interaction and lattice statics. The theory presented in this paper is an improvement to that published previously.Within a reasonable interaction approximation, a new dislocation equation is obtained, which remedies a fault existing in the lattice theory of dislocation. A better simplification of non-diagonal terms of the kernel is given. The solution of the new dislocation equation asymptotically becomes the same as that obtained in the elastic theory, and agrees with experimental data. It is found that the solution is formally identical with that proposed phenomenologically by Foreman et al, where the parameter can be chosen freely, but cannot uniquely determined from theory. Indeed, if the parameter in the expression of the solution is selected suitably, the expression can be well applied to describe the fine structure of the dislocation.     

The interaction of dislocation loop and γ' precipitate in nickel based alloys

The nucleation and growth of interstitial loops during irradiation has a : ontrolling effect on the subsequent swelling behaviour of metals. In nickel based alloys containing ordered γ' precipitate (Ni₃Al, Ti), interactions occur between the nucleated loops and γ' particles. This effect has been studied in two nickel based alloys using a High Voltage Electron Microscope.

For the case of Nimonic 80A alloy containing 18% volume fraction : gamma;' precipitate, dislocation loop-particle interactions obeyed the developed isotropic elasticity theory.²'³'¹² Consequently, rather low dislocation densities were developed and the swelling resistance was high during electron irradiation. In Nimonic 115A alloy, loop nucleation and growth was dependent on the availability of interfacial dislocation surrounding the γ' particles.

With regard to the swelling behaviour of γ' hardened alloys, it : s concluded that several mechanisms contribute to make these materials resistant.

Coherency strains at the γ' particles reduce the density of : limbing dislocations.

The γ' precipitate affects the climb efficiency of the : ucleated dislocations by:

pinning the dislocation line, thus introducing a line tension force : hich opposes dislocation climb and reduces swelling;

reducing the available volume of material in which dislocation loops : an nucleate and grow.     

Atomic-scale study of dislocation–stacking fault tetrahedron interactions. Part I: mechanisms

Stacking fault tetrahedra (SFTs) are formed under irradiation in fcc metals and alloys. The high number density of SFTs observed suggests that they should contribute to radiation-induced hardening and, therefore, be taken into account when estimating mechanical property changes of irradiated materials. The key issue in this is to describe the interaction between a moving dislocation and an individual SFT, which is distinguished by a small physical size of the order of ～1–10?nm. We have performed atomistic simulations of edge and screw dislocations interacting with SFTs of different sizes at different temperatures and strain rates. Five possible interaction outcomes have been identified, involving either partial absorption, or shearing or restoration of SFTs. The mechanisms that give rise to these processes are described and their dependence on interaction parameters, such as SFT size, dislocation–SFT geometry, temperature and stress/strain rate are determined. Mechanisms that help to explain the formation of defect-free channels cleared by gliding dislocations, as observed experimentally, are also discussed. Hardening due to the various mechanisms and their dependence on loading conditions will be presented in a following paper (Part II).     

In situ and tomographic analysis of dislocation/grain boundary interactions in α-titanium

In situ straining in the transmission electron microscope and diffraction-contrast electron tomography have been applied to the investigation of dislocation/grain boundary and dislocation/twin boundary interactions in α-Ti. It was found that, similar to FCC materials, the transfer of dislocations across grain boundaries is governed primarily by the minimization of the magnitude of the Burgers vector of the residual grain boundary dislocation. That is, grain boundary strain energy density minimization determines the selection of the emitted slip system.     

Wavefront motion in the vicinity of a phase dislocation: “optical vortex”

In the scalar approximation, an analysis is made of the light field structure in the vicinity of a line of the ring phase dislocation corresponding to the zero value of the field formed by the interference of two uniaxial Gaussian beams. The formation of an “optical vortex” or the toroidal motion of a portion of a light flow around a ring phase dislocation is shown.     

Non-singular dislocation continuum theories: strain gradient elasticity vs. Peierls–Nabarro model

Abstract

Non-singular dislocation continuum theories are studied. A comparison between Peierls–Nabarro dislocations and straight dislocations in strain gradient elasticity is given. The non-singular displacement fields, non-singular stresses, plastic distortions and dislocation core shapes are analysed and compared for the two models. The main conclusion of this study is that due to their characteristic properties, the non-singular displacement fields, non-singular stresses and dislocation core shape of screw and edge dislocations obtained in the framework of strain gradient elasticity are more realistic and physical than the corresponding fields of the Peierls–Nabarro model. Strain gradient elasticity of dislocations is a continuum dislocation theory including a weak non-locality within the dislocation core and predicting the size and shape of the dislocation core. The dislocation core is narrower in the strain gradient elasticity dislocation model than in the Peierls–Nabarro model and more evenly distributed in two dimensions. The present analysis shows that for the modelling of the dislocation core structure the non-singular dislocation fields of strain gradient elasticity are the suitable ones.     

Intralamellar dislocation networks formed by glide in γ-TiAl I. The mechanism of formation

In a lamellar TiAl alloy deformed at room temperature under an orientation that activates slip parallel to the interfaces, the nphase exhibits intralamellar dislocation networks parallel to the primary slip plane and entirely glissile in their habit plane. Their meshes are mainly rectangular with branches all coplanar, screw or near-screw in character and with Burgers vector of and types. Dislocation organization at and in the near-vicinity of these intralamellar networks suggests a reaction between a family of primary coplanar d011] dislocations that slip in the network habit plane and a family of dislocations that cross-slip from a plane inclined to the lamellae into the network. The reactions result in junctions with Burgers vector that subsequently transform into rectangular units. The presence of these networks is consistent with that of a residual elastic twist between adjacent nlamellae.     

Champ élastique d'une dislocation rectiligne parallèle aux interfaces : une nouvelle approche

The elastic field of a crystalline defect parallel to the two free surfaces of an isotropic thin foil is studied, for plane strain, with a new approach using repeated applications of the classical solution of the Flamant's problem. The case of an edge dislocation placed at any position in the foil and with a Burgers vector parallel to the surfaces is considered in greater detail. To cite this article: R. Bonnet, C. R. Physique 4 (2003).     

The elastic potential energy of a thin foil deformed by an in-plane 60° dislocation

An explicit expression of the elastic potential energy, W ^p, stored in a thin foil by a dissociated dislocation running parallel to the free surfaces is obtained in isotropic elasticity. It is used to discuss the metastable elastic equilibrium of a 60° dislocation in an ultrathin silicon foil when the fault plane is slightly inclined with respect to the free surfaces. The energy W ^p depends in particular on the positions of the two partials in the foil and on the thickness h, a situation not fully considered previously. For such ultrathin foils, propitious to the observation of partial dislocations cores at near atomic resolution, the theory predicts rapid changes with h of the separation distance S. This result is in accordance with previous experimental observations of S realized with the so-called “forbidden-reflection lattice imaging” technique.     

Effect of H impurity on misfit dislocation in Ni-based single-crystal superalloy： molecular dynamic simulations

The effect of H impurity on the misfit dislocation in Ni-based single-crystal superalloy is investigated using the molecular dynamic simulation.It includes the site preferences of H impurity in single crystals Ni and Ni 3 Al,the interaction between H impurity and the misfit dislocation and the effect of H impurity on the moving misfit dislocation.The calculated energies and simulation results show that the misfit dislocation attracts H impurity which is located at the γ/γˊinterface and Ni₃ Al and H impurity on the glide plane can obstruct the glide of misfit dislocation,which is beneficial to improving the mechanical properties of Ni based superalloys.