Dislocation Kinetics Research Articles

Kinetics of dislocations in pure Fe. Part I. In situ straining experiments at room temperature

In situ straining experiments have been carried out in pure Fe, in order to determine the geometry and the kinetics of dislocation glide at room temperature. Straight screw dislocations glide slowly in {1 1 0} elemental slip planes, at a velocity proportional to their length, whereas curved non-screw parts are highly mobile. The exact loop shape can yield the local stress as well as the difference of core energy between pure screw and near-screw orientations. The velocity–stress dependence of screws has been measured at the scale of a single dislocation source, and compared with macroscopic activation areas. The results are discussed in terms of the kink-pair mechanism.

Modeling of flow stress for magnesium alloy during hot deformation

Based on the classical flow stress–dislocation density relation and kinetics of dynamic recrystallization (DRX), a model was developed to determine flow stress of magnesium alloy at hot deformation condition. The proposed model is capable of predicting the flow behavior of work hardening and dynamic recovery (DRV) region as well as the softening caused by DRX. To establish the model, the double-differentiation method was used to identify the critical strain for initiation of DRX, and the DRV parameter Ω was evaluated from the work-hardening behavior prior to critical strain. The net softening attributable to DRX was defined as the difference between the DRV and experimental curves, and Avrami equation was employed to represent this softening behavior. The flow stress curves of ZK60 magnesium alloy predicted by the developed model are in good agreement with experimental results, which confirms the validity of the model.

Raman Spectroscopy for the Analysis οf Temperature-Dependent Plastic Relaxation οf SiGe Layers

Novel architectures for electronics and photonics are expected to be developed using the forthcoming Si1−xGex technology. However, in Si1−xGex-based heterostructures, materials and design issues rely on accurate control of strain and composition of the alloy. The Raman spectroscopy has rapidly emerged as a reliable technique for the quantitative determination of such parameters on a sub-micrometric scale. In this work we present an investigation of the effects of the growth conditions of Si1−xGex graded layers on dislocation nucleation and interaction. In particular, we focus on the crucial role the deposition temperature plays in the dislocation kinetics. The analysis of threading dislocation densities is accompanied by a quantitative measurement of the residual strain in Si1−xGex/Si heterostructures, carried out by means of the Raman scattering. Our approach is effective in studying the physical mechanism governing dislocation multiplication and the sharp transition from a state of brittleness to a state of ductility within a narrow temperature window.

Correlation effects in an ensemble of edge dislocations

A kinetic theory of correlation interaction in an ensemble of edge dislocations is developed taking into account the effects of the fluctuation dynamics of dislocations. Equations of evolution of a dislocation ensemble are derived including the correlation interaction between dislocations. A criterion of instability of a uniform dislocation distribution is established. It is shown that the nucleation of spatially nonhomogeneous dislocation structures due to correlation instability is mainly determined by the specific features of the elastic interaction between dislocations and depends only slightly on the mechanism of dislocation kinetics. The theory is applied to calculating the dispersion of an internal stress field.

STRAIN RATE DEPENDENCE OF DYNAMIC FLOW STRESS OF 2017 ALUMINUM ALLOY AT VERY HIGH STRAIN RATES

To estimate the strain rate dependence of the dynamic flow stress of aluminum alloys, 2017-O and - T4, high strain rate and rate reduction tests are performed at strain rates ranging from about 1000/sec to 30000/sec. A steep increase in the flow stress is observed for 2017-O at the strain rate of about 3000/sec. For 2017-T4, the above phenomenon is observed at the strain rate above about 10000/sec. A simplified model for dislocation kinetics under dynamic plastic deformation is employed which can represent a transition in the rate controlling mechanism of dislocation motion from a thermally activated process to a viscous drag. It is expected that the steep increase in the flow stress observed at high strain rates is attributed to the rate dependence of the viscous drag on the dislocation motion.

An Internal Variable Approach to Inelastic Deformation Including Structural Superplasticity

An internal variable theory has been proposed to account for the essential microstructures during inelastic deformation. The framework of the theory is built on the basis of well known dislocation dynamics to provide the concept of an internal strain tensor as the most fundamental deformation state variable. The plastic and inelastic strain rate tensors are then naturally defined and also a kinematics relation among them can further be derived from the time rate of change of this internal strain tensor, which in fact accounts for the evolution of microstructures during inelastic deformation. To complete the theory, the constitutive relations between the various stress variables and their conjugate deformation rate variables are then derived based on the dislocation kinetics. The theory is then further extended to describe the structural superplasticity, taking this slip zone model with dislocation pile-ups as the major accommodation mechanism for grain boundary sliding. The experimental results obtained from the various crystalline materials are then presented and compared with each other in relation to the internal variable theory for inelastic deformation.

Plasticity and strength of micro- and nanocrystalline materials

This review is devoted to the effect of grain boundaries on the deformational and strength properties of poly-, micro-, and nanocrystalline materials (predominantly metals). The main experimental facts and mechanisms concerning the dislocation structure and mechanical behavior of these materials over wide ranges of temperatures and grain sizes are presented. The experimentally established regularities are analyzed theoretically in terms of equations of dislocation kinetics taking into account the properties of grain boundaries as barriers, sources, and sinks for dislocations and as places where dislocations annihilate. The origin of the Hall-Petch relations for the yield stress and the flow stress as functions of the grain size, as well as the deviations from these relations observed in nano- and microcrystalline materials, is discussed in detail in terms of the dislocation-kinetics approach. Embrittlement of micro- and nanocrystalline materials at low temperatures and superplasticity of these materials at elevated temperatures are also analyzed in terms of the dislocation-kinetics approach.

Dislocation density evaluation using dislocation kinetics model

A dislocation kinetics model called the Haasen–Alexander–Sumino (HAS) model is applicable to the quantitative estimation of dislocation density in semiconducting single crystals. In this model, creep strain rate is related with the dislocation density as well as stress components, together with a time-evolution equation of the dislocation density. This model is originally provided under a uniaxial stress state. Then the HAS model was expanded to a multiaxial stress state by neglecting crystal anisotropy and assuming that a crystal is isotropic. Such constitutive equation enables an axisymmetric finite element analysis of dislocation density evaluation. However, single crystals have anisotropy in the elastic constants and specific slip directions. Therefore, we expanded the HAS model to a multiaxial stress state based on the theory of crystal plasticity in order to take account of the crystal anisotropy. Such a constitutive equation requires a three-dimensional finite element analysis of dislocation density evaluation, even though a single crystal has an axisymmetric shape. We also proposed an approximate method, by which the effect of the crystal anisotropy on the dislocation density can be taken into account in the framework of the axisymmetric analysis. We successfully applied these constitutive equations to dislocation density analysis of crystal growth processes, that of ingot annealing and that of heteroepitaxial growth of a thin film on a substrate.

Strain rate dependence of dynamic flow stress considering viscous drag for 6061 aluminium alloy at high strain rates

In order to evaluate the strain rate dependence of the dynamic flow stress of aluminium alloys, 6061-O and -T6, high strain rate tests are performed at strain rates ranging from about 1000/s to 30000/s, and strain rate reduction tests are also conducted in the strain rate range from about 10000/s to 20000/s. A steep increase in the flow stress is observed for 6061-O at the strain rate of about 5000/s. The above phenomenon, however, is not observed for 6061-T6 in the strain rate range where the strain rate reduction tests is conducted. A simplified model for a dislocation kinetics under a dynamic plastic deformation is used to consider the deformation mechanism in the above strain rate ranges, which reveals that the steep increase in the flow stress of 6061-O is attributed to the rate dependence of the viscous drag on the dislocation motion. It is estimated that the velocity of moving dislocation of 6061-T6 is lower than that of 6061-O at a given strain rate, and that 6061-T6 is higher in a mobile dislocation density than 6061-O. The model predicts also that the increase in the mobile dislocation density shifts the transition region, or the strain rates in which the steep increase in the flow stress becomes to appear, to the higher strain rate side.

Mechanism of strain hardening and dislocation-structure formation in metals subjected to severe plastic deformation

The equations of dislocation kinetics are used to theoretically analyze the mechanism of strain hardening and the formation of fragmented dislocation structures in metals at large plastic strains. A quantitative analysis of the available data on aluminum and an aluminum-magnesium alloy shows that strain hardening at large plastic strains and the formation of fragmented dislocation structures are related to the interaction and self-organization of geometrically necessary dislocations (GNDs). On the microscale, the source of the GNDs is a locally nonuniform plastic deformation induced by a dislocation-density gradient in dislocation-cell boundaries.

Mechanism of recovery of the mechanical properties of neutron-irradiated metals in the course of thermocycling

The mechanism of recovery of the strength and strain characteristics of neutron-irradiated metals and alloys (up to their initial values observed prior to irradiation) during periodic quenching in the temperature range below the irradiation temperature is considered. It is assumed that the removal of radiation-induced defects (interstitial and vacancy loops) from radiation-hardened metals is associated with the formation of defect-free channels along the slip planes (the phenomenon of dislocation channeling) under the thermal stresses arising in each cycle of quenching. The relationships describing both the kinetics of the decrease in the yield strength σY and in the ultimate strength σU and the kinetics of the increase in the uniform strain eU of a preliminarily irradiated material with increasing number of quenching cycles are derived using the equations of dislocation kinetics. The theoretical results obtained are compared with experimental data on the kinetics of recovery of the mechanical properties of neutron-irradiated samples (the austenitic FeNiCr and ferritic FeCrMo structural steels and the titanium alloy TiAlZr) in the course of periodic quenching.

Synergism of Electrochemical and Mechanical Factors in Erosion−Corrosion

A theoretical model was developed on basis of nonequilibrium thermodynamics, dislocation kinetics, and electrochemistry, which may lead to the quantitative assessment of material loss produced by the synergism of mechanical and electrochemical factors in an erosion-corrosion process, As predicted by this model, the synergistic effect results mainly from the interaction of two irreversible fluxes, namely, the anodic dissolution current density and the plastic flowing in the surface layer caused by dynamic plastic deformation. An enhanced anodic dissolution flux is induced by the dynamic surface plastic deformation resulting from the impingement of solid particles, which can be correlated to the wastage rate due to the mechanical erosion. Meanwhile, the anodic current present at the electrode surface, in turn, can increase the mobility of dislocation and reduce the resistance in the surface layer against plastic deformation. Such an effect is demonstrated by the hardness degradation of metals in corrosive media. Theoretical analysis indicates that the corrosion-induced hardness degradation is a linear function of the logarithm of anodic current density. The degradation of mechanical erosion resistance with decreasing hardness suggests that the corrosion-enhanced erosion may result from the degradation in hardness of target material induced by the anodic dissolution and the corresponding wastage is also a linear function of the logarithm of anodic current density. The theoretical predictions were compared with the experimental results of carbon steels obtained form the slurry-erosion tests and the micro-hardness measurements. The results indicate that the hardness degradation in corrosive media is mainly controlled by the anodic current density and is almost independent of the polarization behavior of steels.

Deformation Induced Vacancies with Severe Plastic Deformation: Measurements and Modelling

In discussing hardening characteristics in terms of crystalline lattice defects, in most cases the properties and kinetics of dislocations and their arrangement have been considered. However, during plastic deformation also vacancies and/or vacancy type defects are produced in very high densities which are typically close to those of vacancies in thermal equilibrium at the melting point. The effect of high vacancy concentrations on the hardening characteristics is twofold: (i) direct effects by impeding the movement of dislocations (ii) indirect one by inducing climbing and annihilation of edge dislocations leading to softening or even absolute decreases in strength. This paper presents first measurements of deformation induced vacancies in SPD materials which have been achieved by combined evaluation of resistometry, calorimetry and X-ray diffraction. The density of vacancies during and after SPD deformation is found to be markedly higher than in cases of conventional deformation and/or coarse grained material which may be partly attributed to the particular conditions of SPD namely the enhanced hydrostatic pressure as well as the changes in deformation path. It is suggested to make this high vacancy concentration responsible for both dynamic and static recovery and/or recrystallisation processes recently found during and after SPD, being potential reasons for enhanced ductility and superplasticity which only occur with nanomaterials originating from SPD. Recent publications show that in alloys, SPD induced vacancies can also enable the existence of phases which do not appear in the equilibrium diagram.

Strain Rate Dependence of Dynamic Flow Stress of 6061-T6 Aluminum Alloy at Strain Rates Ranging from 1×103 to 4×104s-1

In order to evaluate the strain rate dependence of the dynamic flow stress of 6061-T6 aluminum alloy, strain rate reduction tests are conducted in the strain rate range from about 2×104 to 4×104s−1, which is the strain rate range before reduction, and the reduction in strain rate is 58.6%. To eliminate an effect of elastic wave dispersion produced in a bar on the measured flow stress, a output bar being 2mm in diameter is employed. A steep increase in the flow stress was observed at the strain rate of about 2×104s−1. A simplified model for dislocation kinetics under dynamic plastic deformation is used which can represent a transition in the rate controlling mechanism of dislocation motion from a thermally activated process to a viscous drag. It is comfirmed that the steep increase in the flow stress of 6061-T6 observed at the strain rate of about 2×104s−1 is attributed to the rate dependence of the viscous drag on the dislocation motion and furthermore, the increase in the mobile dislocation density lowers a velocity of moving dislocations and shifts the transition region, or the strain rates in which the steep increase in the flow stress becomes to appear, to the higher strain rate side.

Monotonic and Cyclic Behavior of Ultrafine Grain Metals:Overview

The available to date experimental results are reviewed with regard to the common aspects and features of monotonic and cyclic stress-strain behavior of various ultra-fine grain materials produced by severe plastic deformation (SPD). Some possible mechanisms of plastic flow and degradation during monotonic and cyclic testing are discussed from the standpoint of initial SPD structure and its evolution upon loading. The role of two strengthening mechanisms – dislocation accumulation and grain reduction - is highlighted. The key importance of grain boundaries for the mechanical behavior, strain localization and fracture of ultra-fine grain metals is argued and the experimental evidence is presented on the significance of grain boundary sliding in their plastic deformation. The results of phenomenological modeling of the monotonic and cyclic response of ultra-fine grain metals are presented in terms of dislocation kinetics and a satisfactory agreement with experimental data is demonstrated.

Vacancies in plastically deformed copper

In discussing hardening characteristics in terms of crystalline lattice defects, in most cases the properties and kinetics of dislocations and their arrangement have been considered. However, during plastic deformation also vacancies and/or vacancy-type defects are produced in very high densities which are typically close to those of vacancies in thermal equilibrium at the melting point. This paper presents measurements of deformation-induced vacancies in deformed copper which have been achieved by combined evaluation of resistometry, calorimetry and X-ray diffraction. The density of vacancies during and after severe plastic deformation (SPD) deformation is found to be markedly higher than in cases of conventional deformation and/or coarse-grained material, which is attributed to the particular conditions of SPD, i. e., the enhanced hydrostatic pressure as well as the- changes in the deformation path. The use of synchrotron radiation allows to apply the XPA method for in-situ deformation monitoring of intrinsic structural parameters. This also includes deformation-induced vacancies, evaluated by the diffuse background of Bragg peak profiles.

６０６１アルミニウム合金の高ひずみ速度域における粘性抵抗を考慮した変形応力のひずみ速度依存性

In the previous paper, in order to evaluate the strain rate dependence of the dynamic flow stress of aluminum alloys, 6061-O and -T6, high strain rate tests were performed at strain rates ranging from 1 × 103s-1 to 3 × 104s-1, and strain rate reduction tests were also conducted in the strain rate range from about 1 × 104s-1 to 2 × 104s-1, which is the strain rate range before reduction. A steep increase in the flow stress was observed for 6061-O at the strain rate of about 5 × 103s-1. The above phenomenon, however, was not observed for 6061-T6 in the strain rate range where the strain rate reduction tests were conducted and also the strain rate dependence of the flow stress was negligibly small. In this paper, to clarify the difference between the above-mentioned phenomenon for 6061-O and -T6, a simplified model for dislocation kinetics under dynamic plastic deformation is used which can represent a transition in the rate controlling mechanism of dislocation motion from a thermally activated process to a viscous drag. The equation derived from the kinetic model reveals that the steep increase in the flow stress of 6061-O observed at the strain rate of about 5 × 103s-1 is attributed to the rate dependence of the viscous drag on the dislocation motion and furthermore, the increase in the mobile dislocation density lowers a velocity of moving dislocations and shifts the transition region, or the strain rates in which the steep increase in the flow stress becomes to appear, to the higher strain rate side. It is expected that the flow stress of 6061-T6 increases abruptly in the strain rate region above about 2 × 104s-1.

Stress and dislocations at cross-sectional heterojunctions in a cylindrical nanowire

The limit of crystal lattice coherency of a cross-sectional heteroepitaxial junction in a nanowire is calculated in terms of the critical nanowire radius R c, based on a general calculation of elastic stresses in a long cylindrical rod. R c is derived from the kinetics of a possible misfit dislocation which can slip in the heterointerface and rest in an energetic minimum, if it occurs at all, regardless of whether it is of zero total energy as assumed in the literature. A close comparison is made with the known models for the critical radius of a dislocation half-loop and the critical thickness h c of a heteroepitaxial film, where all models are refined by including the energy of the slip step formed or accidentally annihilated. For a symmetrical, abrupt heterojunction, we obtain R c as a lower and, therefore, quite safe limit, about five times larger than h c of a comparable thin film. An even larger R c is found for junctions of finite transition width instead of abrupt transitions. It is estimated that nucleating the dislocations in a perfect nanowire is difficult, in agrement with experimental reports of dislocation-free nanowires with R well above the theoretical R c.

Analysis of the parameters of a submicron dislocation structure in metals subjected to severe plastic deformation

Equations of dislocation kinetics are used to quantitatively compare the mechanisms of formation and evolution (with deformation) of cellular dislocation structures at moderate strains and of submicron block dislocation structures at high plastic strains. In both cases, the formation of nonuniform dislocation structures is a result of dislocation self-organization, more specifically, the self-organization of statistically random dislocations during the formation of cellular structures and the self-organization of geometrically necessary dislocations (which appear due to the nonuniform character of plastic deformation on the micron scale) during the formation of block structures.

Dislocation density analysis of GaAs bulk single crystal during ingot annealing process (comparison among several computational methods)

Ingot annealing is an indispensable process for a GaAs single crystal to improve its electric characteristics. One of the technical problems of GaAs ingot annealing is the increase in dislocation density during its annealing that affects the performance of electronic devices. Three computer codes were utilized for dislocation density evaluation of a single crystal ingot during its annealing. These codes employ a dislocation kinetics model called the Haasen–Alexander–Sumino model as the constitutive equation. In this model, creep strain rate is related to dislocation density, and this model is extended to a multiaxial stress state. The first code is an axisymmetric finite element computer code, in which a bulk single crystal is assumed to be isotropic, and crystal anisotropy in elastic constants and specific slip directions is completely neglected. The second one is an axisymmetric finite element computer code, in which the crystal anisotropy is approximately considered using averaging technique. The third one is a fully three-dimensional computer code, in which the crystal anisotropy is completely taken into account. Dislocation density analyses were performed for a GaAs ingot with 4-in diameter, and the time variations and distributions of the dislocation density were obtained by these computer codes. The results are compared among the three computer codes.