Mobile Dislocation Density Research Articles

Quantitative analysis of in situ straining experiments in the case of strong frictional forces

Investigation of frictional forces -Experimental techniques and working conditions in the high voltage electron microscope have already been described (1). Care has been taken in order to minimize both surface and radiation effects under deformation conditions.Dislocation densities and velocities are measured on the records of the deformation. It can be noticed that mobile dislocation densities can be far below the total dislocation density in the operative system. The local strain-rate can be deduced from these measurements. The local flow stresses are deduced from the curvature radii of the dislocations when the local strain-rate reaches the values of ∿ 10-4 s-1.For a straight screw segment of length L moving by double-kink nucleation between two pinning points, the velocity is :where ΔG(τ) is the activation energy and lc the critical length for double-kink nucleation. The term L/lc takes into account the number of simultaneous attempts for double-kink nucleation on the dislocation line.

A dislocation theory of isotropic polycrystalline plasticity

A theory of polycrystalline plasticity is developed in which the polycrystalline solid is modeled as an isotropic continuum. The rate of plastic deformation tensor is shown to be a function of the mobile dislocation density and the dislocation velocity vector summed over all active glide planes. The dislocation velocity vector is expressed in terms of the stress tensor and the normal vector to the dislocation glide plane. The condition of plastic incompressibility yields the fact that the dislocation glide planes are the octahedral shear planes of the stress tensor. As a special case the rate of plastic deformation tensor reduces to a relation analogous to the Prandtl-Reuss flow rule. The theory has been implemented in a 2-dimensional finite element code and two example problems are presented.

Investigation of dislocation dynamics by nuclear magnetic resonance

Inspired by recent experiments of Sleeswyk, Kanert et al. investigating the effect of plastic deformation on the simultaneously measured nuclear spin-lattice relaxation time ${T}_{1\ensuremath{\rho}}$ in the rotating frame, the influence of moving dislocations on ${T}_{1\ensuremath{\rho}}$ is studied theoretically. As illustrated recently by Wolf, this necessitates the calculation of quadrupolar lattice correlation functions associated with the relative motion of dislocations and nuclear spins. Assuming discrete and random dislocation jumps during (i) plastic deformation, (ii) internal friction, and (iii) fatique experiments, these correlation functions are determined. Their general form allows prediction of ${T}_{1\ensuremath{\rho}}$ in both the strong-collision (Rowland-Fradin) and the quadrupolar weak-collision region. It is demonstrated how, from low-field ${T}_{1\ensuremath{\rho}}$ experiments performed during either one of the three types of deformation modes, dislocation parameters such as the mobile and immobile dislocation density, the mean time between successive jumps of a dislocation, and the distribution of loop lengths and jump widths may be extracted. As a declared goal, this article aims at the understanding of the properties of the ${T}_{1\ensuremath{\rho}}$ minimum (i.e., of its position, depth, and width) in terms of the underlying microscopic mechanism of dislocation motion, an information which, in the past, could not be gained from purely mechanical (e.g., internal friction) experiments. Consequently, a variety of new combined NMR-deformation experiments is proposed to investigate the microscopic dynamics of dislocation motion.

Measurement of dislocation velocities in Cu-Al single crystals—I

Dislocation velocities in single crystals of Cu with 0.31 and 0.69 at. % Al, respectively, were measured by applying stresses for less than 100 μs and successive etching. The velocities are found in the range 1ms −1 at the resp. CRSS and increase slightly more than proportional to the stress. The results are well represented by a theory for thermally activated dislocation motion over a statistical array of obstacles published by Labusch et al. The CRSS is characterized by the beginning of a steep rise in the density of mobile dislocations which is to be explained in terms of dislocations overcoming extended solute clusters.

Effect of environment and coating on the creep behavior of commercial Ti alloys

1. o 2. 1. The creep rates of titanium alloys used in the present study were greatly reduced in a vacuum environment in comparison to air. 3. 2. An ion-plated Pt coating improved the creep resistance of the titanium alloys markedly over the uncoated alloys tested in air, but less than in a vacuum. 4. 3. No improvement in creep resistance was observed if there was a loss of coating continuity. 5. 4. The integrity of ion-plated Pt, its thermal stability and its inertness to oxygen provided an effective barrier against oxygen for the titanium substrate, and simulating to a certain extent, a vacuum environment. 6. 5. It is proposed that in the uncoated material tested in air, the atmospheric oxygen diffuses along the α/β boundaries. Being an α stabilizer element, oxygen enhances the transformation of the residual β into the α phase. The localized transformation stresses increase mobile dislocation densities and thus reduce the creep resistance of the material. 7. 6. Because of high reactivity and solubility of oxygen with titanium and the formation of unstable titanium oxides at the surface, the creep behavior in vacuum represents the intrinsic creep property of titanium alloys. 8. 7. The effectiveness of a coating in terms of creep resistance can be rated in terms of its ability to lower the creep rates as close as possible to that measured in vacuum.

Plastic flow and the normal-superconducting transition in lead single crystals

Plastic flow and the influence of a transition between the normal (N) and the superconducting (S) states have been studied in single crystals of lead around 4 K. Experiments have been performed in which either the strain rate or the applied stress was kept constant. The strain rate sensitivity of the flow stress and the temperature sensitivity of the strain rate at constant stress have been measured as a function of resolved shear stress in the normal and in the superconducting state. In addition, the change in flow behavior after an N-S transition has been studied. It is shown that the mobile dislocation density is stress dependent and that the differences in the N and the S state are due to the movement of underdamped dislocations.

Yield Strength and Dislocation Mobility of KCl–KBr Solid Solution Single Crystals

The concentration and strain rate dependence of the critical shear stress in KCl–KBr solid solutions was measured by compression tests. These data were compared with the stress dependence of the dislocation velocity measured by an etch pit technique. Edge dislocation moved slower than screw dislocation at the same stress level. The critical stress was determined by the edge dislocation mobility, and the mobile dislocation density at yielding was about 1.2×1011 m-2 for the three kinds of composition tested. An analytical model of the hardening mechanism is proposed on the basis of the elastic interaction (size misfit) between an edge dislocation and solute atoms. When compared with experimental results, this model gives satisfactory results not only for KCl–KBr but also for NaCl–NaBr, and NaBr–KBr solid solutions.

The mobile dislocation density and length of slip lines in dispersion-hardened copper crystals

The cyclic deformation of monocrystalline and polycrystalline metal of wavy slip mode is briefly reviewed and connected to crack nucleation in long life fatigue by the idea of surface roughening. It is shown that the cyclic deformation of planar slip alloy is closely connected with that of the wavy slip base metal, even to the value of the plateau stress in the cyclic stress-strain curve. It is pointed out that persistent slip bands deform by strain avalanches and the consequences of this for both crack nucleation and propagation are considered. Speculation about ductility exhaustion at a crack tip in less ductile metals is also offered.

Determination of the velocity of mobile dislocations by nuclear spin relaxation measurements

AbstractWolf's general theory of rotating‐frame nuclear spin‐lattice relaxation is applied to the effect caused by dislocations moving at an average velocity v. Equations are presented for the dependence of the NMR relaxation rate R on the mean waiting time τ of a dislocation before an obstacle, valid in both the weak‐and the strong‐collision regions. In the latter the Slichter‐Ailion‐Rowland‐Fradin theory applies. Nuclear spin relaxation tests on 23NaCl and 23NaF single crystals deformed at constant strain rates ϵ confirm the theory. The experimental data for the predicted maximum in R (reached only for NaCl at ϵm = 20 s―1) yield directly τm = 2.8 × 10―5 s, the mobile fraction of dislocations Qm/Qt = 0.26. The value of ϵm, together with the mean distance between obstacles of ≈ 2 × 10―4 cm, derived from the slope of the curve in the strong‐collision region, leads to vm = 7.1 cm s―1, corresponding to a mobile dislocation density ϱm = 1.4 × 108 cm−2.

The effect of compressive stress on the Young's modulus of unirradiated and irradiated nuclear graphites

The Young's moduli of unirradiated and high temperature (800–1000°C) irradiated graphites for HTGR were measured by the ultrasonic method in the direction of applied compressive stress during and after stressing. The Young's moduli of all the tested graphites decreased with increasing compressive stress both during and after stressing. In order to investigate the reason for the decrease in Young's modulus by applying compressive stress, the mercury pore diameter distributions of a part of the unirradiated and irradiated specimens were measured. The change in pore distribution is believed to be associated with structural changes produced by irradiation and compressive stressing. The residual strain, after removing the compressive stress, showed a good correlation with the decrease in Young's modulus caused by the compressive stress. The decrease in Young's modulus by applying compressive stress was considered to be due to the increase in the mobile dislocation density and the growth or formation of cracks. The results suggest, however, that the mechanism giving the larger contribution depends on the brand of graphite, and in anisotropic graphite it depends on the direction of applied stress and the irradiation conditions.

Mechanism of yield strength enhancement in heavily cold rolled phosphor bronze

Experiments were performed to identify the strengthening mechanism responsible for the increase in the 0.01 pct offset yield strength upon heat treatment of heavily cold rolled phosphor bronze, CDA 510. The effects of alloy chemistry, crystallographic texture, and microstructure upon this heat treatment response were examined with tensile testing, differential thermal analysis and transmission electron microscopy. No evidence for precipitation was observed over the range of thermal treatments for which enhancement of the 0.01 pct offset yield strength is exhibited. This strength enhancement can be explained by a reduction of the mobile dislocation density by rearrangement into stable arrays and/or dislocation pinning by tin atoms.

Cu-2.5 at%Al合金単結晶の高温定常変形

Copper-2.5 at%Al alloy single crystals oriented for a single slip system were deformed in tension at 600 and 700°C. In the later stage of deformation, the condition of steady state deformation was satisfied; namely the specimens have been deformed at a constant stress, independent of strain. In this steady state deformation stage, the internal stress and the effective stress were determined by the stress dip test. The dislocation substructure formed in this stage were observed by the etch pit technique. The results obtained are as follows:(1) The tensile axis rotated into the direction predicted by the single glide on the (111)[\bar101] slip system. When the tensile axis approached the [001]-[\bar111] symmetry line, the steady state deformation was observed.(2) The strain rate is proportional to the nth power of the steady state stress and the n value is about 5.(3) The ratio of the internal stress to the applied stress is 0.6∼0.9 and depends on the applied stress. The effective stress increases with the applied stress.(4) The parameter m* describing the effective stress sensitivity of dislocation glide velocity was estimated assuming the mobile dislocation density to be proportional to the square of the applied stress and the m* value was found to be 1.1.(5) The subgrains elongating in the [1\bar21] direction are found on the (111) plane. On the (1\bar11) plane the rows of dislocations are found along the direction roughly parallel to the trace of the primary slip plane, and the high dislocation density regions, approximately perpendicular to the slip trace, are observed.

Some aspects of plastic deformation theory with an account for thermally activated dislocation transformations

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Mobile dislocations during stress relaxation in an Fe-0.056 at. % Ti alloy

Stress relaxation tests have been made on an Fe-0.056 at.% Ti alloy below room temperature to obtain various plastic deformation thermal activation parameters. Special attention has been given to examining the variation of the mobile dislocation density and the athermal component of the flow stress during stress relaxation, both of which have been implicitly assumed to be constant in the conventional analysis of stress relaxation data. The present results show that this implicit assumption is not valid, for both the mobile dislocation density and the athermal component remain constant only for the first short period of relaxation and then decrease with increasing relaxation time. The effect of the variation of the mobile dislocation density during stress relaxation on the thermal activation parameters such as the dislocation velocity-stress exponent, m∗, athermal component of the flow stress. σ μ and activation area, A∗ is discussed in detail.

A new approach to the Portevin-LeCatelier effect

Results of investigations of Portevin-LeChatelier Effect (PLE) in α-brasses in the anealed and cold worked conditions are given. It was established that the effect occurs only if the deformation has athermal character and disappears if the process becomes thermally activated. Measurements of bands parameters (deformation in the band, velocity and width of the band) indicate that the velocity of the band decreases as the strain increases, while the density of mobile dislocations ρ m increases. It was also found that the experimental points fit a common curve of band's velocity vs dislocations density independent of initial history of alloys. The shape of that curve is consistent with the earlier predictions on collective properties of sets of dislocations. It was shown that some characteristic features of the effect can be explained on the base of these collective properties, without requiring diffusion.

The microstructure and properties of a quenched and tempered low-carbon-manganese-niobium steel

The effects of rolling parameters (deformation schedule and finishing temperature), cooling rate (direct quench and air cool), and heat treatment have been investigated for a low carbon-manganese-niobium steel. Microstructure was characterized by optical and transmission electron microscopy, and correlated with tensile and impact properties. The best combination of strength and toughness was obtained by controlled rolling low in the austenite temperature range, finishing close to the austenite-ferrite transformation temperature, and direct quenching. Such a treatment produces a fine acicular ferrite containing a substructure of subgrains and a high density of mobile dislocations. Subsequent heat treatment effects a very small strength increase due to the limited amount of niobium available for precipitation and due to partial recovery of the random dislocation substructure during aging.

Comparison of dislocation mobility in LiF measured by direct and indirect methods

A comparison is made of the effective stress dependence of the dislocation velocity V in LiF crystals as determined by stress relaxation tests and by direct etch pit measurements. The stress relaxation technique used permits to study both the effective stress dependence of V and the evolution of the total and mobile dislocation densities during the dynamic loading of the crystals. The data obtained by the two methods are in good agreement. It is shown that the density of mobile dislocations is decreasing with the strain, whereas the total dislocation density is growing during the dynamic straining to 1%. [Russian Text Ignored]

On stress relaxation of zirconium tubing

Stress relaxation offers a means for evaluating the deformation dynamics of metals. A previously suggested equation relating the stress rate and stress which avoids the indeterminacy of machine stiffness is applied to this type of experiments on zirconium tubes at room temperature and 400° C. The choice of zirconium tubes and temperatures is related with technological applications. Good agreement is found at room temperature and no agreement at 400°C. Parameters of this equation are discussed in terms of mobile and total dislocation densities. La relaxation des contraintes offre un moyen d'évaluer la dynamique de la déformation des métaux. Une équation antérieurement proposée reliant la constrainte et la vitesse de mise en contrainte, ce qui évite d'apprécier la rigidité de la machine de traction, est appliquée à ce type d'expériences sur des tubes de zirconium à la température ambiante et à 400°C. Le choix des tubes de zirconium et des températures est relié aux applications technologiques. On a trouvé un bon accord pour les essais à la température ambiante, mais désaccord à 400°C. Les paramètres de cette équation sont discutés en termes des densités de dislocations mobiles et totales. Die Verformungsdynamik von Metallen kann durch Spannungsrelaxation untersucht werden. Eine kürzlich vorgeschlagene Beziehung zwischen der Spannungsgeschwindigkeit und der Spannung, die die Unbestimmtheit der Maschinenfestigkeit umgeht, findet auf diese Art von Experimenten an Zirkon-Rohren bei Raumtemperatur und 400°C Anwendung. Die Wahl von Zirkon-Rohren und der Temperaturen steht im Zusammenhang mit ihrer technologischen Anwendung. Gute Übereinstimmung besteht bei Raumtemperatur, jedoch nicht bei 400° C. Die Parameter dieser Gleichung werden mit Hinblick auf die Dichte der beweglichen und der Gesamtzahl der Versetzungen diskutiert.

Flux motion and moving dislocations in type II superconductors

Abstract The interaction of mobile dislocations with Abrikosov vortices is described and shown to be reversible with the motion of dislocations, the dislocations sweeping flux into the specimen. In addition the flux change varies linearly with the strain rate. This interaction is observed to be independent of temperature, between 0·2 and 0·6 Tc, which rules out a surface barrier model. A model, which relates the change in flux to the mobile dislocation density, is presented and compared with the observations.

Mobile and immobile dislocations in LiF crystals under straining

Immobile dislocations are observed by the method of selective etching in the course of crystal deformation of lithium fluoride crystals with the yield stress values 70 and 200 p/mm2. The method is described in the paper. The density of mobile dislocations in glide bands is obtained as the difference between the total dislocation density ϱ and that of immobile dislocations. The total density of dislocations is detected by a repeated etching of the crystal in the unloaded state. Mean values ϱi and ϱ of the immobile and mobile dislocation densities ϱ and ϱb, respectively, are established taking into account the active glide volume Va which is assumed to be equal to the volume of the glide layers involved in the deformation. An increase of ϱ and ϱi with the growth of the plastic strain e has been observed. The data obtained are compared with the information supplied by indirect experiments, and a qualitative agreement is established. [Russian Text Ignored.]