ON CORE STRUCTURE PROPERTIES AND PEIERLS STRESS OF DISSOCIATED SUPERDISLOCATIONS IN ALUMINIDES: NiAl AND FeAl

<正>The study of dislocation properties in B2 structure intermetallics NiAl and FeAl is crucial to understand their mechanical behaviors.In this paper,the core structure and Peierls stress of collinear dissociated〈111〉{110} edge superdislocations in NiAl and FeAl are investigated with the modified P-N dislocation equation.The generalized stacking fault energy curve along〈111〉direction in {110} slip plane contains two modification factors that can assure the antiphase energy and the unstable stacking fault energy to change independently.The results show that the core width of superpartials decreases with the increasing unstable stacking fault energy,and increases with the increasing antiphase boundary energy.The calculated Peierls stress of〈111〉{110} edge superdislocations in NiAl and FeAl are 475 MPa and 3042 MPa,respectively.The values of Peierls stress in NiAl is in accordance in magnitude with the experimental and the molecular statics simulations results.     

超晶格的位错模型与系统的动力学稳定性

在经典力学框架内和Seeger方程基础上,讨论了超晶格界面附近的位错动力学行为,指出了由于系统的分叉或混沌将导致位错的运动与堆积,造成了超晶格的分层或断裂;同时,也指出了,将生长过程中的超晶格置于适当的声场中将应力减至最小,或者适当调节系统参数就可最大限度的保证系统的动力学稳定性.首先,引入阻尼项,把描述一般位错运动的...     

Peierls stress for （110） {001} mixed dislocation in SrTiO3 within framework of constrained path approximation

The core structure of （110）{001} mixed disloca- tion in perovskite SrTiO3 is investigated with the modified two-dimensional Peierls-Nabarro dislocation equation con- sidering the discreteness effect of crystals. The results show that the core structure of mixed dislocation is independent of the unstable energy in the （100） direction, but closely related to the unstable energy in the （110） direction which is the direction of total Burgers vector of mixed dislocation. Furthermore, the ratio of edge displacement to screw one nearly equals to the tangent of dislocation angle for differ- ent unstable energies in the （110） direction. Thus, the con- strained path approximation is effective for the （110）{001} mixed dislocation in SrTiO3 and two-dimensional equation can degenerate into one-dimensional equation that is only related to the dislocation angle. The Peierls stress for （110） {001 } dislocations can be expediently obtained with the one-dimensional equation and the predictive values for edge, mixed and screw dislocations are 0.17, 0.22 and 0.46 GPa, respectively.     

剪切力作用下螺位错的运动

利用分子动力学方法研究了金属钨中螺位错在剪切力作用下的运动特性.根据弹性理论在BCC晶体中形成位错线沿<111>的螺位错,在合适的边界条件下获得平衡态的位错结构.发现位错由{110}平面沿<112>方向三个呈对称的皱褶组成.对平衡态结构施加剪切力,发现剪力很小时,位错核心不动,核心形状有畸变;当剪力增大到一定程度时位错开始运动.位错运动后,剪切力较小时,核心呈“之”字形运动;在较大剪力下,位错开始阶段呈“之”字形运动,一段距离后主要沿[211]方向作直线运动.位错运动的速度随着剪切力的增加而增大.     

Interaction of an edge dislocation with a coated elliptic inclusion

This paper presents an analytical solution for plane elasticity problems of an elliptically cylindrical layered media subject to an arbitrary edge dislocation. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, the general expressions of the displacements and stresses, where an edge dislocation is located in matrix, coating layer and inclusion are obtained. The numerical results of image forces exerted on a generalized edge dislocation are carried out by using the generalized Peach–Koehler equation. As a numerical illustration, both the image forces and equilibrium positions are presented for different material combinations and relative thickness of a coating layer. The result shows that the thickness and the shear modulus of the coating layer have a strong influence on the stability of dislocation.     

对裂纹扩展规律Paris公式物理本质的探讨

首先讨论了著名力学家K.Krausz和A.S.Krausz关于Paris公式物理本质研究的成果，从材料的微观结构和裂纹尖端的应力场出发，应用位错动力学理论，热激活能理论和速率过程理论对疲劳裂纹扩展规律进行了微观到宏观的探讨。最终推导出疲劳裂纹扩展速率的一个解析表示式，该式严格地定了Paris公式的两个试验常数，赋予了Paris公式明确的物理意义，从而真实地揭示了Paris公式的物理本质，为这一经验的普遍规律奠定了理论基础。     

COUPLED VIBRATION OF STRUCTURAL THIN-WALLED CORES

This paper presents an analysis of the coupled vibration of asymmetric core structures in tall buildings. The governing equation of free vibration and its corresponding eigenvalue problem, which is a set of equations for laterally flexural vibrations in two different directions coupled by a warping-St. Venant torsional vibration, are derived. Based on the Calerkin method, a generalized approximate method is developed for the analysis of coupled vibration and thus proposed for determining the natural frequencies and mode shapes of the structure in triply-coupled vibration. The results of the proposed method for the example structure show good agreement with those of the FEM analysis. The proposed method has been shown to provide a simple and rapid, yet accurate, means for coupled vibration analysis of core structures.     

Screw and edge dislocations with time-dependent core width: From dynamical core equations to an equation of motion

Building on ideas introduced by Eshelby in 1953, and on recent dynamical extensions of the Peierls model for screw and edge dislocations, an approximate equation of motion (EoM) to govern non-uniform dislocation motion under time-varying stress is derived, allowing for time variations of the core width. Non-local in time, it accounts for radiative visco-inertial effects and non-radiative drag. It is completely determined by energy functions computed at constant velocity. Various limits are examined, including that of vanishing core width. Known results are retrieved as particular cases. Notably, the EoM reduces to Rosakis's Model I for steady motion [Rosakis, P., 2001. Supersonic dislocation kinetics from an augmented Peierls model. Phys. Rev. Lett. 86, 95–98]. The frequency-dependent effective response coefficients are obtained within the linearized theory, and the dynamical self-force is studied for abrupt or smooth velocity changes accompanied by core variations in the full theory. A quantitative distinction is made between low- and high-acceleration regimes, in relation to occurrence of time-logarithmic behavior.     

Singularity-free dislocation dynamics with strain gradient elasticity

The singular nature of the elastic fields produced by dislocations presents conceptual challenges and computational difficulties in the implementation of discrete dislocation-based models of plasticity. In the context of classical elasticity, attempts to regularize the elastic fields of discrete dislocations encounter intrinsic difficulties. On the other hand, in gradient elasticity, the issue of singularity can be removed at the outset and smooth elastic fields of dislocations are available. In this work we consider theoretical and numerical aspects of the non-singular theory of discrete dislocation loops in gradient elasticity of Helmholtz type, with interest in its applications to three dimensional dislocation dynamics (DD) simulations. The gradient solution is developed and compared to its singular and non-singular counterparts in classical elasticity using the unified framework of eigenstrain theory. The fundamental equations of curved dislocation theory are given as non-singular line integrals suitable for numerical implementation using fast one-dimensional quadrature. These include expressions for the interaction energy between two dislocation loops and the line integral form of the generalized solid angle associated with dislocations having a spread core. The single characteristic length scale of Helmholtz elasticity is determined from independent molecular statics (MS) calculations. The gradient solution is implemented numerically within our variational formulation of DD, with several examples illustrating the viability of the non-singular solution. The displacement field around a dislocation loop is shown to be smooth, and the loop self-energy non-divergent, as expected from atomic configurations of crystalline materials. The loop nucleation energy barrier and its dependence on the applied shear stress are computed and shown to be in good agreement with atomistic calculations. DD simulations of Lomer–Cottrell junctions in Al show that the strength of the junction and its configuration are easily obtained, without ad-hoc regularization of the singular fields. Numerical convergence studies related to the implementation of the non-singular theory in DD are presented.     

黏弹性体界面裂纹的冲击响应

研究两半无限大黏弹性体界面Griffith裂纹在反平面剪切突出载荷下,裂纹尖端动应力强度因子的时间响应,首先,运用积分变换方法将黏弹性混合黑社会问题化成变换域上的对偶积分方程,通过引入裂纹位错密度函数进一步化成Cauchy型奇异积分方程,运用分片连续函数法数值求解奇异积分方程,得到变换域内的动应力强度因子,再用Laplace积分变换数值反演方法,将变换域的解反演到时间域内,最终求得动应力强度因子的时间响应,并对黏弹性参数的影响进行分析。     

Piezoelectric screw dislocations interacting with a circular inclusion with imperfect interface

The electroelastic coupling interaction between multiple screw dislocations and a circular inclusion with an imperfect interface in a piezoelectric solid is investigated. The appointed screw dislocation may be located either outside or inside the inclusion and is subjected to a line charge and a line force at the core. The analytic solutions of electroelastic fields are obtained by means of the complex-variable method. With the aid of the generalized Peach–Koehler formula, the explicit expressions of image forces exerted on the piezoelectric screw dislocations are derived. The motion and the equilibrium position of the appointed screw dislocation near the circular interface are discussed for variable parameters (interface imperfection, material electroelastic mismatch, and dislocation position), and the influence of the nearby parallel screw dislocations is also considered. It is found that the piezoelectric screw dislocation is always attracted by the electromechanical imperfect interface. When the interface imperfection is strong, the impact of material electroelastic mismatch on the image force and the equilibrium position of the dislocation becomes weak. Additionally, the effect of the nearby dislocations on the mobility of the appointed dislocation is very important.     

Modeling of thermally activated dislocation glide and plastic flow through local obstacles

A unified phenomenological model is developed to study the dislocation glide through weak obstacles during the first stage of plastic deformation in metals. This model takes into account both the dynamical responses of dislocations during the flight process and thermal activations while dislocations are bound by obstacle arrays. The average thermal activation rate is estimated using an analytical model based on the generalized Friedel relations. Then, the average flight velocity after an activation event is obtained numerically by discrete dislocation dynamics (DD). To simulate the dynamical dislocation behavior, the inertia term is implemented into the equation of dislocation motion within the DD code. The results from the DD simulations, coupled with the analytical model, determine the total dislocation velocity as a function of the stress and temperatures. By choosing parameters typical of the face centered cubic metals, the model reproduces both obstacle control and drag control motion in low and high velocity regimes, respectively. As expected by other string models, dislocation overshoots of obstacles caused by the dislocation inertia at the collisions are enhanced as temperature goes down.     

Transient dislocation emission from a crack tip under dynamic mode III loading

Summary  Transient dislocation emission from a crack tip under dynamic mode III loading is analyzed. By taking into account the dynamic interaction between the crack and dislocation, the governing equation for the dislocation motion is derived under the quasi-steady assumption. The behavior of dislocation emission is explored in detail by solving this equation numerically. A critical initial speed can be determined, which must be exceeded by dislocations to escape from the crack tip. The dislocation emission process is found to be completed in such a short time period that the applied load may be approximately treated as constant during dislocation emission. Based on this fact, an asymptotic criterion for transient dislocation emission is developed, from which the critical initial speed can be evaluated. In the case that the dislocation is emitted from rest, we recover the quasi-static criterion of dislocation emission. Received 22 November 2000; accepted for publication 20 March 2001     

Simulation of edge dislocation emission from a crack under in-plane shear

Considered is the tandem emission of dislocations and dislocation dipoles from a crack under in-plane shear in one slip system as well as multiple slip systems. Effective stress intensity factors are determined by considering zones of local distortion similar to that in macro-plasticity. The dislocation free zone (DFZ) is also obtained which is analogous to the core region in fracture mechanics. Studied are effects of dislocation emission or development of plastic zone in front of the crack tip on the potential crack propagation based on the strain energy density factor criterion.     

Nonlocal stress field of interface dislocations

Summary The basic theory of nonlocal elasticity is stated with emphasis on the difference between the nonlocal theory and classical continuum mechanics. The concept of Nonlocal Interface Residual (NIR) is introduced in nonlocal theory. With the concept of NIR and the nonlocal constitutive equation, we calculate nonlocal stresses due to an edge dislocation on the interface of bi-materials. The nonlocal stress distribution along an interface is quite different from the classical one. Instead of the singularity in the dislocation core, nonlocal stress gives a finite value in the core. A maximum of the stress is also found near the dislocation core. Received 27 May 1997; accepted for publication 1 July 1997     

On the screw dislocation in a functionally graded piezoelectric plane and half-plane

In this paper closed-form expressions of the electroelastic field induced by a piezoelectric screw dislocation in a functionally graded piezoelectric plane and half-plane are derived. The material properties are assumed to vary exponentially along the x and y-directions. The solution for a screw dislocation in a functionally graded piezoelectric plane is obtained through introduction of two generalized stress functions. The solution for a screw dislocation in a functionally graded piezoelectric half-plane is derived by using the method of image. It is also found that the interaction between a piezoelectric screw dislocation and a circular insulating hole in the functionally graded piezoelectric material can be solved by using series expansion method.     

Theoretical analysis of generalized loadings and image forces in a planar magnetoelectroelastic layered half-plane

The problem of a planar transversely isotropic magnetoelectroelastic layered half-plane subjected to generalized line forces and edge dislocations is analyzed. The complete solutions consist only of the simplest solutions for an infinite magnetoelectroelastic medium with applied loadings. The physical meaning of this solution is the image method. It is shown that the explicit solutions include Green's function for originally applied singularities in an infinite medium and the other image singularities are induced to satisfy free surface and interface continuity conditions. The mathematical method used in this study provides an automatic determination for the locations and magnitudes of all image singularities. The locations and magnitudes of image singularities are dependent on the roots of the characteristic equation which is related to the material constants of the layered half-plane. With the aid of the generalized Peach-Koehler formula, the explicit expressions of image forces acting on dislocations are easily derived from the full-field solutions of the generalized stresses. Numerical results for the full-field distributions of stresses, electric fields, and magnetic fields in the layered half-plane medium are presented based on the analytical solutions. The image forces and equilibrium positions of one dislocation, two dislocations, and an array of dislocations are presented by numerical calculations and are discussed in detail.     

Analysis of dislocation nucleation from a crystal surface based on the Peierls-Nabarro dislocation model

Dislocation nucleation from a stressed crystal surface is analyzed based on the Peierls-Nabarro dislocation model. The variational boundary integral approach is used to obtain the profiles of the embryonic dislocations in various three-dimensional nucleation configurations. The stress-dependent activation energies required to activate dislocations from their stable to unstable saddle point configurations are determined. Compared to previous analyses of this type of problem based on continuum elastic dislocation theory, the present analysis eliminates the uncertain core cutoff parameter by allowing for the existence of an extended dislocation core as the embryonic dislocation evolves. Moreover, atomic information can be incorporated to reveal the dependence of the nucleation process on the profile of the atomic interlayer potential as compared to continuum elastic dislocation theory in which only elastic constants and Burgers vector are relevant. Finally, the presented methodology can also be readily used to study dislocation nucleation from the surface heterogeneities such as cracks, steps, and quantum structures of electronic devices.     

On a new extended finite element method for dislocations: Core enrichment and nonlinear formulation

A recently developed finite element method for the modeling of dislocations is improved by adding enrichments in the neighborhood of the dislocation core. In this method, the dislocation is modeled by a line or surface of discontinuity in two or three dimensions. The method is applicable to nonlinear and anisotropic materials, large deformations, and complicated geometries. Two separate enrichments are considered: a discontinuous jump enrichment and a singular enrichment based on the closed-form, infinite-domain solutions for the dislocation core. Several examples are presented for dislocations constrained in layered materials in 2D and 3D to illustrate the applicability of the method to interface problems.