Dislocation Jogs Research Articles

Mean mobile dislocation velocity in lif crystals under strain

Results of a study of mobile dislocation assembly structure of the LiF crystal under straining are used to determine the dislocation mean velocity, as well as its dependence on the assembly structure and its variation during work hardening. The velocity is found to be several orders of magnitude in excess of the separate dislocation velocity in the undeformed crystal for the same shear stress. An anomalous change in the activation “volume” is discovered as the process changes from microplastic deformation to plastic flow. Elastic interaction of sign-similar mobile dislocations and kinetics of jogs in screw dislocations are treated as sources of the effects observed. [Russian Text Ignored].

Inhomogeneous positron trapping in fatigued aluminum single crystals

Surface fatigue phenomena have been studied in 99.9999% aluminum single-crystal cantilever beams subjected to reverse bending, by using positron annihilation and X-ray diffraction techniques. The coincidence of about the same penetration depth of the surface fatigue damage and of the positrons resulted in a very high sensitivity of the positron technique which, combined with X-ray diffraction, yielded information after single fatigue cycles for a fatigue life of about 107 cycles. A linear positron trapping model based on an inhomogeneous distribution of two different types of traps has been developed by using and extending the principles of the simple linear trapping model for one type of traps. The lifetimes and the relative integrated intensities at annihilation of positrons in pairs of aluminum single-crystal specimens were measured as functions of the number of fatigue cycles during the fatigue hardening stages I and II, the two crystals being subjected to the same strain amplitude of 0.17%. Correlation between the positron results and the corresponding spots of von Laue back-reflections was obtained. In early stages of fatigue, two characteristic position lifetimes, the first being (215±15) ps and the second varying during fatigue from 230 ps to (260±15) ps, have been found and have been interpreted to originate from trapping of positrons at dislocation jog elements and voids/vacancy dipoles, respectively.

A review of recent theoretical developments in the understanding of the migration of helium in metals and its interaction with lattice defects

Abstract Recent theoretical calculations of the properties of rare gases, and in particular Helium, in the common f.c.c. and b.c.c. metals, are reviewed from the viewpoint of the investigator concerned with the behaviour of rare gas in such radiation damage processes as surface blistering and void swelling. Particular attention is paid to mechanisms by which Helium may migrate in a damaged metal lattice during irradiation and to the properties of small gas and vacancy clusters which may represent bubble or void nuclei. Initially the proposed rapid migration of interstitial Helium is discussed together with the substitutional de-trapping mechanism, whereby thermally activated Helium jumps from a substitutional to an interstitial position. This enables a mechanism of substitutional Helium diffusion to be proposed which may proceed at temperatures below those of self-diffusion. The formation, binding, migration and dissociation energies of gas-vacancy clusters have been reviewed. The relevance of the predicted trend towards the optimum stability of clusters composed of equal numbers of gas atoms and vacancies is discussed. The limited data available concerned with the binding of a Helium atom to a pure dislocation line is presented together with comments on the possible nature of the interaction of Helium with the dislocation jog.

Dislocation relaxation processes in body-centred cubic metals

This paper consists of three parts. In the first part the properties of dislocations and kinds in b.c.c. metals are studied in some detail, with special emphasis on screw dislocations. The unusual features associated with 〈111〉screw dislocations in b.c.c metals («polarity», asymmetry of glide, unusually large Peierls energies) are derived partly from geometry and partly from the results of computer calculations, and are compared with the properties of dislocations in f.c.c. metals and in the diamond structure. The second part reviews the theory of the relaxation processes associated with the migration of kinks along dislocation lines, with the formation of kink pairs and with the trapping and detrapping of kinks at point defects. In the third part the experimental results on dislocation relaxation processes in b.c.c. metals are compared with the theoretical findings reviewed in the earlier parts. It is shown that the so-called γ-relaxation process should be attributed to the formation of kink pairs on screw dislocations, as proposed earlier. The experimental evidence on the α and α′ maxima appears to be in favour of a suggestion of Igataet al., who interpreted the α-peak as due to kink pair formation on nonscrew dislocations and the α′-peak (observed in some metals) as due to the migration of kinks on screw dislocations. The β-relaxation processes appear to be of a nonintrinsic nature. According to Kuke, Kronmüller and Schultz, a further intrinsic dislocation relaxation process, namely the nonconservative movement of jogs in screw dislocations, is responsible for the high-temperature magnetic after-effect in iron.

Effect of temperature on the dislocation structure of the ordered alloy Ni3(Fe, Cr)

Transmission electron microscopy is used to study the dislocation structure of ordered polycrystalline Ni3(Fe, Cr) alloy after deformation at temperatures of 293, 473, 673, and 773°K. The flow stress σ is plotted as a function of the density of dislocations ρ. It is observed that there is a direct proportionality between σ and ρ1/2, which indicates that the relation τ= αGbρ1/2 is satisfied, where τ is the shear stress, G is the shear modulus, b is the Burgers vector, and α is a coefficient weakly dependent on the density of dislocations. The values of α are found for different deformation temperatures from the slope of the lines. It is found that α decreases with increasing deformation temperature. When the temperature is increased from 293 to 773°K the reduction in α is about 20% in agreement with estimates of the resistance to motion by superdislocations caused by nonconservative drag of dislocation jogs.

Effects of electron irradiation on creep of aluminium

Abstract Theoretical analysis of the effects of radiation on creep of metals, made on assumption of predominance of radiation-enhanced interstitial diffusion, has shown that irradiation should accelerate the motion of vacancy-emitting dislocation jogs, while, on the other hand, slowing down the motion of jogs emitting interstitials. Under such conditions, irradiation should slow down the creep controlled by jogged screw dislocation glide, and increase the creep-rate, when it's controlled by edge dislocation climb. The conclusion to this effect has been substantiated by experimental study of the effects of electron irradiation on creep of aluminium within the temperature range of 10 to 50°C. It has been found that electron irradiation causes the creep-rate to decrease; simultaneously, one observes a substitution of a mechanism controlled by the glide of jogged screw dislocations by one controlled by edge dislocation climb.

Load-Elongation Curves of Pure Body-Centred Cubic Metals at Low Temperatures

Theoretical calculations of various load-elongation curves of the [100] crystals are made on a model in which (1) velocity of screw dislocations is expressed as a function of temperature, stress, and average spacing of drag points and that of edge dislocations is infinite under finite stress, and (2) interactions between dislocations and their effects on multiplication and annihilation of dislocations are treated quantitatively. The main conclusions are (1) forest cuttings give very small work hardening, (2) a drag of densely distributed large jogs in screw dislocations gives very high work hardening, and (3) non-uniform distribution of dislocations gives instantaneous changes in flow stress at strain-rate changes.

Dislocation Jog and Kink Interactions in Ionic Crystals

AbstractJogs and kinks on dislocations in ionic crystals interact both elastically and electrically. In cubic crystals the electrical interaction can be calculated by simple isotropic theory. Anisotropic calculations of the elastic interaction have been performed for a number of ionic crystals of the NaCl type in order to decide whether the net interaction is attractive or repulsive and whether neutral superjogs tend to form.

High temperature creep characteristics of Al-6.3at%Mg alloys containing small additional elements

The effects of small amounts of an additional element (Ag, Si or Zn) on the creep characteristics of Al-6.3at% Mg alloys were investigated for the specimens which had been subjected to two kinds of heat-treatments.The heat-treatment (A) was an attempt to obtain dispersed coarse particles. The specimens were solution heat treated at 400°C for 1hr. and furnace-cooled to 250°C at a cooling rate of 25°C/hr. Then, they were maintained at that temperature for 6 days and water quenched.The heat-treatment (B) was to produce dispersed fine particles by much nucleation. The specimens were solution heat treated at 400°C for 1hr. and water quenched. Then, they were maintained at 150°C for 2 days, at 200°C for 2 days, and at 250°C for 6 days, and then again water quenched. The heat treatments had remarkable effects on the creep characteristics such as activation energy (Q) and stress exponent (n) expressed in the following state equation of steady creep;es=Aσnexp(-Q/RT)The activation energy (Q) and the stress exponent (n) for the creep at 250°C of the specimens heat-treated by (A) method were about 37kcal/mol and about 3, respectively. These values were approximately equal to those of Al-4.4at%Mg solid solution alloys. On the other hand, the activation energy and the stress exponent for the specimens heat-treated by (B) method were 2731kcal/mol and about 4 respectively, under the same testing conditions. The rate controlling step of the former treatment (A) would be the dragging of solute atmospheres around the jogs in screw dislocations and that of the latter treatment (B) would be due to the cross slip of dislocations. The difference between the effects of both treatments would be attributed to the change in transition temperature range from the cross-slip mechanism to the vacancy controlling mechanism.The three kinds of additional elements had little effects on the high temperature creep characteristics of Al-6.3at%Mg alloys. It would be attributed to the fact that the additional elements had been dissolved in β phases of Al-Mg alloys during the heat treatments before the creep.

The strain-rate sensitivity of the plastic properties of α-iron at high temperatures

Abstract The tensile stress-strain behaviour of high purity iron has been examined over a range of temperatures from 0° to 900°C and strain rates from 0·04 min−1 to 40 min−1. The changes in flow stress which occur during instantaneous changes in strain rate have been measured and calculations of the activation volume for the thermally activated part of the flow stress have been made. The activation volume is found to be independent of strain for a given set of testing conditions and equal to the activation volume calculated from the strain-rate variation of the yield stress. The activation volume ranges from 10−21 cm3 to 9 × 10−21 cm3, increasing with increasing temperature and decreasing strain rate but it is not a unique function of the effective stress in the deforming material. The results can be best explained if the thermally activated part of the flow stress is controlled by the non-conservative motion of jogs in screw dislocations.

High temperature creep characteristics of dilute aluminum base alloys

The high temperature creep characteristics of dilute aluminum base alloys containing as solute copper, magnesium, silicon and germanium have been investigated with particular emphasis on the activation energy for creep. The activation energies for creep are about 36kcal/mol for all alloys in the temperature range from 250°C to 300°C, and they gradually decrease as the temperature is decreased from 250°C to 200°C.The measurements of micro-vickers hardness for the specimens subjected to steady state creep show that the larger the difference in size between a solute atom and a solvent atom, the higher the micro-vickers hardness with an exception of Al-Si alloy. These results can be interpreted by the dragging motion of solute atmospheres around the jogs in screw dislocations.

In-reactor creep of Zr-2.5 at % Nb

Tensile specimens of heat treated Zr-2.5 at % Nb rod have been tested under constant creep loads both unirradiated and during neutron irradiation. No significant differences were found in creep rates for temperatures of 350, 375 and 400 °C. The in-reactor creep rates were faster at 300 °C and stresses of 25.6, 31.6, and 38.7 kg/mm 2 and at 320 °C and 38.7 kg/mm 2 than the corresponding unirradiated control creep rates. The total creep rate during irradiation under these stresses and temperatures can be expressed by the equation: ε = ε u + ε i , where ε is the measured in-reactor creep rate, ε u is the unirradiated control creep rate, and ε i is the increase in creep rate due to neutron irradiation. The values of ε i show little if any dependence upon stress or temperature. The activation energy for creep Q c , determined for a stress of 38.7 kg/mm 2 is approximately 60 000 cal/ mole. Due to the contribution of ε i there is an apparent decrease in the activation energy at the lower strain rates. There is also a decrease in the activation energy of the control data at lower stresses and temperatures which may be due to measurement of faster primary creep rates instead of minimum creep rates, or a different creep process which has a lower activation energy. The mechanism for the increased creep rate during irradiation observed at 300 and 320 °C is tentatively proposed to be due to growth of stress oriented dislocation loops limited by the generation rate of point defects. The possibility of the increased creep rate resulting from a non-conservative dislocation mechanism limited by point defects produced by irradiation is not excluded. The mechanism of the creep represented by an activation energy of approximately 60 000 cal/mole is most likely a diffusion controlled process such as dislocation climb or non-conservative motion of jogs in screw dislocations.

Application of the generalised theory of yielding creep to irradiation creep in Zirconium alloys

The theory of yielding creep, in its generalised form of accelerated thermal creep, is extended to include the temperature, neutron flux and time dependence of irradiation creep. The theory is consistent with the author's data at 78 °K and 40 °C and with Canadian data at 300 °C. The growth coefficient, G, of Zircaloy-2 at the respective temperatures is deduced to be 2.3, 1.2 and 1.5. Direct measurement by Buckley gives G ≈ 1.2 at ~ 100 ° C. If the short term thermal creep behaviour continues to reactor lifetimes of 200 000 h the analysis suggests that linear extrapolation of the irradiation creep rate over-estimates the final strain by a factor of five. The insensitivity to neutron irradiation of creep processes which are controlled by diffusion is discussed, e.g. Nabarro-Herring creep, the climb of edge dislocations and jogs in screw dislocations.

The effect of dispersed phases upon dislocation distributions in plastically deformed copper crystals

Abstract The effect of dispersions of either cobalt or silica upon the dislocation distributions in deformed copper crystals has been investigated. The crystals were deformed in tension, and three-stage stress-strain curves, similar to those of single-phase copper, were obtained. However, the precipitates caused an increase in the yield stress and in the rate of hardening in stage I. Electron microscopy of sections cut from crystals deformed into stage I showed the alignment of primary dislocation loops, helices, jogs and dipole ends in the direction of the primary Burgers vector, and these effects are interpreted in terms of dislocation cross-slip at the particles. The incidence of particle shearing in the copper-cobalt crystals causes these features to be less pronounced than in the copper-silica crystals. Electron microscopy of crystals deformed into stage II shows that the precipitate causes lattice misorientations to be decreased, and less inhomogoneous dislocation structures than in single-phase crystals to occur.

Elastic self-energies of undissociated dislocation jogs

Abstract Analytic expressions are derived for the elastic energy of an undissociated jog lying perpendicular to an undissociated straight dislocation line of arbitrary Burgers vector in an otherwise perfect infinite isotropic elastic medium. These expressions are the most accurate which can presently be obtained, but the analysis still involves minor approximations. In particular, those associated with the contribution to the energy arising from the work done by core surface tractions at the corners in the dislocation are important for short jogs and are discussed in detail. Numerical results are presented and these and the analytic expressions are compared with those of previous workers, which involve major approximations. It is concluded that even the new expressions are not reliable for short jogs.

PLASTIC ANISOTROPY OF TANTALUM, NIOBIUM, AND MOLYBDENUM

The stress–strain behavior of single crystals of tantalum, niobium, and molybdenum has been studied in both tension and compression in the temperature range 4.2–400 °K. The crystals were stressed in both the [Formula: see text] and the [Formula: see text] directions.At high temperatures, the yield stress of all three metals is independent of the direction and sense of the applied stress. At low temperatures, the yield stress depends markedly on the orientation of the crystals and the sense of the applied stress. This anisotropic behavior cannot be satisfactorily explained in terms of any of the mechanisms proposed so far, such as the mobility of jogs in screw dislocations, or the dissociation of a/2 [Formula: see text] screw dislocations on {112} planes.

DISLOCATION CONTRIBUTION TO THE FLOW STRESS OF POLYCRYSTALLINE IRON

New information confirms the existing evidence that, after subtracting any friction stress, the flow stress during cold work and creep of polycrystalline iron is determined mainly by the attractive junctions and general stress field of the three-dimensional dislocation network. Thus, recent experiments show none of the preference among the dislocations for the screw orientation that would be expected if jogs in screw dislocations were a main factor, and the grain boundaries during cold work and the subboundaries during creep also have no direct influence. On the other hand, the three-dimensional network is of the tightly linked type envisaged by this theory, and therefore contains a concentration of attractive junctions as well as of dislocations which fits the theory. The unevenness of the three-dimensional network, when the well-known cellular dislocation pattern has developed, does not affect the quantitative relationship between flow stress and network density, probably because it is the average density which is always measured and the weakest links which always determine the flow stress. The average proportionate contributions to the flow stress from the various sources are more or less calculable, but the actual contributions at individual weak links must vary greatly.

Temperature and Strain Rate Dependence of the Flow Stress in Molybdenum

AbstractThe effect of orientation on the temperature and strain rate ependence of the flow stress of molybdenum single crystals is investigated over the temperature range from 195 to 413°K. The values of the activation parameters ΔH, w, and v are calculated assuming that a single mechanism is rate controlling. It is found that the activation volume at constant stress is a function of the temperature. This together with other results suggest that the deformation is controlled by more than one thermally activated mechanism. An explanation is proposed based on both the overcoming of the Peierls barrier, and the non‐conservative movement of jogs in screw dislocations. The results also indicated that in the range of temperatures from 300 to 350°K there is a change in the rate controlling deformation process.

The Effect of Orientation on the Yielding and Flow of Molybdenum Single Crystals

AbstractThe influence of the orientation with respect to the direction of stresses has been investigated over the temperature range 77 to 413 °K. At temperatures below 300 °K the limit of the proportionality of strain to stress and the rate of work‐hardening depend markedly on the orientation. At temperatures above 300 °K the yield stress is practically independent of the orientation and the crystals can experience a large elongation without necking. Crystals with the tensile axis orientated in a direction near the centre of the unit stereographic triangle exhibit three work‐hardening stages. Slip lines and etch pit observations have shown that profuse cross‐slip of screw dislocations is a characteristic feature of the deformation of molybdenum single crystals. An explanation, based on the mobility of the jogs in screw dislocations, is proposed for the orientation dependence of the yield stress.

Long‐Range Elastic Field of Semi‐Infinite Dislocation Dipole and of Dislocation Jog

AbstractExpressions are given for the displacement field and the dilatation stress of a semi‐infinite dipole of infinitesimal width. This corresponds to a long‐range approximation for a dipole of finite width terminated within the crystal. The expressions also apply to a jog in a dislocation. Apart from these angular dependence, the displacement field decreases with distance as r−1 and the stress field as r−2.