Analysis of dislocation wall formation in a disclinated nanograin

Disclinations are common defects in nanocrystalline materials processed via the severe plastic deformation technique. A disclination, depending on its strength, may remain stable or partially relax into other structures such as cracks and dislocation walls. This paper develops closed-form analytical expressions for the energy of a nanograin containing a negative wedge disclination and a wall of periodic edge dislocations. Using these expressions, it is found that (1) a critical disclination strength is required for emitting dislocations and that this critical value demonstrates a strong power law dependence on the nanograin size, (2) there exists a favorable dislocation spacing, which decreases with increase in the disclination strength, in the dislocation wall formed by the emitted dislocations, and (3) the misorientation of the dislocation wall lies between 5° and 12° for disclination strength in the range of 15–35°.     

Dislocations and disclinations: continuously distributed defects in elasto-plastic crystalline materials

The paper deals with elasto-plastic models for crystalline materials with defects, dislocations coupled with disclinations. The behaviour of the material is described with respect to an anholonomic configuration, endowed with a non-Riemannian geometric structure. The geometry of the material structure is generated by the plastic distortion, which is an incompatible second-order tensor, and by the so-called plastic connection which is metric compatible, with respect to the metric tensor associated with the plastic distortion. The free energy function is dependent on the second-order elastic deformation and on the state of defects. The tensorial measure of the defects is considered to be the Cartan torsion of the plastic connection and the disclination tensor. When we restrict to small elastic and plastic distortions, the measures of the incompatibility as well as the dislocation densities reduced to the classical ones in the linear elasticity. The constitutive equations for macroforces and the evolution equations for the plastic distortion and disclination tensor are provided to be compatible with the free energy imbalance principle.     

An elasto-plastic theory of dislocation and disclination fields

A linear theory of the elasto-plasticity of crystalline solids based on a continuous representation of crystal defects – dislocations and disclinations – is presented. The model accounts for the translational and rotational aspects of lattice incompatibility, respectively associated with the presence of dislocations and disclinations. The defects content relates to the incompatible plastic strain and curvature tensors. The stress state is described by using the conjugate variables to strain and curvature, i.e., the stress and couple-stress tensors. Defect motion is described by two transport equations. A dynamic interplay between dislocations and disclinations results from a disclination-induced source term in the transport of dislocations. Thermodynamic guidance provides the driving forces conjugate to dislocation and disclination velocity in a continuous context, as well as admissible constitutive relations for the latter. When dislocation and disclination velocity vanish, the model reduces to deWit’s elasto-static theory of crystal defects. It also reduces to Acharya’s linear elasto-plastic theory for dislocation fields when the disclination density is ignored. The theory is intended for use in instances where rotational defects matter, such as grain boundaries. To illustrate its applicability, a finite high-angle tilt boundary is modeled using a disclination dipole and its behavior under tensile loading normal to the boundary is shown.     

沉淀对Al-Cu-Mg合金中锯齿形屈服现象影响及其微观实验研究

经固溶处理的Al-Cu-Mg合金在常应变率拉伸实验中具有显著的锯齿形屈服现象,且屈服行为随固溶处理温度的改变而呈现不同的特征。塑性变形特性与合金材料的微细观结构,尤其是位错运动的演化密切相关。本文运用透射电子显微镜,研究在不同温度下固溶处理的Al-Cu-Mg合金的微观结构,尤其是析出颗粒的大小和含量。并结合宏观的拉伸实验结果,分析Al-Cu-Mg合金动态应变时效的机制。     

Dislocation dynamics and acoustic emission during plastic deformation of crystals

A soliton approach to acoustic emission during plastic deformation of crystals is presented. The approach is based on a microscopic Frenkel-Kontorova model where the rigidity of the substrate is removed in order to establish the interaction mechanism between a dislocation and both longitudinal and transverse acoustic waves. It is shown that this interaction is described by a sine-Gordon-d' Alembert system. Within the framework of this system, two basic mechanisms of acoustic emission are investigated both analytically and numerically. One mechanism is related to nonstationary dislocation motion and the other one to the annihilation of dislocation kink-antikink pairs during Frank-Read source operation. In both cases, computer simulations are obtained which illustrate graphically the analytical considerations and model the acoustic radiation. The obtained results are in agreement with existing experimental data and may provide a better physical insight to the acoustic emission mechanisms during plastic deformation of crystals.     

沉淀对A1-Cu—Mg合金中锯齿形屈服现象影响及其微观实验研究

经固溶处理的A1-Cu—Mg合金在常应变率拉伸实验中具有显著的锯齿形屈服现象，且屈服行为随固溶处理温度的改变而呈现不同的特征。塑性变形特性与合金材料的微细观结构，尤其是位错运动的演化密切相关。本文运用透射电子显微镜，研究在不同温度下固溶处理的Al—Cu—Mg合金的微观结构，尤其是析出颗粒的大小和含量。并结合宏观的拉伸实验结果，分析Al—Cu—Mg合金动态应变时效的机制。     

Special rotational deformation effect on the emission of dislocations from a crack tip in deformed nanocrystalline solids

The interaction between the special rotational deformation and the crack in deformed nanocrystalline ceramics and metals is investigated by the complex variable method. We have theoretically described the effects of the disclination quadrupole produced by the special rotational deformation on the emission of lattice dislocations from the crack tip. The complex form expressions of the stress field and the force field are divided. The critical stress intensity factors for the first dislocation emission are calculated. The influence of the disclination strength, the grain size (the quadrupole arms), the location of the disclinations and the angle between the crack plane and one of the quadrupole arms, as well as the crack length on the critical stress intensity factors is discussed in detail. And the results show that, the special rotational deformation has great influence on the dislocation emission from the crack tip.     

Continuum theory of dislocations and disclinations in nonlinearly elastic micropolar media

A nonlinear theory of continuously distributed dislocation and disclination type defects in elastic media with intrinsic rotational degrees of freedom and couple stresses is proposed. The mediumstrains are assumed to be finite. The solving equations of the continuum theory of defects are obtained by passing to the limit from a discrete set of isolated dislocations and disclinations to their continuous distribution. The notions of dislocation and disclination densities in a micropolar body under large deformations are introduced. Incompatibility equations are obtained and a boundaryvalue problem of equilibriumis posed for an elastic micropolar body with a given density of distributed defects. A nonlinear problem of determining the intrinsic stresses in a hollow circular cylinder due to a given distribution of disclinations is solved.     

Representations of elastic fields of circular dislocation and disclination loops in terms of spherical harmonics and their application to various problems of the theory of defects

Elastic fields of circular dislocation and disclination loops are represented in explicit form in terms of spherical harmonics, i.e. via series with Legendre and associated Legendre polynomials. Representations are obtained by expanding Lipschitz-Hankel integrals with two Bessel functions into Legendre series. Found representations are then applied to the solutions of elasticity boundary-value problems of the theory of defects and to the calculation of elastic fields of segmented spherical inclusions. In the framework of virtual circular dislocation–disclination loops technique, a general scheme to solving axisymmetric elasticity problems with boundary conditions specified on a sphere is given. New solutions for elastic fields of a twist disclination loop in a spherical particle and near a spherical pore are demonstrated. The easy and straightforward way for calculations of elastic fields of segmented spherical inclusion with uniaxial eigenstrain is shown.     

Oscillations of the plastic wave front under high‐rate loading

Two models of elastoplastic wave propagation in metals under uniaxial deformation are considered. The first model treats plastic deformation as being due to dislocation motion during heterogeneous formation of dislocations. The second model assumes that plastic deformation occurs by motion of dipoles of partial disclinations. It is shown that in both cases, certain conditions can give rise to damped oscillations of the plastic wave front, which were detected in shock loading experiments with flat specimens made of 28Kh3SNMFA steel.     

镁合金塑性机制研究综述

纯镁具有丰富的微观塑性机制,尤其是孪晶,导致其塑性变形错综复杂,力学性能也与常见的面心及体心立方金属有显著差异。由于现今学界对位错滑移与孪晶变形等塑性机制缺乏充分认识,镁合金性能调控效果尚不理想,与铝合金相比,镁合金的力学性能还有很大的提升空间。基于此背景,本文首先回顾了镁合金的发展历史与应用现状。然后介绍了镁中位错滑移与孪晶变形等塑性机制的研究进展,重点阐述位错、孪晶、晶界、析出相、溶质原子等重要的微结构,并简要介绍了计算机模拟方法。最后展望了强韧性能方面值得重视的若干研究方向。     

A physically based gradient plasticity theory

The intent of this work is to derive a physically motivated mathematical form for the gradient plasticity that can be used to interpret the size effects observed experimentally. The step of translating from the dislocation-based mechanics to a continuum formulation is explored. This paper addresses a possible, yet simple, link between the Taylor’s model of dislocation hardening and the strain gradient plasticity. Evolution equations for the densities of statistically stored dislocations and geometrically necessary dislocations are used to establish this linkage. The dislocation processes of generation, motion, immobilization, recovery, and annihilation are considered in which the geometric obstacles contribute to the storage of statistical dislocations. As a result, a physically sound relation for the material length scale parameter is obtained as a function of the course of plastic deformation, grain size, and a set of macroscopic and microscopic physical parameters. Comparisons are made of this theory with experiments on micro-torsion, micro-bending, and micro-indentation size effects.     

Randomness and slip avalanches in gradient plasticity

While localization of deformation at macroscopic scales has been documented and carefully characterized long ago, it is only recently that systematic experimental investigations have demonstrated that plastic flow of crystalline solids on mesoscopic scales proceeds in a strongly heterogenous and intermittent manner. In fact, deformation is characterized by intermittent bursts (‘slip avalanches’) the sizes of which obey power-law statistics. In the spatial domain, these avalanches produce characteristic deformation patterns in the form of slip lines and slip bands. Unlike to the case of macroscopic localization where gradient plasticity can capture the width and spacing of shear bands in the softening regime of the stress–strain graph, this type of mesoscopically jerky like localized plastic flow is observed in spite of a globally convex stress–strain relationship and may not be captured by standard deterministic continuum modelling. We thus propose a generalized constitutive model which includes both second-order strain gradients and randomness in the local stress–strain relationship. These features are related to the internal stresses which govern dislocation motion on microscopic scales. It is shown that the model can successfully describe experimental observations on slip avalanches as well as the associated surface morphology characteristics.     

Constitutive Model for the Thermo-viscoplastic Behavior of Hexagonal Close-Packed Metals with Application to Ti-6A1-4V Alloy

In this paper, a new physically based constitutive model is developed for hexagonal close-packed metals, especially the Ti-6 A1-4V alloy, subjected to high strain rate and different temperatures based on the microscopic mechanism of plastic deformation and the theory of thermally activated dislocation motion. A global analysis of constitutive parameters based on the Latin Hypercube Sampling method and the Spearman's rank correlation method is adopted in order to improve the identification efficiency of parameters. Then, an optimal solution of constitutive parameters as a whole is obtained by using a global genetic algorithm composed of an improved niche genetic algorithm, a global peak determination strategy and the local accurate search techniques. It is concluded that the proposed constitutive modal can accurately describe the Ti-6 Al-4V alloy's dynamic behavior because the prediction results of the model are in good agreement with the experimental data.     

Inelastic constitutive equations of polycrystalline metals subjected to finite deformation part I: Effect of grain rotation

In this article, a set of inelastic constitutive equations of polycrystalline metals is derived by combining a finite deformation kinematics of single crystal component, and a shear stress-shear strain relation of slip system based on a thermoactivated motion of dislocation. Interactions among grains are incorporated by “constant deformation gradient assumption.” The forms of these equations are rather simple internal variable theory types. By using these equations, some fundamental effects of grain rotations on inelastic behaviors of polycrystalline metals in a finite deformation range under complex loading and elevated temperature conditions are demonstrated. Some comments are given on a problem of plastic spin tensor.     

Defects in gradient micropolar elasticity—II: edge dislocation and wedge disclination

A theory of gradient micropolar elasticity based on first gradients of distortion and bend-twist tensors for an isotropic micropolar medium has been proposed in Part I of this paper. Gradient micropolar elasticity is an extension of micropolar elasticity such that in addition to double stresses double couple stresses also appear. The strain energy depends on the micropolar distortion and bend-twist terms as well as on distortion and bend-twist gradients. We use a version of this gradient theory which can be connected to Eringen's nonlocal micropolar elasticity. The theory is used to study a straight-edge dislocation and a straight-wedge disclination. As one important result, we obtained nonsingular expressions for the force and couple stresses. For the edge dislocation the components of the force stress have extremum values near the dislocation line and those of the couple stress have extremum values at the dislocation line and for the wedge disclination the components of the force stress have extremum values at the disclination line and those of the couple stress have extremum values near the disclination line.     

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.     

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.     

Influence of uniaxial plastic deformation on surface magnetic field in steel

Under geomagnetic field, surface magnetization measurements were made on 1045 and a3 steels samples uniaxially deformed to differing magnitudes of plastic strain, to study the dependence of surface magnetic field and its distribution on plastic deformation. The results indicated initial increase in surface magnetic field with increasing plastic strain followed by a decrease at higher plastic deformation. At still higher plastic deformation, the surface magnetic field was found to be almost independent of plastic strain. In the middle part of the sample, the uneven plastic deformation interrupted the linear distribution of surface magnetic field. The behavior of surface magnetic field and its distribution with plastic deformation were largely controlled by the different mechanisms of interaction of domain walls with isolated dislocation, dislocation tangles and dislocation cellular structures.