Dislocation Length Research Articles

The precipitation of point defects near grown-in dislocations during neutron irradiaton

Abstract Radiation damage associated with grown-in dislocations in crystals which have been irradiated with neutrons between 200 and 400°C is described. It is proposed that point defects precipitate near climbing grown-in dislocations because the capacity of these dislocations to absorb point defects is limited by the rate at which jogs can be nucleated. This limitation is likely to be important only in the early stages of damage formation when the total line length of dislocation in the crystal is low.

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.

超音波伝ぱ速度の応力依存性に関する実験的研究

Ultrasonic velocities in elastic materials vary with stress applied to them and this phenomenon has been used to determine the third order elastic constants of materials. On the other hand, a new experimental method of stress analysis, named“Acoustoelasticity”, has been developed which utilizes polarized ultrasonic shear waves similar to photoelasticity. This technique, however, has not been put into practice for commercial materials, because of the influences of some uncontrollable factors such as the rate of pre-worked plastic deformation to them.To study a possibility of practical application of this method, the ultrasonic velocities of longitudinal waves propagating perpendicularly to the stress axis of specimens stressed uniaxially were measured precisely in the present work. The materials used were carbon steel“S45C”, aluminum “A3B2”(92%), copper“CuBl-H”(99.9%) and 6-nylon. Furthermore, the modulus deviation calculated from the relation between strains and travelling time deviations was discussed.Using the sing-around method, the ultrasonic velocities were obtained from the travelling time of ultrasonic wave (5MHz) in the 10mm thick specimens. The experimental procedure was as follows: The stress was applied on the specimen and then released abruptly, and the change in travelling time responding to the instantaneous change in stress was measured.The results are summarized as follows:(1) In every material used, the travelling time deviation ΔT/T0 and the modulus deviation ΔM/M0 under a given stress are of the same order of the strain caused by the stress.(2) In copper, the relation between the modulus deviation and the strain is representable by a parabolic curve with little scattering. The results can be expressed by the equation ΔM/M0=Aε-Bε2, where A is a constant relating to the third order elastic constants, and B a constant relating to the density and the pinnig length of dislocation.(3) In annealed aluminum, the modulus deviation measured was in accordance with that expected from the third order elastic constants, but not in steel. The former was explained from that, because of a lot of impurity atoms, the mobility of dislocation would be reduced, and the later seemed to be due to pre-existent structures which would still remain after annealing at a relatively low temperature (250°C).(4) In 6-nylon, the relation between the modulus deviation and the strain shows almost a straigtht line with little scattering.

The acoustic emission from moving dislocations in aluminium

The acoustic emission during tensile tests is investigated for several types of aluminium alloys. It is found that the mean square amplitude of the continuous emission is proportional to strain rate and sample length. It is assumed that the continuous emission is generated by dislocation loops, which are created continuously at Frank-Read sources. According to this model the mean square amplitude of the continuous emission U2 is proportional to the total length of the mobile dislocations L and the size of the loops l: ∼LI. Information about l was taken from Kuhlmann and Wilsdorf's observations of slip lines at the surface of deformed aluminium single crystals.

Atomic simulation of the dislocation core structure and Peierls stress in alkali halide

Abstract Dislocation core behaviour was studied by determining the equilibrium arrangement of ions surrounding an a/2〈110〉 {110} edge dislocation in potassium chloride. A computer simulation method was used to solve the equations of motion of the ions interacting through a Coulombic potential, with a Born-Mayer repulsive contribution, between nearest neighbours. Two flexible boundary schemes were employed and their application and importance to the results are described. The observed difference between the Volterra description of the ion positions and the calculated equilibrium position constitutes the core field. This core field was examined in detail but its most important feature is a lattice expansion of about 0-5 b2 per unit dislocation length. Shear stresses were also applied to the models using flexible boundary conditions with results indicating a Peierls stress in the range of 12-7 to 32-4 MPa which is in reasonable agreement with experiment. The case of moving the dislocation was quite sensitive...

Dynamic observations in the HVEM of the influence of crystal orientation on the deformation and fracture behaviour of molybdenum single crystals

In-situ tensile experiments have been carried out on single crystals of molybdenum with four different orientations for the tensile axis [hkl] and foil plane (h′k′l′), namely [011](011), [100](011), [011](100), and [100](001). In all specimens the primary source of dislocation generation was observed to occur at particles, the specimen orientation influencing only the mode of dislocation propagation from the particles. The operative slip systems are found to be those having both a large Schmid factor and a small angle α between the operative Burgers vector b and the projection of b in the slip plane on to the foil surface, i.e. those for which screw dislocations can escape more easily at the foil surface. Quantitative application of a combined Schmid and surface-orientation factor has been examined in the present work and is discussed. The detailed dislocation interactions observed during straining are very dependent on specimen geometry. In the [011](011) specimen dislocation interaction is limited because only short lengths of edge dislocations propagate significant distances. For other orientations dislocation multiplication occurs by the interaction of mobile screw dislocations with either grown-in dislocations or other gliding dislocations. At higher strains, prolific dislocation activity is associated with the propagation of cracks. The movement of dislocations which have a Burgers vector inclined to the foil surface results in an effective thinning of the foil perpendicular to the foil surface and eventual failure is observed to occur by crack propagation along these thinned regions.

亜鉛単結晶の底面辷りの初期段階

An experimental study has been carried out to investigate the contribution of basal and nonbasal dislocations (forest dislocations) to the early stage of basal glide in 99.999% pure zinc single crystals compressed at room temperature. The relation between the basal shear stress and the shear strain was plotted and the increase of dislocation density during deformation was observed by means of the etch pit technique. The initial dislocation etch pit densities of the specimens used were 2.9×104∼3.7×104/cm2 on (0001) surface and 6.1×104∼5.2×105/cm2 on (11\bar20) surface. From these data, the length of basal and nonbasal dislocations per unit volume was calculated using equations developed by G. Schoeck. It was assumed that the density of forest dislocations did not change during the deformation since the critical resolved shear stresses for nonbasal slip systems are considerably higher than the stress employed in the experiments. The results obtained were as follows.(1) The multiplication stresses were approximately equal to the stresses required to break up the attractive junctions between basal and forest dislocations. (2) The yield stresses were represented by the sum of the stress necessary for the forest cutting and the internal stress due to the basal dislocations. From this result, it was concluded that the yield stress, was controlled by the forest cutting under the internal stress field of the basal dislocations.

Changes in strain-dependent internal friction during fatigue (of Al-alloys)

An investigation on the fatigue of an Al-3.5% Mg alloy in the annealed state has been performed by means of internal friction measurements evaluating, at different fatigue stresses and numbers of cycles, the curves expressing the dependence of the internal friction on the amplitude of vibration. By using the parameters of the Granato-Lücke segment of these curves, the total length of movable dislocation line per unit volume Λ and the mean free-to-vibrate dislocation length L c have been determined. Plots of Λ versus number of cycles may be divided into three stages: the first is characterized by an increase in the dislocation density up to a maximum whose magnitude depends on the applied fatigue stress; during the second stage the dislocation density decreases at a rate independent of the stress. The third stage, which progresses to fracture, is due to a second increase in dislocation density. These trends have been interpreted in terms of evolution of the dislocations structure due to the fatigue stress.

Model for dislocation climb by a pipe diffusion mechanism

Abstract A model for dislocation climb is presented which is suitable for treating climb processes such as those expected in dislocation networks. In the model mass transport is considered to occur by a special pipe diffusion mechanism where the climb force on a dislocation acts as the ‘driving force’. It is shown that the climb velocity is proportional to the second derivative of the climb force with respect to the dislocation length. Possible applications of the theoretical model are discussed.

Spannungsverläufe Nach Wechseln der Verformungsgeschwindigkeit an Metalleinkristallen I. Ursachen von Übergangsvorgängen Nach Wechseln der Abgleitgeschwindigkeit

The exact shape of the stress variations after a change in strain rate is influenced not only by the rate dependence of effective glide obstacles, but also by the changes in dislocation multiplication mechanism. Especially the density of active sources and the total length of dislocations emitted by one source per unit of time are rate sensitive. Various types of sources are discussed and also the strain dependence of source density is considered.

A new representation of the strain field associated with the cube-edge dislocation in a model of a α-iron

The displacement field around an edge dislocation core is examined in an attempt to quantitatively modify the linear elastic Volterra solution. The approach derives from a computer simulation to obtain the equilibrium atomic positions in a dislocated bcc crystallite using Johnson's potential to model α-iron. Unlike many previous calculations of this nature which employ rigid boundary conditions throughout the relaxation, the elastic media bounding the crystallite is here allowed to adjust in response to atomic readjustments within the crystallite. The procedure used to achieve flexible boundaries and its application to this problem is discussed in detail. This scheme permits linear elastic displacements at distances relatively far from the dislocation center. The difference between the computed strain field and the Volterra prescription results from nonlinear effects in the core, and is found to correspond to a net expansion of 0.25b2 per unit dislocation length. This is in accord with findings of experimental studies relating lattice parameters to dislocation densities. The details of this residual field are fairly well described in terms of an elliptical line source expansion center located approximately two Burgers vectors below the tip of the extra half-plane. Thus, these results, while obtained for model material, suggest that an edge dislocation may be characterized by the sum of two linear elastic fields; the Volterra field and an elliptical expansion field. It is found that this result is not explainable by third-order perturbation theories. Finally, we note that the addition of an elliptical dilatation field should have a number of important applications to dislocation theory and specific examples are outlined.

The elastic energy of a straight dislocation in an infinite anisotropic elastic medium

AbstractAn expression for the elastic energy per unit length of a straight dislocation in a medium of arbitrary anisotropy is derived in a form which is simply suited for numerical calculations. The expression utilizes laboratory coordinates throughout and, unlike previous analyses, its evaluation does not rely upon solving the roots of a sextic algebraic equation. Numerical results are presented for glide dislocations in three cubic metals of low, intermediate and large anisotropy — niobium: copper, and lithium.

MESURE DU FROTTEMENT INTÉRIEUR DE L'OR ÉCROUI ET IRRADIÉ AUX NEUTRONS SUR UNE INSTALLATION TRAVAILLANT DANS LE DOMAINE DU KILCHERTZ

The author studies properties of the Bordoni peak in 99,999 % gold. The following features are considered : influence of type and rate of coldwork on relaxation strength. After traction coldwork, the height of the Bordoni peak is roughly proportional to the rate of plastic deformation, relaxation features. The relaxation energies and attempt frequencies of the Bordoni peak are determined for poly — and single crystals. The broadening of experimental peaks is studied, effect of dislocation pinning on the Bordoni peak. One shows that the experience leads to a relation : Qmax-1 Λl2 where Qmax-1 is the height of the peak, Λ the dislocation density and l the mean loop length of dislocations which are implied in the phenomenon.

An evaluation of rate-controlling obstacles for low-temperature deformation of zirconium

The low-temperature plastic flow of alpha-zirconium was studied by employing constantrate tensile tests and differential-stress creep experiments. The activation parameters, enthalpy and area, have been obtained as a function of stress for pure, as well as commercial zirconium. The activation area is independent of grain size and purity and falls to about 9b2 at high stresses. The deformation mechanism below about 700° K is found to be controlled by a single thermally activated process, and not a two-stage activation mechanism. Several dislocation mechanisms are examined and it is concluded that overcoming the Peierls energy humps by the formation of kink pairs in a length of dislocation is the rate-controlling mechanism. The total energy needed to nucleate a double kink is about 0.8 eV in pure zirconium and 1 eV in commercial zirconium.

A critical test on theories of work-hardening for the case of drawn iron wire

A recent extensive set of experimental data and electron micrographs derived from drawn iron wire by G. Langford and M Cohen have been employed for a critical test of the most important theories of work-hardening. As a first step, electron micrographs taken by the named authors were compared with the dislocation models used in the different theories. When these micrographs were found qualitatively to conform to the model of the “unified theory of work-hardening” and to none other, they were employed to determine the numerical values of a few simply defined parameters, describing the geometry of the dislocation structure, which appear in that theory. The thus measured values of the geometrical parameters were inserted into the equations derived from the theory for a quantitative test of it. Specifically compared were the theoretical and experimental values of the average free dislocation length, and of the linear work-hardening coefficient, the shape of the composite stress strain curve, and the rate of energy storage. In all cases agreement within the accuracy of the measurements was found over the whole range of deformation used by Langford and Cohen, extending between 22 and 740 pct true tensile strain.

Time Dependent Internal Friction in Tin Crystals

The time changes in the amplitude dependent internal friction are studied in β-tin crystals, 99.99% pure, and oriented for the [001] slip. The measurements are made during the free decay of transverse vibration. Comparison of the results with the theory of Granato and Lucke leads to the following conclusions: (a) The length of movable dislocation increases as the amplitude of excitation is increased. (b) The length also increases with the duration of excitation at constant driving force, as log (γ t +1). This is considered to be due to breakaway from the atmosphere of solute atoms. After the breakaway, the diffusion of solute atoms from the atmosphere of the movable dislocation takes place, around room temperature. At low temperatures, the diffusion does not take place, but the brokenaway dislocation moves large distances in the lattice. The amplitude dependent internal friction is in this case caused by the interaction of the movable dislocation with the solute atoms distributed in the lattice.

Factors Affecting the Precipitation of NbC on Frank Partial Dislocations in Fe–Ni–16% Cr Austenitic Steels

AbstractThe effect of variations in alloy composition, quench rate, and deformation on the formation of FPP (Frank partial precipitation) has been studied by means of hardness measurements and electron microscopy. Solute concentration is the most important factor controlling the maximum area of FPP. The numbers of precipitate particles increase with dislocation density but the number per unit length of dislocation is generally lower the higher is the dislocation density. The efficiency of nucleation by a dislocation is therefore not increased by the prior cold work and this is consistent with nucleation by climbed loops. The free-vacancy profile near grain boundaries is used to explain the FPP-free zone (PFZ) width, and this is controlled by the rate of precipitation. Silicon additions accelerate the nucleation of NbC and promote FPP formation.

Electrical Properties of Dislocations in Ge and Si

AbstractThe occupation statistics of the energy levels which are introduced by dislocations in Ge and Si are carried out taking into account that charged dislocations are a strong perturbation for the energy levels of the valence and the conduction band. The result is a theoretical relation between the line charge of the dislocation and the apparent experimental Fermi energy which is obtained from the number of free carriers. Comparing this relation with Hall effect measurements the position of the neutral dislocation level in the energy gap and the dislocation length per unit volume that is electrically active can be determined. Possible mechanisms for the screening of charged dislocations are discussed. It turns out that former screening models are appropriate only at very low temperatures and that for a wide range of experimental conditions the screening is done by a rearrangement of free carriers.

Effects of Alloying Elements on the Mechanical Properties of Steels at Low Temperatures

The low-temperature tensile properties of dilute Fe–C, Fe–Nb–C, Fe–V–C, Fe–N, Fe–Nb–V–N, and Fe–V–N steels have been analysed. The major differences in the plastic behaviour of the alloys arise from their athermal stress/strain behaviour. The lower yield strength vs. temperature relations correspond qualitatively with the Peierls mechanism for thermally activated deformation. The activation volumes also agree well with expectations based only on the Peierls mechanism. The results suggest that the Peierls stress, kink energy, and shapes of the Peierls hills are insensitive to alloy composition and heat-treatment. The fact that higher yield stresses at 298° K also gave higher values of Tc , the temperature at which plastic behaviour becomes athermal, has been interpreted to mean that the product, ρL, of the density of mobile dislocations times the dislocation length swept out by a pair of kinks decreased as the athermal component of stress increased.

Stress Tensor of a Finite Dislocation

Expressions for the stress field of a dislocation segment are given in a general dyadic form, without reference to a particular coordinate system. They are derived from the formulae of Peach and Koehler, and limited to the case of a linear, isotropic, infinite continuum. The stress tensor due to a finite length of dislocation is expressed in the form c σ ∞ + σ ', which in the extreme case reduces to σ ∞ , the well-known result of an infinitely long dislocation. The stress field of an arbitrary dislocation network can be deduced by the simple addition of the stress field of each component segment, as a direct application of the present study.