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.     

Transmission of a screw dislocation across a coherent, non-slipping interface

Current research on nanocrystalline metals and nanoscale multilayer thin films suggests extraordinary plastic strength is due to confinement of slip to individual grains or layers. To assess the magnitude of confinement, a Peierls model of slip transmission of a screw dislocation across a coherent, non-slipping interface is presented. The results reflect that large interfacial barriers to transmission are generated by rapid fluctuations in dislocation line energy near the interface due to elastic modulus mismatch, stacking fault energy mismatch, and antiphase boundary energy for transmission into an ordered phase. Coherency stress is predicted to dramatically alter the dislocation core configuration and impart additional strength regardless of the sign. Contributions to strength are not additive due to nonlinear coupling via the dislocation core configuration. The predicted barrier strength for a coherent (0 0 1) Cu/Ni interface is comparable to atomistic (EAM) results but larger than estimates from hardness data.     

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.     

Configurational force on a lattice dislocation and the Peierls stress

The solution for a crystalline edge dislocation is presented within a framework of continuum linear elasticity, and is compared with the Peierls–Nabarro solution based on a semi-discrete method. The atomic disregistry and the shear stress across the glide plane are discussed. The Peach–Koehler configurational force is introduced as the gradient of the strain energy with respect to the dislocation position between its two consecutive equilibrium positions. The core radius is assumed to vary periodically between equilibrium positions of the dislocation. The critical force is expressed in terms of the core radii or the energies of the stable and unstable equilibrium configurations. This is used to estimate the Peierls stress for both wide and narrow dislocations.     

级联碰撞对层状珠光体力学行为的影响

铁素体合金钢是目前在核能工程界应用最为广泛的一种金属结构材料,以渗碳体和铁素体基体构成的层状珠光体是铁素体合金钢中常见的金相结构。深入理解辐照效应对层状珠光体力学性能的影响对高辐照条件下铁素体钢的材料设计与寿命评估有着重要的理论参考意义。基于以上考虑,本文采用分子动力学（MD）模拟,研究了连续低能铁原子级联碰撞对渗碳体/铁素体两相界面的破坏情况,探讨了经历不同程度级联碰撞的两相结构在单向拉伸以及压缩荷载下的初始屈服情况。通过对MD模拟结果的深入分析,得到了以下主要结论：a.辐照会破坏渗碳体/铁素体两相界面的失配位错结构,引起渗碳体的分解,并促进碳原子向铁素体的扩散;b.在单轴拉伸荷载作用下,级联碰撞会使初始屈服机制由{112}<111>位错滑移系的开动转变为间隙原子团簇附近位错环的形核与长大;c.在单轴压缩荷载作用下,级联碰撞会使初始塑性变形机制由{110}<111>滑移系的开动转变为{112}<111>滑移系的开动;d)无论在单轴拉伸还是压缩情况下,级联碰撞（及辐照效应）都会导致位错初始形核应力的提升。本文的研究结果为铁素体合金钢的辐照硬化和辐照脆化行为提供了新的微观解释,对于辐照条件下铁素体合金钢材料的优化设计有一定的参考意义。     

级联碰撞对层状珠光体力学行为的影响

铁素体合金钢是目前在核能工程界应用最为广泛的一种金属结构材料，以渗碳体和铁素体基体构成的层状珠光体是铁素体合金钢中常见的金相结构。深入理解辐照效应对层状珠光体力学性能的影响对高辐照条件下铁素体钢的材料设计与寿命评估有着重要的理论参考意义。基于以上考虑，本文采用分子动力学（MD）模拟，研究了连续低能铁原子级联碰撞对渗碳体/铁素体两相界面的破坏情况，探讨了经历不同程度级联碰撞的两相结构在单向拉伸以及压缩荷载下的初始屈服情况。通过对MD模拟结果的深入分析，得到了以下主要结论：a.辐照会破坏渗碳体/铁素体两相界面的失配位错结构，引起渗碳体的分解，并促进碳原子向铁素体的扩散；b.在单轴拉伸荷载作用下，级联碰撞会使初始屈服机制由{112}<111>位错滑移系的开动转变为间隙原子团簇附近位错环的形核与长大；c.在单轴压缩荷载作用下，级联碰撞会使初始塑性变形机制由{110}<111>滑移系的开动转变为{112}<111>滑移系的开动；d)无论在单轴拉伸还是压缩情况下，级联碰撞（及辐照效应）都会导致位错初始形核应力的提升。本文的研究结果为铁素体合金钢的辐照硬化和辐照脆化行为提供了新的微观解释，对于辐照条件下铁素体合金钢材料的优化设计有一定的参考意义。     

不同晶向金属纳米线拉伸力学性能分子动力学研究

在经典等温分子动力学框架下,采用位移加载方式,准静态条件下数值模拟常温条件下金属纳米线的单向拉伸,研究了面心立方晶格（FCC）单晶金属纳米线的弹塑性力学性能。研究发现 <100>,<110>,<111>三个不同晶向纳米线拉伸时呈现不同的拉伸变形力学性能。其中<111>晶向拉伸有最高的屈服强度,<110>晶向屈服屈服最小,特别的是<100>晶向拉伸时屈服应变最大。由于不同的晶向对应纳米线的不同表面,三个晶向的纳米线拉伸呈现不同的应力应变关系曲线,变形过程中的局部结构具有不同的演化方式。分析了纳米单晶铜线的三个晶向拉伸表现不同的等效弹性刚度和屈服强度,讨论了相关的局部位错结构演化过程和与位错发射分解剪应力相关的纳米线塑性变形机理。     

First-principles study of full a-dislocations in pure magnesium

Full a-dislocations on the (0001) basal plane, \((10\bar 10)\) prismatic plane, and \((10\bar 11)\) and \((10\bar 12)\) pyramidal planes in pure magnesium are investigated by using the Peierls-Nabarro model combined with generalized stacking fault (GSF) energies from first-principles calculations. The results show that the \(\left( {10\bar 11} \right)\left\langle {11\bar 20} \right\rangle\) and \(\left( {10\bar 12} \right)\left\langle {11\bar 20} \right\rangle\) slip modes have nearly the same GSF energy barriers, which are obviously larger than the GSF energy barriers of the \(\left( {0001} \right)\left\langle {11\bar 20} \right\rangle\) and \(\left( {10\bar 10} \right)\left\langle {11\bar 20} \right\rangle\) slip modes. For both edge and screw full dislocations, the maximum dislocation densities, Peierls energies, and stresses of dislocations on the \((10\bar 10)\) , (0001), \((10\bar 11)\) , and \((10\bar 12)\) planes eventually increase. Moreover, the Peierls energies and the stresses of screw full dislocations are always lower than those of edge full dislocations for all slip systems. Dislocations on the \((10\bar 11)\) and \((10\bar 12)\) pyramidal planes possess smaller core energies, while the \((10\bar 10)\) prismatic plane has the largest ones, implying that the formation of full dislocations on the \((10\bar 10)\) plane is more difficult.     

The Peierls stress in non-local elasticity

The effect of non-locality on the Peierls stress of a dislocation, predicted within the framework of the Peierls-Nabarro model, is investigated. Both the integral formulation of non-local elasticity and the gradient elasticity model are considered. A modification of the non-local kernel of the integral formulation is proposed and its effect on the dislocation core shape and size, and on the Peierls stress are discussed. The new kernel is longer ranged and physically meaningful, improving therefore upon the existing Gaussian-like non-locality kernels. As in the original Peierls-Nabarro model, lattice trapping cannot be captured in the purely continuum non-local formulation and therefore, a semi-discrete framework is used. The constitutive law of the elastic continuum and that of the glide plane are considered both local and non-local in separate models. The major effect is obtained upon rendering non-local the constitutive law of the continuum, while non-locality in the rebound force law of the glide plane has a marginal effect. The Peierls stress is seen to increase with increasing the intrinsic length scale of the non-local formulation, while the core size decreases accordingly. The solution becomes unstable at intrinsic length scales larger than a critical value. Modifications of the rebound force law entail significant changes in the core configuration and critical stress. The discussion provides insight into the issue of internal length scale selection in non-local elasticity models.     

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.     

An atomistically-informed dislocation dynamics model for the plastic anisotropy and tension-compression asymmetry of BCC metals

Atomistic simulations have shown that a screw dislocation in body-centered cubic (BCC) metals has a complex non-planar atomic core structure. The configuration of this core controls their motion and is affected not only by the usual resolved shear stress on the dislocation, but also by non-driving stress components. Consequences of the latter are referred to as non-Schmid effects. These atomic and micro-scale effects are the reason slip characteristics in deforming single and polycrystalline BCC metals are extremely sensitive to the direction and sense of the applied load. In this paper, we develop a three-dimensional discrete dislocation dynamics (DD) simulation model to understand the relationship between individual dislocation glide behavior and macro-scale plastic slip behavior in single crystal BCC Ta. For the first time, it is shown that non-Schmid effects on screw dislocations of both {110} and {112} slip systems must be implemented into the DD models in order to predict the strong plastic anisotropy and tension-compression asymmetry experimentally observed in the stress-strain curves of single crystal Ta. Incorporation of fundamental atomistic information is critical for developing a physics-based, predictive meso-scale DD simulation tool that can connect length/time scales and investigate the underlying mechanisms governing the deformation of BCC metals.     

EXTENDED CORE STRUCTURE OF DISSOCIATED EDGE DISLOCATIONS IN FCC CRYSTALS WITH CONSIDERATION OF DISCRETENESS

The extended core structure of the dissociated edge dislocation in Al, Au, Ag, Cu and Ni is determined within lattice theory of dislocation. The 2D dislocation equation governing the displacements is coupled by the restoring forces that are determined by the parameterization of the generalized stacking fault energies. The Ritz variational method is presented to solve the dislocation equation and the trial solution is constituted by two arctan-type functions with two undetermined parameters. The core widths of partial dislocations are wider than that obtained in generalized Peierls-Nabarro model due to the consideration of discreteness of crystal.     

Life study of nickel-based single crystal turbine blades: viscoplastic crystallographic constitutive behavior

Based on dislocation theory, an anisotropic crystallographic constitutive relation has been developed for nickel-based single crystal superalloys. Octahedral {111}110, {111}112 and cubic {100}110 systems are considered. Drag stress and back stress state variables are used to model the local inelastic flow. Results are compared with test data for nickel-based crystal superalloy DD3 at 700°C and 950°C for evaluating the model parameters at these temperatures. The constitutive relation is applied to a finite element program for estimating the strength and life of a nickel-based single crystal turbine blade.     

A dislocation density based crystal plasticity finite element model: Application to a two-phase polycrystalline HCP/BCC composites

We present a multiscale model for anisotropic, elasto-plastic, rate- and temperature-sensitive deformation of polycrystalline aggregates to large plastic strains. The model accounts for a dislocation-based hardening law for multiple slip modes and links a single-crystal to a polycrystalline response using a crystal plasticity finite element based homogenization. It is capable of predicting local stress and strain fields based on evolving microstructure including the explicit evolution of dislocation density and crystallographic grain reorientation. We apply the model to simulate monotonic mechanical response of a hexagonal close-packed metal, zirconium (Zr), and a body-centered cubic metal, niobium (Nb), and study the texture evolution and deformation mechanisms in a two-phase Zr/Nb layered composite under severe plastic deformation. The model predicts well the texture in both co-deforming phases to very large plastic strains. In addition, it offers insights into the active slip systems underlying texture evolution, indicating that the observed textures develop by a combination of prismatic, pyramidal, and anomalous basal slip in Zr and primarily {110}〈111〉 slip and secondly {112}〈111〉 slip in Nb.     

An analysis of key characteristics of the Frank-Read source process in FCC metals

A well-known intragranular dislocation source, the Frank-Read (FR) source plays an important role in size-dependent dislocation multiplication in crystalline materials. Despite a number of studies in this topic, a systematic investigation of multiple aspects of the FR source in different materials is lacking. In this paper, we employ large scale quasistatic concurrent atomistic-continuum (CAC) simulations to model an edge dislocation bowing out from an FR source in Cu, Ni, and Al. First, a number of quantities that are important for the FR source process are quantified in the coarse-grained domain. Then, two key characteristics of the FR source, including the critical shear stress and critical dislocation configuration, are investigated. In all crystalline materials, the critical stresses and the aspect ratio of the dislocation half-loop height to the FR source length scale well with respect to the FR source length. In Al, the critical stress calculated by CAC simulations for a given FR source length agrees reasonably well with a continuum model that explicitly includes the dislocation core energy. Nevertheless, the predictions of the isotropic elastic theory do not accurately capture the FR source responses in Cu and Ni, which have a relatively large stacking fault width and elastic anisotropy. Our results highlight the significance of directly simulating the FR source activities using fully 3D models and shed light on developing more accurate continuum models.     

Nucleation of partial dislocations at a crack and its implication on deformation mechanisms of nanostructured metals

Nucleation of partial dislocations at a crack is analyzed based a multiscale model that incorporates atomic information into continuum-mechanics approach. The crack and the slip plane as the extension of the crack are modeled as a surface of displacement discontinuities embedded in an elastic medium. The atomic potential between the adjacent atomic layers along the slip plane is assumed to be the generalized stacking fault energy, which is obtained based on atomic calculations. The relative displacements along the slip plane, corresponding to the configurations of partial dislocations and stacking faults, are solved through the variational boundary integral method. The energetics of partial dislocation nucleation at the crack in FCC metals Al and Cu are comparatively studied for their distinctive difference in the intrinsic stacking fault energy. Compared with nucleation of perfect dislocations in previous studies, several new features have emerged. Among them, the critical stress and activation energy for nucleation of partial dislocations are markedly lowered. Depending on the value of stacking fault energy and crack configuration, the saddle-point configurations of partial dislocations can be vastly different in terms of the nucleation sequence and the size of the stacking fault. These findings have significant implication for identifying the fundamental dislocation and grain-boundary-mediated deformation mechanisms, which may account for the limiting strength and the high strain rate sensitivity of nanostructured metals.     

Analysis of thermally activated formation and breakdown of Kear-Wilsdorf barriers in Ni<Subscript>3</Subscript>Ge single crystals of various orientations

The orientation dependence of the yield stress in Ni₃Ge single crystals has been examined both theoretically and experimentally. The positive temperature dependence of the yield stress in the low temperature region is attributed to formation of Kear-Wilsdorf barriers. The forces driving the formation and breakdown of barriers are calculated within the framework of the Hirsch scheme. A distinctive feature of the model proposed is that the barrier is considered on the screw component of the a/2[ 01](111) superdislocation in the primary octahedral plane. The major role in barrier formation belongs to anisotropy of elastic moduli, energy of antiphase boundaries in the octahedral plane, shear stresses in the cubic and octahedral planes, and friction-induced stress in the cubic plane. A comparison of predicted values of the driving force of barrier formation and breakdown with experimental values reveals their good agreement. An analysis of the orientation dependence of the driving force of barrier formation in the temperature range T = 77–293 K shows that the dependence (T) has an extremum for crystals deformed along the [ 39] crystallographic direction, which is confirmed experimentally.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 116–125, January–February, 2005.     

单晶铜中的类层错四面体稳定性

层错四面体作为受核辐照作用金属材料中一类常见的三维缺陷，会极大的改变材料塑性变形行为。本文借助分子静力学和分子动力学方法，针对不同构型、不同尺寸的类层错四面体，考察了不同形状空位团簇演化为类层错四面体的位错反应机理和形成能变化趋势，研究了类层错四面体附近空位形成能分布特征和最小空位形成能随类层错四面体尺寸增大的变化规律，分析了含不同构型、不同尺寸的类层错四面体铜单晶体的微观变形机理和单晶体屈服应力随类层错四面体尺寸增大的变化规律。研究发现：类层错四面体通过Silcox-Hirsch机制形成，且经历了空位团簇坍塌、Frank位错环分解和Shockley位错交汇形成层错四面体棱边三个过程；类层错四面体附近最小空位形成能随着类层错四面体尺寸变化而变化，且变化趋势与类层错四面体构型在稳态、亚稳态和非稳态之间过渡相关，稳态无尖端类层错四面体的最小空位形成能变化趋势表现出明显的尺寸效应；剪切会导致含类层错四面体铜单晶体产生两类层错四面体位错开动模式，即：斜面Shockley偏位错滑移和层错四面体底面压杆位错分解，且含类层错四面体的单晶体屈服应力基本上随着类层错四面体尺寸增大而逐渐减小。     

单晶铜中的类层错四面体稳定性

层错四面体作为受核辐照作用金属材料中一类常见的三维缺陷,会极大的改变材料塑性变形行为。本文借助分子静力学和分子动力学方法,针对不同构型、不同尺寸的类层错四面体,考察了不同形状空位团簇演化为类层错四面体的位错反应机理和形成能变化趋势,研究了类层错四面体附近空位形成能分布特征和最小空位形成能随类层错四面体尺寸增大的变化规律,分析了含不同构型、不同尺寸的类层错四面体铜单晶体的微观变形机理和单晶体屈服应力随类层错四面体尺寸增大的变化规律。研究发现：类层错四面体通过Silcox-Hirsch机制形成,且经历了空位团簇坍塌、Frank位错环分解和Shockley位错交汇形成层错四面体棱边三个过程;类层错四面体附近最小空位形成能随着类层错四面体尺寸变化而变化,且变化趋势与类层错四面体构型在稳态、亚稳态和非稳态之间过渡相关,稳态无尖端类层错四面体的最小空位形成能变化趋势表现出明显的尺寸效应;剪切会导致含类层错四面体铜单晶体产生两类层错四面体位错开动模式,即：斜面Shockley偏位错滑移和层错四面体底面压杆位错分解,且含类层错四面体的单晶体屈服应力基本上随着类层错四面体尺寸增大而逐渐减小。     

快凝粉末冶金铝合金的微观结构

利用Ｘ射线衍射,透射电镜及高分辨电镜对快凝粉末冶金Ａ１－８．５Ｆｅ－１．３Ｖ－１．７Ｓｉ铝合金的微观结构进行了初步观察。结果表明,合金中仅含有一种硅化物强化相,即Ａｌ＿１３（Ｆｅ,Ｖ）＿３Ｓｉ,点阵常数为１．２５６ｎｍ。发现有些分布于晶内的硅化物相与合金基体具有确定的取向关系,即｛１１０｝Ａ１基体／｛１１０｝硅化物＜１１１＞Ａｌ基体／（１１０）硅化物但是位于晶界上的硅化物与基体没有确定的取向关系,而常常存在厚度约为５０Ａ的非晶层。