The solid angle and the Burgers formula in the theory of gradient elasticity: Line integral representation

A representation of the solid angle and the Burgers formula as line integral is derived in the framework of the theory of gradient elasticity of Helmholtz type. The gradient version of the Eshelby–deWit representation of the Burgers formula of a closed dislocation loop is given. Such a form is suitable for the numerical implementation in 3D dislocation dynamics (DD).     

Dynamic drag of edge dislocation by circular prismatic loops and point defects

Motion of edge dislocation in the presence of prismatic loops and point defects is studied analytically. It is shown that at certain conditions, the velocity dependence of the drag force has two maximums and two minimums.     

On the correspondence between a screw dislocation in gradient elasticity and a regularized vortex

We show the correspondence between a screw dislocation in gradient elasticity and a regularized vortex. The effective Burgers vector, nonsingular distortion and stress fields of a screw dislocation and the effective circulation, smoothed velocity and momentum of a vortex are given and discussed.     

Fundamentals in generalized elasticity and dislocation theory of quasicrystals: Green tensor,dislocation key-formulas and dislocation loops

The present work provides fundamental quantities in generalized elasticity and dislocation theory of quasicrystals. In a clear and straightforward manner, the three-dimensional Green tensor of generalized elasticity theory and the extended displacement vector for an arbitrary extended force are derived. Next, in the framework of dislocation theory of quasicrystals, the solutions of the field equations for the extended displacement vector and the extended elastic distortion tensor are given; that is, the generalized Burgers equation for arbitrary sources and the generalized Mura–Willis formula, respectively. Moreover, important quantities of the theory of dislocations as the Eshelby stress tensor, Peach–Koehler force, stress function tensor and the interaction energy are derived for general dislocations. The application to dislocation loops gives rise to the generalized Burgers equation, where the displacement vector can be written as a sum of a line integral plus a purely geometric part. Finally, using the Green tensor, all other dislocation key-formulas for loops, known from the theory of anisotropic elasticity, like the Peach–Koehler stress formula, Mura–Willis equation, Volterra equation, stress function tensor and the interaction energy are derived for quasicrystals.     

氢离子辐照纯钒中形成的位错环

钒合金作为聚变堆候选材料, 其辐照损伤行为一直是关注的重点. 研究辐照时形成的位错环的性质, 其意义在于揭示纯钒中辐照空洞的长大机理. 这种机理表现为不同类型位错环对点缺陷吸收的偏压不同, 从而影响金属的辐照肿胀. 本文利用加速器对纯钒薄膜样品进行氢离子辐照, 然后, 利用透射电镜的inside-outside方法分析氢离子辐照所形成的位错环的类型. 结果表明, 在氢离子辐照纯钒中没有发现柏氏矢量b=<110>的位错环, 只有柏氏矢量b=1/2<111>和b=<110>的位错环, 这两种位错环的惯性面处于{110}-{112}之间. 能确定性质的位错环全部为间隙型位错环, 未发现空位型位错环.     

Precipitate assemblies formed on dislocation loops in aluminium-silver-copper alloys

The precipitation microstructure of the γ′ (AlAg₂) intermetallic phase has been examined in aluminium-silver-copper alloys. The microstructure developed in an Al-0.90at.%Ag-90at.Cu alloy was significantly different from that reported for binary Al-Ag alloys. The orientation relationship between the matrix and precipitate was unchanged; however, the γ′ phase formed assemblies with a two-dimensional, open arrangement of precipitates. Each such assembly contained two variants of the γ′ phase alternately arranged to form a faceted elliptical unit. The θ′ (Al₂Cu) phase formed on these assemblies after further ageing. Each assembly was formed via repeated precipitation of the γ′ phase on dissociated segments of a single dislocation loop. This faceted elliptical assembly has not been previously reported for the γ′ precipitate. The difference between the precipitation behaviour of the γ′ phase in Al-Ag and Al-Ag-Cu alloys was attributed to copper modifying the as-quenched defect structure of the matrix. The formation of faceted elliptical γ′ phase assemblies clarifies earlier observations on the precipitate number density and mechanical properties of aluminium-silver-copper alloys.     

注氢纯铝中间隙型位错环一维迁移现象的原位观察

核聚变堆材料在高能粒子辐照过程中会产生大量点缺陷,导致辐照脆性和辐照肿胀等现象.因而,研究点缺陷在辐照过程中的演变过程至关重要.点缺陷团簇的一维迁移现象是这种演变过程的主要研究内容之一.本文采用普通低压(200 kV)透射电镜,在室温条件下对注氢纯铝中的间隙型位错环在电子辐照下的一维迁移现象进行了观察和分析.在200 keV电子辐照下,注氢纯铝中的位错环可多个、同时发生一维迁移运动,也可单个、独立进行一维迁移运动.位错环沿柏氏矢量1/3<111>的方向可进行微米尺度的一维长程迁移,沿柏氏矢量1/2<110>的方向一维迁移也可达数百纳米.电子束辐照时产生的间隙原子浓度梯度是引起位错环一维迁移并决定其迁移方向的原因.位错环发生快速一维迁移时,其后会留下一条运动轨迹;位错环一维迁移的速率越快,运动的轨迹则越长,在完成迁移过后的几十秒内这些运动轨迹会逐渐消失.     

On gradient field theories: gradient magnetostatics and gradient elasticity

In this work, the fundamentals of gradient field theories are presented and reviewed. In particular, the theories of gradient magnetostatics and gradient elasticity are investigated and compared. For gradient magnetostatics, non-singular expressions for the magnetic vector gauge potential, the Biot–Savart law, the Lorentz force and the mutual interaction energy of two electric current loops are derived and discussed. For gradient elasticity, non-singular forms of all dislocation key formulas (Burgers equation, Mura equation, Peach–Koehler stress equation, Peach–Koehler force equation, and mutual interaction energy of two dislocation loops) are presented. In addition, similarities between an electric current loop and a dislocation loop are pointed out. The obtained fields for both gradient theories are non-singular due to a straightforward and self-consistent regularization.     

Evolution of dislocation loops in austenitic stainless steels implanted with high concentration of hydrogen

Abstract

It has been found that under certain conditions, hydrogen retention would be strongly enhanced in irradiated austenitic stainless steels. To investigate the effect of the retained hydrogen on the defect microstructure, AL-6XN stainless steel specimens were irradiated with low energy (100 keV) H₂⁺ so that high concentration of hydrogen was injected into the specimens while considerable displacement damage dose (up to 7 dpa) was also achieved. Irradiation induced dislocation loops and voids were characterised by transmission electron microscopy. For specimens irradiated to 7 dpa at 290 °C, dislocation loops with high number density were found and the void swelling was observed. At 380 °C, most of dislocation loops were unfaulted and tangled at 7 dpa, and the void swellings were observed at 5 dpa and above. Combining the data from low dose in previous work to high dose, four stages of dislocation loops evolution with hydrogen retention were suggested. Finally, molecular dynamics simulation was made to elucidate the division of large dislocation loops under irradiation.     

Bosonic loops and gluon condensate

Contributions to the vacuum polarisation inQCD are calculated separately with fermion as well as boson loops to have an idea of results expected for possible supersymmetric extension. It is found that the results are not altered in any significant way.     

Interaction of point defects with an edge dislocation in the gradient theory of elasticity

Interaction between a point defect and an edge dislocation is studied in the framework of the gradient theory of elasticity. The change in the energy of the system caused by a displacement of the point defect relative to the dislocation line is calculated. The results of the theoretical analysis are used to describe edge dislocation pinning by impurity atoms.     

Introducing dislocation climb by bulk diffusion in discrete dislocation dynamics

We report a method to incorporate dislocation climb controlled by bulk diffusion in a three-dimensional discrete dislocation dynamics (DDD) simulation for fcc metals. In this model we couple the vacancy diffusion theory to the DDD in order to obtain the climb rate of the dislocation segments. The capability of the model to reproduce the motion of climbing dislocations is examined by calculating several test-cases of pure climb-related phenomena and comparing the results with existing analytical predictions and experimental observations. As test-cases, the DDD is used to study the activation of Bardeen–Herring sources upon the application of an external stress or under vacancy supersaturation. Loop shrinkage and expansion due to vacancy emission or absorption is shown to be well described by our model. In particular, the model naturally describes the coarsening of a population of loops having different sizes.     

Misfit dislocation loops in composite nanowires

A new mechanism for relaxation of misfit stresses in composite nanowires (quantum wires) is suggested and theoretically examined, namely the formation of misfit dislocation loops. The stress field of a prismatic dislocation loop in a cylinder (nanowire) is calculated. The parameters of two-phase composite nanowires at which the formation of misfit dislocation loops is energetically favourable are estimated. The effect of stress fields of dislocation loops on the formation of compositionally modulated nanowires is discussed.     

A non-singular continuum theory of point defects using gradient elasticity of bi-Helmholtz type

In this paper, we develop a non-singular continuum theory of point defects based on a second strain gradient elasticity theory, the so-called gradient elasticity of bi-Helmholtz type. Such a generalised continuum theory possesses a weak nonlocal character with two internal material lengths and provides a mechanics of defects without singularities. Gradient elasticity of bi-Helmholtz type gives a natural and physical regularisation of the classical singularities of defects, based on higher order partial differential equations. Point defects embedded in an isotropic solid are considered as eigenstrain problem in gradient elasticity of bi-Helmholtz type. Singularity-free fields of point defects are presented. The displacement field as well as the first, the second and the third gradients of the displacement are derived and it is shown that the classical singularities are regularised in this framework. This model delivers non-singular expressions for the displacement field, the first displacement gradient and the second displacement gradient. Moreover, the plastic distortion (eigendistortion) and the gradient of the plastic distortion of a dilatation centre are also non-singular and are given in terms of a form factor (shape function) of a point defect. Singularity-free expressions for the interaction energy and the interaction force between two dilatation centres and for the interaction energy and the interaction force of a dilatation centre in the stress field of an edge dislocation are given. The results are applied to calculate the finite self-energy of a dilatation centre.     

Misfit dislocation loops in composite core-shell nanoparticles

The critical conditions have been calculated for the generation of circular prismatic loops of misfit dislocations at the interfaces in spherically symmetric composite core-shell nanoparticles. It has been shown that the formation of these loops becomes energetically favorable if the misfit parameter exceeds a critical value, which is determined by the geometry of the system. The most preferred position of the dislocation loop is in the equatorial plane of the nanoparticle. For a given radius of the nanoparticle, there is a minimum value of the critical misfit parameter below which the generation of a misfit dislocation is energetically unfavorable for any ratio of the core and shell radii. For a misfit parameter exceeding the minimum critical value, there are two critical values of the reduced radius of the particle core in the interval between which the generation of a dislocation loop is energetically favorable. This interval increases with increasing misfit parameter for a fixed particle size and decreases with decreasing particle size for a fixed misfit parameter.     

Wilson loops T-dual to short strings

We show that closed string solutions in the bulk of AdS space are related by T-duality to solutions representing an open string ending at the boundary of AdS. By combining the limit in which a closed string becomes small with a large boost, we find that the near-flat space short string in the bulk maps to a periodic open string world surface ending on a wavy line at the boundary. This open string solution was previously found by Mikhailov and corresponds to a time-like near-BPS Wilson loop differing by small fluctuations from a straight line. A simple relation is found between the shape of the Wilson loop and the shape of the closed string at the moment when it crosses the horizon of the Poincaré patch. As a result, the energy and spin of the closed string are encoded in properties of the Wilson loop. This suggests that closed string amplitudes with one of the closed strings falling into the Poincaré horizon should be dual to gauge theory correlators involving local operators and a Wilson loop of the T-dual (“momentum”) theory.     

Generation of dislocation loops in deformed nanocrystalline materials

A theoretical model is suggested which describes the generation of lattice perfect, lattice partial and grain boundary dislocation loops (DLs) at pre-existent DLs in mechanically loaded nanocrystalline materials (NCMs). The energy characteristics of various modes of the DL generation are calculated and compared. With these calculations and comparison, the two basic ranges of the grain size in NCMs are revealed each is characterized by its specific set of effectively operating modes of the DL generation and plastic deformation. The role of the DL generation in plastic and superplastic deformation processes in NCMs is discussed.     

Homogeneous nucleation of glide dislocation loops in nanoceramics

A theoretical model is proposed for the homogeneous nucleation of glide dislocation loops in nanocrystalline ceramics under deformation at low and high temperatures. The nucleation of a dislocation loop in a crystalline grain is considered an ideal nanoscopic shear whose magnitude (the Burgers vector of the dislocation) increases gradually as the loop is nucleating. The characteristics of the homogeneous nucleation of glide dislocation loops in nanocrystalline ceramics based on cubic silicon carbide are calculated. It is shown that, in general, the homogeneous nucleation of a dislocation loop in nanocrystalline ceramics at high temperatures proceeds in two stages, namely, the athermal nucleation of a loop of a “noncrystallographic” partial dislocation and its thermally activated transformation into an ordinary partial lattice dislocation loop.