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.     

Tensile response of passivated films with climb-assisted dislocation glide

The tensile response of single crystal films passivated on two sides is analysed using climb enabled discrete dislocation plasticity. Plastic deformation is modelled through the motion of edge dislocations in an elastic solid with a lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation incorporated through a set of constitutive rules. The dislocation motion in the films is by glide-only or by climb-assisted glide whereas in the surface passivation layers dislocation motion occurs by glide-only and penalized by a friction stress. For realistic values of the friction stress, the size dependence of the flow strength of the oxidised films was mainly a geometrical effect resulting from the fact that the ratio of the oxide layer thickness to film thickness increases with decreasing film thickness. However, if the passivation layer was modelled as impenetrable, i.e. an infinite friction stress, the plastic hardening rate of the films increases with decreasing film thickness even for geometrically self-similar specimens. This size dependence is an intrinsic material size effect that occurs because the dislocation pile-up lengths become on the order of the film thickness. Counter-intuitively, the films have a higher flow strength when dislocation motion is driven by climb-assisted glide compared to the case when dislocation motion is glide-only. This occurs because dislocation climb breaks up the dislocation pile-ups that aid dislocations to penetrate the passivation layers. The results also show that the Bauschinger effect in passivated thin films is stronger when dislocation motion is climb-assisted compared to films wherein dislocation motion is by glide-only.     

THERMODYNAMIC VARIATIONAL APPROACH FOR CLIMB OF AN EDGE DISLOCATION

A general thermodynamic variational approach is applied to study the force on an edge dislocation, which drives the dislocation to climb. Our attention is focused on the physical mechanism responsible for dislocation climb. A dislocation in a material element climbs as a result of vacancies diffusing into or out from the dislocation core, with the dislocation acting as a source or a sink for vacancy diffusion in the material element. The basic governing equations for dislocation climb and the climb forces on the dislocation are obtained naturally as a result of the present thermodynamic variational approach.     

A model for the deformations and thermodynamics of liquids involving a dislocation kinetics

A model for the deformation and thermodynamics of liquids is developed that depends on dislocation kinetics. The approach uses concepts from statistical mechanics to model a stochastic evolution equation for a scalar dislocation density function. The dislocation density is used in an idealized model for the discrete discontinuous deformation due to dislocation motion and dislocation creation kinetics. The total deformation functional for a liquid is modelled as a continuum deformation of an idealized lattice structure plus the discontinuous deformation due to dislocation kinetics. This results in a thermodynamic model that has an elastic response from the continuum lattice structure and a fluid response from the dislocation kinetics.In the thermodynamics, a generalized internal energy functional is assumed to exist and to have a dependence on the functions of entropy, continuum lattice strain, scalar dislocation density, velocity, and mass density. The continuum lattice strain is termed the recoverable strain and its conjugate variable is the thermodynamic stress. The conjugate variable to the scalar dislocation density is the thermodynamic chemical potential for a dislocation configuration, somewhat analogous to Gibbs' treatment of chemical potential for various mass species.This model implies that a liquid and a crystalline solid have analogous deformation and thermodynamic responses. Their differences appear in the dislocation densities and in the dislocation chemical potentials. To illustrate the deformation response analogy, some solutions are developed for simple laminar shear flows. Also, using some concepts primarily from Kuhlmann-Wilsdorf's melting model, a definition for a specific dislocation creation heat equivalent is given. This thermodynamic formalism suggests that the melting process can be modelled as the consequence of a continuous change in the dislocation density function.Work performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under contract No. W-7405-ENG-48.     

INTERACTION OF A DISLOCATION DIPOLE WITH A MODE III INTERFACE CRACK

Interaction between a screw dislocation dipole and a mode III interface crack is investigated. By using the complex variable method, the closed form solutions for complex potentials are obtained when a screw dislocation dipole lies inside a medium. The stress fields and the stress intensity factors at the tip of the interface crack produced by the screw dislocation dipole are given. The influence of the orientation, the dipole arm and the location of the screw dislocation dipole as well as the material mismatch on the stress intensity factors is discussed. The image force and the image torque acting on the screw dislocation dipole center are also calculated. The mechanical equilibrium position of the screw dislocation dipole is examined for various material property combinations and crack geometries. The results indicate that the shielding or anti-shielding effect on the stress intensity factor increases abruptly when the dislocation dipole approaches the tip of the crack. Additionally, the disturbation of the interface crack on the motion of the dislocation dipole is also significant.     

穿透夹杂界面的半无限楔形裂纹尖端螺型位错的发射研究

摘要：研究了穿透圆形夹杂界面的半无限楔形裂纹与裂纹尖端螺型位错的干涉问题。应用复变函数解析延拓技术与奇性主部分析方法,得到了位错位于半圆形夹杂内部时,半无限基体和半圆形夹杂内复势函数的解析解。然后利用保角映射技术得到了穿透圆形夹杂界面的半无限楔形裂纹尖端螺型位错产生的应力场以及作用在位错上的位错力的解析表达式。主要讨论了螺型位错对裂纹的屏蔽效应以及从楔形裂纹尖端发射位错的临界载荷条件。研究结果表明正的螺型位错可以削弱楔形裂纹尖端的应力强度因子,屏蔽裂纹的扩展,屏蔽效应随位错方位角的增大而减小。位错发射所需的无穷远临界应力随发射角的增加而增大,最可能的位错发射角度为零度,直线裂纹尖端位错的发射比楔形裂纹尖端位错的发射更容易,硬基体抑制位错的发射。     

Interface effects on elastic behavior of an edge dislocation in a core–shell nanowire embedded to an infinite matrix

The elastic behavior of an edge dislocation located inside the core of a core–shell nanowire which is embedded in an infinite matrix is studied within the surface/interface elasticity theory. The corresponding boundary value problem is solved exactly by using complex potential functions. An important parameter so-called interface characteristic parameter which has the dimension of length and is a combination of the interface moduli enters the formulations. The stress field of the dislocation, image force acting on the dislocation, and the dislocation strain energy is calculated by considering the interface effect. The introduced characteristic parameter allows the examination of the core–shell size on the image forces acting on the dislocation. The repelling and attracting effects of the interface parameter on the image force are discussed. The equilibrium position of the dislocation is also studied. The dislocation strain energy in the interface elasticity framework is only slightly different from that of traditional elasticity when the dislocation is placed in the central region of the core and reaches its maximum value when it is located near the core–shell interface.     

Multiscale dislocation dynamics analyses of laser shock peening in silicon single crystals

Although laser shock peening (LSP) has been applied in metals for property enhancement for a long time, its application on brittle materials has not been investigated so far. The present work is the first computational attempt to show that strong dislocation activity can be generated in silicon crystal by a modified LSP process. Multiscale dislocation dynamics plasticity (MDDP) simulations are conducted to predict the dislocation structure and stress/strain distribution in silicon crystal during LSP. In the modified LSP process, dislocation mobility of silicon and shock pressure is sufficiently high to generate and transport dislocation. The relationships between dislocation activities, the laser processing conditions and ablative coating material are systematically investigated. It is found that dislocation density, dislocation multiplication rate, and dislocation microstructure strongly depend on LSP processing conditions. This LSP process can also be applied in other brittle materials.     

INTERACTION OF A DISLOCATION DIPOLE WITH A MODE Ⅲ INTERFACE CRACK

Interaction between a screw dislocation dipole and a mode Ⅲ interface crack is investigated. By using the complex variable method, the closed form solutions for complex potentials are obtained when a screw dislocation dipole lies inside a medium. The stress fields and the stress intensity factors at the tip of the interface crack produced by the screw dislocation dipole are given. The influence of the orientation, the dipole arm and the location of the screw dislocation dipole as well as the material mismatch on the stress intensity factors is discussed. zThe image force and the image torque acting on the screw dislocation dipole center are also calculated. The mechanical equilibrium position of the screw dislocation dipole is examined for various material property combinations and crack geometries. The results indicate that the shielding or anti-shielding effect on the stress intensity factor increases abruptly when the dislocation dipole approaches the tip of the crack. Additionally, the disturbation of the interface crack on the motion of the dislocation dipole is also significant.     

纵向剪切下含共焦刚性核弹性椭圆夹杂中的螺型位错干涉

摘 要 研究了无穷远纵向剪切下无限大基体中含共焦刚性核弹性椭圆夹杂内任意位置螺型位错的干涉问题。运用复变函数保角映射、解析延拓等方法,获得了基体与夹杂区域的应力场的级数形式精确解,并得出了位错像力的解析表达式,导出了纵向剪切下两椭圆界面最大应力及其比值公式。分析结果表明：夹杂内部的刚性核对位错与夹杂的干涉产生明显的扰动效应,排斥硬夹杂内位错,并使之不断趋近弹性夹杂界面。对于软夹杂,夹杂中的位错存在稳定的平衡位置,当位错位于刚性核和平衡位置之间时,位错会趋于弹性夹杂界面;当位错位于平衡位置和弹性夹杂界面之间时,位错会离开界面。结果还显示,夹杂的长轴和短轴之比对位错与夹杂的干涉也有着不可忽视的影响,尤其当位错在刚性核附近时,随着夹杂的长、短轴比值的减小,核对位错的排斥力也明显减弱。本文解答包含了多个以往文献成果。     

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     

位错偶极子和Ⅲ型界面裂纹的干涉效应

研究了多晶体材料中螺型位错偶极子和界面裂纹的弹性干涉作用.利用复变函数方法,得到了该问题复势函数的封闭形式解答.求出了由位错偶极子诱导的应力场和裂纹尖端应力强度应子,分析了偶极子的方向,偶臂和位置以及材料失配对应力强度因子的影响.推导了作用在螺型位错偶极子中心的像力和力偶矩,并讨论了界面裂纹几何条件和不同材料特征组合对位错偶极子平衡位置的影响规律.结果表明,裂纹尖端的螺型位错偶极子对应力强度因子会产生强烈的屏蔽或反屏蔽效应.同时,界面裂纹对螺型位错偶极子在材料中运动有很强的扰动作用.     

Quantifying dislocation microstructure evolution and cyclic hardening in fatigued face-centered cubic single crystals

Discrete dislocation dynamics simulations were performed to investigate the dislocation microstructure evolution and cyclic hardening during the early stages of fatigue loading in nickel single crystals. The effects of the crystal size and initial dislocation densities on both the mechanical response and the evolution of dislocation microstructure were quantified. Crystals having an initial dislocation density of 10¹²  m⁻² and diameter less than $2.0\mathrm{\mu }\mathrm{m}$ do not show any dislocation density multiplication or cyclic hardening. In contrast, crystals having the same initial dislocation density and diameters larger than $2.0\mathrm{\mu }\mathrm{m}$ show a significant dislocation density accumulation in the form of dislocation cell-like structures, even after only a few number of loading cycles. This dislocation density accumulation was also accompanied by considerable cyclic hardening. The dislocation cell size and its wall thickness increase with increasing crystal size. With increasing dislocation density the critical crystal size, at which dislocation cell-structures form, decreases. The information theoretic entropy is utilized as a metric to quantify the extent of dislocation patterning and the formation and evolution of dislocation cell structures over time. Cross-slip was found to play a dominant role in the dislocation cell-structure formation. Further insights on the mechanisms contributing to the observed behavior are presented and discussed.     

The interaction between a screw dislocation and a circular inhomogeneity in gradient elasticity

The interaction between a screw dislocation and a circular inhomogeneity in gradient elasticity is investigated. The screw dislocation is located inside either the inhomogeneity or the matrix. By using the Fourier transform method, closed analytical solutions are obtained when the inhomogeneity and the matrix have the same gradient coefficient. The explicit expressions of image forces exerted on screw dislocations are derived. The motion of the appointed screw dislocation and its equilibrium positions are discussed. The results show that the classical singularity is eliminated. Especially, for the case of a tiny inhomogeneity, the relation of dislocations and inhomogeneities become quite different. The screw dislocation may be attracted by the stiff inhomogeneity and repelled by the soft inhomogeneity when it tends to the interface. So there is an unstable equilibrium position when a dislocation tends to a tiny stiff inhomogeneity and there is a stable equilibrium position when a dislocation tends to a tiny soft inhomogeneity.     

Dislocation equilibrium conditions revisited

If there is an equilibrium arrangement of a given collection of dislocations, each having a fixed size and shape, in an externally loaded or unloaded elastic body, the corresponding potential energy will be stationary with respect to infinitesimal perturbations of the dislocation positions. This leads to the dislocation equilibrium conditions: the Peach–Koehler forces along the dislocation line of each dislocation due to externally applied stress and the interaction of the dislocation with other dislocations and its own image field is a set of self-equilibrated forces. The earlier proof of this result presented in the literature was based on an incomplete expression for the elastic strain energy. This is modified here by using the elastic strain energy expression that accounts for all dislocation core energy.     

A New dynamic model for study of dislocation pattern formation

Based on the principle given in nonlinear diffusion-reaction dynamics, a new dynamic model for dislocation patterning is proposed by introducing a relaxation time to the relation between dislocation density and dislocation flux. The so-called chemical potential like quantities, which appear in the model can be derived from variation principle for free energy functional of dislocated media, where the free energy density function is expessed in terms of not only the dislocation density itself but also their spatial gradients. The linear stability analysis on the governing equations of a simple dislocation density shows that there exists an intrinsic wave number leading to bifurcation of space structure of dislocation density. At the same time, the numerical results also demonstrate the coexistence and transition between different dislocation patterns. The project supported by the National Natural Science Foundation of China, Grant No.19392300     

An analysis of dislocation nucleation near a free surface

Molecular dynamics analyses of defect-free aluminum single crystals subject to bending are carried out to investigate dislocation nucleation from free surfaces. A principal aim of the analyses is to provide background for the development of dislocation nucleation criteria for use in discrete dislocation plasticity calculations. The molecular dynamics simulations use an embedded atom potential for aluminum. Bending is imposed on a strip by specifying a linear variation of displacement rate on opposite edges. The overall bending response is determined and the character of the dislocations nucleated is identified. It is found that the stress magnitudes at the instant of dislocation nucleation are nearly an order of magnitude smaller than for homogeneous bulk dislocation nucleation. The characterization of dislocation nucleation in terms of various phenomenological nucleation criteria is explored, in particular: (i) a critical resolved shear stress; (ii) the onset of an elastic instability; and (iii) a critical stress-gradient criterion. It is found that dislocation nucleation is not well-represented by a critical value of the resolved shear stress but is reasonably well-represented by the critical stress-gradient criterion.     

Surface versus bulk nucleation of dislocations during contact

The indentation of single crystals by a periodic array of flat rigid contacts is analyzed using discrete dislocation plasticity. Plane strain analyses are carried out with the dislocations all of edge character and modeled as line singularities in a linear elastic solid. The limiting cases of frictionless and perfectly sticking contacts are considered. The effects of contact size, dislocation source density, and dislocation obstacle density and strength on the evolution of the mean indentation pressure are explored, but the main focus is on contrasting the response of crystals having dislocation sources on the surface with that of crystals having dislocation sources in the bulk. When there are only bulk sources, the mean contact pressure for sufficiently large contacts is independent of the friction condition, whereas for sufficiently small contact sizes, there is a significant dependence on the friction condition. When there are only surface dislocation sources the mean contact pressure increases much more rapidly with indentation depth than when bulk sources are present and the mean contact pressure is very sensitive to the strength of the obstacles to dislocation glide. Also, on unloading a layer of tensile residual stress develops when surface dislocation sources dominate.     

EFFECTS OF DISLOCATION CONFIGURATION, CRACK BLUNTING AND FREE SURFACES ON THE TRIGGERING LOAD OF DISLOCATION SOURCES

The effects of dislocation configuration,crack blunting and free surfaces on the triggering load of dislocation sources in the vicinity of a crack or a wedge tip subjected to a tensile load in the far field are investigated.An appropriate triggering criterion for dislocation sources is proposed by considering the configurational forces acting on each dislocation.The triggering behaviors of dislocation sources near the tips of a crack and a wedge are compared.It is also found that the blunting of crack tip and the presence of free surfaces near the crack or the wedge have considerable influences on the triggering load of dislocation sources.This study might be of significance to gaining a deeper understanding of the brittle-to-ductile transition of materials.     

Continuum dynamics of the formation,migration and dissociation of self-locked dislocation structures on parallel slip planes

In continuum models of dislocations, proper formulations of short-range elastic interactions of dislocations are crucial for capturing various types of dislocation patterns formed in crystalline materials. In this article, the continuum dynamics of straight dislocations distributed on two parallel slip planes is modelled through upscaling the underlying discrete dislocation dynamics. Two continuum velocity field quantities are introduced to facilitate the discrete-to-continuum transition. The first one is the local migration velocity of dislocation ensembles which is found fully independent of the short-range dislocation correlations. The second one is the decoupling velocity of dislocation pairs controlled by a threshold stress value, which is proposed to be the effective flow stress for single slip systems. Compared to the almost ubiquitously adopted Taylor relationship, the derived flow stress formula exhibits two features that are more consistent with the underlying discrete dislocation dynamics: (i) the flow stress increases with the in-plane component of the dislocation density only up to a certain value, hence the derived formula admits a minimum inter-dislocation distance within slip planes; (ii) the flow stress smoothly transits to zero when all dislocations become geometrically necessary dislocations. A regime under which inhomogeneities in dislocation density grow is identified, and is further validated through comparison with discrete dislocation dynamical simulation results. Based on the findings in this article and in our previous works, a general strategy for incorporating short-range dislocation correlations into continuum models of dislocations is proposed.