The formation of dislocation networks

The formation of small angle boundaries consisting of dislocation networks is considered mainly on the basis of studies concerning the hot-deformation of Al-Mg alloys solidified with well developed sub-structures. It is shown that different kinds of network are built up on dislocation forests by dislocations which encounter the forest by glide and then change the mode of motion from glide to climb. Special attention is given to the mechanism of climb which enables the rapid knitting of networks during hot-deformation, and also to the annihilation of dislocations which prevents the increase in flow stress.     

Diffusive fluxes associated with interfacial defeet motion and interaction

The diffusional flux associated with the motion of interfacial defects is described by an equation expressed in terms of the topological parameters which characterise defects, namely their Burgers vectors and step heights, the defect velocity and the concentration of each atomic species in the two adjacent crystals. This expression demonstrates that glide/climb behaviour of grain boundary defects is analogous to motion of dislocations in single crystals; climb motion results if a component of b is perpendicular to the interface plane. However, the situation is more complex in the case of interphase interface defects, but the present approach, which considers the step and dislocation portions of defects separately, enables a straightforward analysis. Several examples are illustrated to show the various possibilities, such as climb motion even when b is parallel to the interface, and glide motion when b is not. The latter case arises in martensitic transformation where the existence of an invariant-plane-strain relation at the interface leads to equal and opposite fluxes to the step and dislocation portions of transformation defects so that overall the motion is diffusionless.Interfacial processes involve the motion and interaction of defects. The present analysis facilitates the consideration of diffusive fluxes associated with defect interaction since the step and dislocation portions can be treated independently. A general expression is derived for the total flux arising, and a particular case, the interaction of transformation dislocations with crystal dislocations which have reached the interface during lattice-invariant deformation in martensite formation, is considered.     

Duality in 2 + 1D quantum elasticity: superconductivity and quantum nematic order

Superfluidity and superconductivity are traditionally understood in terms of an adiabatic continuation from the Bose-gas limit. Here we demonstrate that at least in a 2 + 1D Bose system, superfluidity can arise in a strict quantum field-theoretic setting. Taking the theory of quantum elasticity (describing phonons) as a literal quantum field theory with a bosonic statistic, superfluidity and superconductivity (in the EM charged case) emerge automatically when the shear rigidity of the elastic state is destroyed by the proliferation of topological defects (quantum dislocations). Off-diagonal long range order in terms of the field operators of the constituent particles is not required. This is one of the outcomes of the broader pursuit presented in this paper. In essence, it amounts to the generalization of the well known theory of crystal melting in two dimensions by Nelson et al. [Phys. Rev. B 19 (1979) 2457; Phys. Rev. B 19 (1979) 1855], to the dynamical theory of bosonic states exhibiting quantum liquid-crystalline orders in 2 + 1 dimensions. We strongly rest on the field-theoretic formalism developed by Kleinert [Gauge fields in Condensed Matter, vol. II: Stresses and Defects, Differential Geometry, Crystal Defects, World Scientific, Singapore, 1989] for classical melting in 3D. Within this framework, the disordered states correspond to Bose condensates of the topological excitations, coupled to gauge fields describing the capacity of the elastic medium to propagate stresses. Our focus is primarily on the nematic states, corresponding with condensates of dislocations, under the topological condition that disclinations remain massive. The dislocations carry Burgers vectors as topological charges. Conventional nematic order, i.e., the breaking of space-rotations, corresponds in this field-theoretic duality framework with an ordering of the Burgers vectors. However, we also demonstrate that the Burgers vectors can quantum disorder despite the massive character of the disclinations. We identify the physical nature of the ‘Coulomb nematic’ suggested by Lammert et al. [Phys. Rev. Lett. 70 (1993) 1650; Phys. Rev. E 52 (1995) 1778] on gauge-theoretical grounds. The 2 + 1D quantum liquid crystals differ in fundamental regards from their 3D classical counterparts due to the presence of a dynamical constraint. This constraint is the glide principle, well known from metallurgy, which states that dislocations can only propagate in the direction of their Burgers vector. In the present framework this principle plays a central role. This constraint is necessary to decouple compression rigidity from the dislocation condensate. The shear rigidity is not protected, and as a result the shear modes acquire a Higgs mass in the dual condensate. This is the way the dictum that translational symmetry breaking goes hand in hand with shear rigidity emerges in the field theory. However, because of the glide principle compression stays massless, and the fluids are characterized by an isolated massless compression mode and are therefore superfluids. Glide also causes the shear Higgs mass to vanish at orientations perpendicular to the director in the ordered nematic, and the resulting state can be viewed as a quantum smectic of a novel kind. Our most spectacular result is a new hydrodynamical way of understanding the conventional electromagnetic Meissner state (superconducting state). Generalizing to the electromagnetically charged elastic medium (‘Wigner Crystal’) we find that the Higgs mass of the shear gauge fields, becoming finite in the nematic quantum fluids, automatically causes a Higgs mass in the electromagnetic sector by a novel mechanism.     

Elastic interaction between two parallel dislocations in non-parallel slip planes

The elastic interaction between two parallel dislocations which can glide in non-parallel slip planes is studied under the simplifying assumption that the dislocation glide velocity is proportional to stress. The motion of the two dislocations is represented by a motion of one reference point in a configuration plane. It is concluded that the contribution of the long-range elastic interaction between individual dislocations from different slip systems to work hardening is negligible, compared to the contribution from the formed attractive junctions. Especially, two parallel edge dislocations with mutually perpendicular Burgers vectors can co-exist in minimum energy positions, however, they can be separated by an arbitrarily small external stress.     

Climb via vacancy diffusion of edge dislocations in 2D dislocation microstructures

The prevention of strength degradation of components is one of the great challenges in solid mechanics. In particular, at high temperatures material may deform even at low stresses, a deformation mode known as deformation creep. One of the microstructural mechanisms that governs deformation creep is dislocation motion due to the absorption or emission of vacancies, which results in motion perpendicular to the glide plane, called dislocation climb. However, the importance of the dislocation network for the deformation creep remains far from being understood. In this study, a climb model that accounts for the dislocation network is developed, by solving the diffusion equation for vacancies in a region with a general dislocation distribution. The definition of the sink strength is extended, to account for the contributions of neighbouring dislocations to the climb rate. The model is then applied to dislocation dipoles and dislocation pile-ups, which are dense dislocation structures and it is found that the sink strength of dislocations in a pile-up is reduced since the vacancy field is distributed between the dislocations. Finally, the importance of the results for modelling deformation creep is discussed.     

Mechanisms of high-temperature creep of nickel-based superalloys under low applied stresses

[001] single-crystal specimens of the superalloys CMSX-4 and CMSX-10 were tested for creep at 1100°C under tensile stresses between 105 and 135?MPa, where they show pronounced steady creep. The deformed superalloys were analysed by density measurements, scanning electron microscopy and transmission electron microscopy which supplied information about porosity growth, evolution of the γ–γ′ microstructure, dislocation mobility and reactions during creep deformation. It is shown that, under the testing conditions used, steady creep strain mostly results from transverse glide–climb of (a/2) ?011? interfacial dislocations. A by-product of the interfacial glide–climb are vacancies which diffuse along the interfaces to growing pores or to a ?100? edge dislocations climbing in the γ′ phase. Climb of a ?100? dislocations in the γ′ phase is a recovery mechanism which reduces the constraining of the γ phase by the γ′ phase, thus enabling further glide of (a/2) ?011? dislocations in the matrix. Moreover the γ′ dislocations act as vacancy sinks facilitating interfacial glide–climb. The creep rate increases when the γ–γ′ microstructure becomes topologically inverted; connection of the γ′ rafts results in extensive transverse climb and an increase of the number of a?100? dislocation segments in the γ′ phase.     

On the non-uniform motion of dislocations: the retarded elastic fields,the retarded dislocation tensor potentials and the Liénard–Wiechert tensor potentials

The topic of this paper is the fundamental theory of the non-uniform motion of dislocations in two and three space dimensions. We investigate the non-uniform motion of an arbitrary distribution of dislocations, a dislocation loop and straight dislocations in infinite media using the theory of incompatible elastodynamics. The equations of motion are derived for non-uniformly moving dislocations. The retarded elastic fields produced by a distribution of dislocations and the retarded dislocation tensor potentials are determined. New fundamental key formulae for the dynamics of dislocations are derived (Jefimenko type and Heaviside–Feynman type equations of dislocations). In addition, exact closed-form solutions of the elastic fields produced by a dislocation loop are calculated as retarded line integral expressions for subsonic motion. The fields of the elastic velocity and elastic distortion surrounding the arbitrarily moving dislocation loop are given explicitly in terms of the so-called three-dimensional elastodynamic Liénard–Wiechert tensor potentials. The two-dimensional elastodynamic Liénard–Wiechert tensor potentials and the near-field approximation of the elastic fields for straight dislocations are calculated. The singularities of the near-fields of accelerating screw and edge dislocations are determined.     

Kinematics of edge dislocations. I. Involutive distributions of local slip planes

The geometry of continuous distributions of dislocations and secondary point defects created by these distributions is considered. Particularly, the dependence of a distribution of dislocations on the existence of secondary point defects is modeled by treating dislocations as those located in a time-dependent Riemannian material space describing, in a continuous limit, the influence of these point defects on metric properties of a crystal structure. The notions of local glide systems and involutive distributions of local slip planes are introduced in order to describe, in terms of differential geometry, some aspects of the kinematics of the motion of edge dislocations. The analysis leads, among others, to the definition of a class of distributions of dislocations with a distinguished involutive distribution of local slip planes and such that a formula of mesoscale character describing the influence of edge dislocations on the mean curvature of glide surfaces is valid.     

纯物质晶界结构及运动的晶体相场法模拟

采用晶体相场模型,分别模拟了纯物质小角度晶界和大角度晶界结构及变形过程中的晶粒转动及晶界迁移.结果表明,小角度晶界迁移的主要机理是构成晶界的位错的滑移和攀移,而大角度晶界的迁移主要依靠晶界两侧原子的跳动及晶界位错等缺陷的运动. 关键词： The phase field crystal model was used to simulate the structure of the small angle and the large angle grain boundary (GB) the grain rotation and the GB migration during deformation. Simulated results show that the dislocation glide and climb are the ma     

Numerical calculation of the rate of strain of interstitial solid solutions under irradiation. I. Model of radiation creep

A model of radiation creep of interstitial solid solutions is developed on the basis of the combined motion of dislocations, including their glide and climb past obstacles. The obstacles considered are forest dislocations and pileups of radiation-induced point defects. A computational formula for the rate of strain is derived which describes creep at high stresses, when the gliding dislocations overcome some of the barriers by force, and a method is described for determining the average distance traversed by a dislocation in the glide plane under the influence of the stress until it is stopped by barriers. The results are compared with those of other authors. It is shown that the formula obtained for the rate of strain goes over in particular cases to those given by the previously known SIPA, Gittus-Mansur, and glide-climb models of radiation creep. Zh. Tekh. Fiz. 69, 64–71 (January 1999)     

Kink formation and motion in carbon nanotubes at high temperatures

We report that kink motion is a universal plastic deformation mode in all carbon nanotubes when being tensile loaded at high temperatures. The kink motion, observed inside a high-resolution transmission electron microscope, is reminiscent of dislocation motion in crystalline materials: namely, it dissociates and multiplies. The kinks are nucleated from vacancy creation and aggregation, and propagate in either a longitudinal or a spiral path along the nanotube walls. The kink motion is related to dislocation glide and climb influenced by external stress and high temperatures in carbon nanotubes.     

A computational approach towards modelling dislocation transmission across phase boundaries

To study the nanoscopic interaction between edge dislocations and a phase boundary within a two-phase microstructure the effect of the phase contrast on the internal stress field due to the dislocations needs to be taken into account. For this purpose a 2D semi-discrete model is proposed in this paper. It consists of two distinct phases, each with its specific material properties, separated by a fully coherent and non-damaging phase boundary. Each phase is modelled as a continuum enriched with a Peierls–Nabarro (PN) dislocation region, confining dislocation motion to a discrete plane, the glide plane. In this paper, a single glide plane perpendicular to and continuous across the phase boundary is considered. Along the glide plane bulk induced shear tractions are balanced by glide plane shear tractions based on the classical PN model. The model's ability to capture dislocation obstruction at phase boundaries, dislocation pile-ups and dislocation transmission is studied. Results show that the phase contrast in material properties (e.g. elastic stiffness, glide plane properties) alone creates a barrier to the motion of dislocations from a soft to a hard phase. The proposed model accounts for the interplay between dislocations, external boundaries and phase boundary and thus represents a suitable tool for studying edge dislocation–phase boundary interaction in two-phase microstructures.     

Asymptotic behaviors of the stress fields in the vicinity of dislocations and dislocation segments

We obtain the singular asymptotic behavior of the stress field in the vicinity of a non-planar dislocation in three dimensions and the nearly singular behavior of the full self-force of the dislocation including both glide and climb forces, using asymptotic analysis. We also derive asymptotic formulas for the stress field in the vicinity of a curved dislocation segment. Numerical examples are presented to examine the asymptotic formulas. The obtained formulas can be used for qualitative understanding of the stress tensor associated with dislocations and efficient and accurate calculation of the stress tensor in dislocation dynamics simulations.     

Influence of the phonon viscosity and dislocation interaction on the glide of a pair of edge dislocations in a crystal with point defects

The motion of a pair of edge dislocations in an elastic field of point defects is investigated taking into account the interaction of dislocations both with each other and with the phonon subsystem of the crystal. It is demonstrated that the retarding force is a nonmonotonic function of the velocity of dislocation glide with two extrema displayed under certain conditions.     

Influence of collective effects on the dynamic behavior of a single edge dislocation in a crystal with point defects

The glide of a single edge dislocation in an elastic field of point defects randomly distributed over a crystal is investigated taking into account the influence of the phonon subsystem of the crystal. The force of retardation of the dislocation motion is calculated, and the velocities at which this force has a local maximum and a local minimum are determined. A comparative analysis of the glide of a single dislocation and the glide of a pair of edge dislocations is performed.     

Dislocation dynamics in multiwalled carbon nanotubes at high temperatures

Dislocation dynamics dictate the mechanical behavior of materials. Dislocations in periodic crystalline materials have been well documented. On the contrary, dislocations in cylindrical carbon nanotubes, particularly in multiwalled carbon nanotubes (MWCNTs), remain almost unexplored. Here we report that a room temperature 1/2<0001> sessile dislocation in a MWCNT becomes highly mobile, as characterized by its glide, climb, and the glide-climb interactions, at temperatures of about 2000 degrees C. The dislocation glide leads to the cross-linking of different shells; dislocation climb creates nanocracks; and the interaction of two 1/2<0001> dislocations creates kinks. We found that dislocation loops act as channels for mass transport. These dislocation dynamics are drastically different from that in conventional periodic crystalline materials due to the cylindrical, highly anisotropic structures of MWCNTs.     

On the elastic fields produced by non-uniformly moving dislocations: a revisit

We investigate the non-uniform motion of straight dislocations in infinite media using the theory of incompatible elastodynamics. The equations of motion are derived for non-uniformly moving screw dislocations, gliding edge and climbing edge dislocations. The exact closed-form solutions of the elastic fields are calculated. The fields of the elastic velocity and elastic distortion surrounding the arbitrarily moving dislocations are given explicitly in the form of integral representations free of non-integrable singularities. The elastic fields describe the response in the form of non-uniformly moving elastic waves caused by the motion of the dislocation.     

Dislocations jam at any density

Crystalline materials deform in an intermittent way via dislocation-slip avalanches. Below a critical stress, the dislocations are jammed within their glide plane due to long-range elastic interactions and the material exhibits plastic response, while above this critical stress the dislocations are mobile (the unjammed phase) and the material flows. We use dislocation dynamics and scaling arguments in two dimensions to show that the critical stress grows with the square root of the dislocation density. Consequently, dislocations jam at any density, in contrast with granular materials, which only jam below a critical density.     

Defect structure in EuS single crystals grown from the melt

The defect structure in EuS single crystals grown form the melt is studied by etch pitting, scanning and high-voltage electron microscopy. Circular and square etch pits and a second phase in the shape of thin hexagonal platelets are observed by etching. Microprobe analysis indicates the platelets to consist of Eu metal. In the transmission electron microscope, smoothly curved dislocations and helical dislocations, small dislocation loops and inclusions associated with dislocations are observed. The possible origin of the detected dislocation structure is considered with reference to climb and glide processes occurring during cooling down the grown crystals. The results corroborate the glide geometry of the NaCl lattice for EuS. On leave from Institute of Physics, Academic Sinica, Peking, VR China