Single Glide Research Articles

Investigations of Plastically Deformed Copper Single Crystals in the Stress‐Applied State. I. A Study of the Dislocation Behaviour in the Surface Region and in the Bulk

AbstractCopper single crystals oriented for single glide were deformed in tension at 78 °K to various resolved shear stresses and were then neutron‐irradiated at 4 to 20 °K before stress‐removal in order to pin the dislocations in the stress‐applied state. A comparison of transmission electron micrographs obtained from the centre and the surface regions shows that, from early stage II onwards, the dislocation arrangement in the surface region corresponds to a lower stress than that in the centre. At the same time the dislocation density is distinctly lower in the surface region than in the interior. Furthermore, X‐ray investigations show that during deformation the primary glide plane is bent characteristically near the surface in the direction of the slip vector. Details of these results, which are in good qualitative agreement with flow stress measurements and electron microscope work of Fourie, are discussed and compared with the literature.

The interaction of dislocations with coherent cobalt particles in a copper matrix

Single crystals of copper oriented for single glide, and containing coherent precipitates of cobalt, were deformed in tension into stage I, and the dislocation distributions were determined by transmission electron microscopy of sections cut parallel to the primary glide plane. It was found that coherent particles with a radius of 120 Å remained coherent after deformation and were sheared with the matrix. However particles with a radius of 170 Å and above, spontaneously lost coherency on deformation and in some cases dislocations were found to have by-passed the precipitate by cross-slip, resulting in rows of prismatic loops of primary Burgers vector. These results are at variance with the conclusions of Gleiter, (1) but it is shown that his results are more consistent with the above interactions than with the mechanism which he proposes.

Relations entre lórientation de monogristaux de fer, leurs mecanismes de deformation par laminage et la nature des textures de laminage

The plastic deformation by cold-rolling of large monocrystalline iron samples can be analysed in terms of a triaxial stress system. The rolling textures have been experimentally determined by means of an X ray technique (Schulz method) for monocrystalline iron samples with various orientations; the results show that single and double glide deformation is preponderant and important enough to explain the origin of the various components of polycrystalline iron rolling texture, namely: {100} 〈110〉, {112} 〈110〉, {111} 〈112〉. It has been possible too, to discriminate the various cristallographic planes parallel to the rolling plane for one family, and the various possible rolling directions for one given orientation of the rolling plane.

Magnetostrictive Crystalline Energy of Dislocations in Ni Single Crystals and the Anisotropy of the Approach to Saturation

Recent micromagnetic calculations have shown that magnetostrictive interactions of internal stresses with the magnetization produce an additional magnetocrystalline energy. In cubic crystals the additional anisotropy energy processes orthorhombic symmetry. The crystalline energy induced by plastic deformation in Ni single crystals (oriented for single glide) has been investigated through an analysis of the anisotropy of the approach to saturation. Measurements were carried out on cylindrical disks for different applied fields and several degress of deformation. In particular in the (111)-plane the plastically deformed disks show a twofold and a fourfold symmetry axis in addition to the sixfold symmetry axis of the ideal crystal.

Forest Dislocations in Silver Single Crystals

Abstract The distributions of primary and forest dislocations in silver single crystals deformed in single glide by varying amounts into stage I and stage II of the work-hardening curve have been studied by the etch-pitting technique. The distributions of the primary dislocations found are in agreement with previous etch-pitting studies on f.c.c. metals. The distributions of forest dislocations are markedly different from those of the primary dislocations in that dense ‘strings’ of dislocations lying roughly perpendicular to the primary Burgers vector and parallel to the primary glide plane were found throughout stage I and into stage II. The number of strings and the dislocation density within them increase with strain while the density of the forest dislocations outside of the strings remains approximately equal to that of the virgin, as-grown crystal until the onset of stage II. The etch-pitted strings are believed to correspond to the primary dislocation bundles seen in transmission electron microscopy.

Experiments on the deformation of niobium single crystals

Abstract Thin foils were prepared from slices taken in selected orientations from crystals deformed in compression by single glide on (101) or (211) or by double glide on (211) and (211). At room temperature the structures observed after single glide were quite similar to those which have been reported for copper. In stage I, braids in the primary slip plane consisted mainly of edge dislocation multipoles, but more complex tangles containing many secondary dislocations were formed in stage II, and were joined into the continuous walls of a cell structure. The main new feature observed in crystals orientated for double slip was the formation of high angle boundaries after large strains. Few screw dislocations were retained in the room temperature structures, but foils from crystals deformed at 158°K contained fairly uniform distributions of long primary screw dislocations, together with many small prismatic loops. It is believed that screw dislocations from different sources cross-slip and mutually annihilate at room temperature, but are prevented from doing this by the frictional stress at low temperatures.

LATENT HARDENING AND THE FLOW STRESS IN COPPER SINGLE CRYSTALS

The latent hardening produced by straining copper crystals in single glide was investigated by measuring the flow stress on secondary systems. Specimens oriented for slip on these systems were spark cut from large prestrained crystals and tested in tension. These specimens did not always yield on the most highly stressed system; this behavior is a manifestation of the anisotropy introduced by the prestrain and was found only in certain portions of the stereographic projection.When the glide plane was changed, the flow stress increased. The increase ranged from 160% in early stage I to 40% in late stage II, except for systems with Burgers vectors at 90° to the prestrain slip direction, where systematically smaller increases were observed. The flow stress did not increase significantly when only the slip direction was altered.The anisotropy of the flow stress is closely related to the anisotropy of the dislocation distribution produced by single glide. In particular a reasonably good correlation appears to exist between the flow stress and the forest density. The strain rate and temperature sensitivity of the flow stress are unaffected by a change in stress system.The results are discussed in terms of current theories of the flow stress. It is concluded that while impurity interactions may be important in stage I, the flow stress is controlled mainly by forest interactions.

THE DEFORMATION OF NIOBIUM SINGLE CRYSTALS

Various orientations of single crystals of niobium, purified by ultra-high vacuum annealing, have been tested in compression at 295 °K and in tension at temperatures between 77 °K and 295 °K. The shear stress – shear strain curves show three-stage hardening in a manner similar to f.c.c. crystals. Analysis of the orientation dependence of the operative slip system suggests an asymmetry in the critical resolved shear stress for slip on {112} planes which increases with decreasing temperature. Explanations for this in terms of the various ways in which a [Formula: see text] type screw dislocation can dissociate have been proposed. It is found that dissociation on two {112} planes or composite dissociation on {110} and {112} planes leads to a satisfactory qualitative explanation of the experimental results.The dislocation distribution occurring as a function of strain has been studied for crystals of a single glide orientation deformed in tension at 295 °K. [Formula: see text] sections from crystals deformed into stage I contain clusters of primary edge dipoles. The density of secondary dislocations is low (~10%). Sections from crystals deformed into stage II were chosen such that the three-dimensional nature of the dislocation arrays could be investigated. The distribution shows strong similarities to those observed in copper crystals (Steeds 1966), i.e. edge multipole walls, tilt and twist boundaries. The density of secondary dislocations is high, being of the same order as the primary density.

Versetzungsanordnung und Verfestigung im Bereich II plastisch verformter Goldeinkristalle

Single crystals of gold oriented for single glide were deformed plastically in tension at 4.2°K or 295°K into stage II and the dislocation arrangement was subsequently stabilised by neutron irradiation. The largescale dislocation arrangment is characterized essentially by the predominance of the primary glide plane (layers, grids, dislocation groups) as well as of the plane perpendicular to the primary glide plane and the primary glide direction (walls). In contrast to stage I, the dislocation configurations in stage II involve also essentially dislocations of the secondary glide system. The existence of long-range internal stress fields of the order of magnitude of half the flow stress could be demonstrated by means of curved dislocations. The conclusion which can be drawn from the existence of the long-range internal stresses, the relatively small temperature effect on work-hardening, and the predominance of the primary glide system in the dislocation configurations in the slip-line pattern, and in the character of the axial path, is that the work hardening in stage II results from a distinct process related to the primary glide plane, in which the elastic interaction between the dislocations should provide the main contribution. The observations are briefly compared with the relevant work-hardening theories.

Influence of Plastic Deformation on the Clustering of Quenched-in Vacancies in Aluminum

Plastic deformation after a quench of aluminum is found to increase the densities of voids and dislocation loops remarkably. This effect is observed only when quenched specimens are deformed in a very early stage of aging which is comparable to the nucleation period of the defects. The increment of the defect density increases with increasing amount of deformation, depending on the mode of deformation: the deformation by a multiple glide is more effective than that by a single glide. The increment of the defect density does not depend on the quenching temperature, that is, the amount of quenched-in vacancies. These results indicate that the localized vacancies produced by the motion of jogs which are formed by the mutual cutting between dislocations enhance the nucleation of the defects.

Dynamical Dislocation Theory of Crystal Plasticity. I. The Yield Stress

The derivation is outlined of a general relation connecting the macroscopic plastic strain rate with the configuration and velocity distribution of dislocations in a monocrystal with a single active glide system. This can be simplified for particular cases, the most simple being the case of parallel straight dislocation lines. A new form of the dynamical theory of plasticity is applied to detailed calculations and compared with previous work. The major modification is the use of the equation v=v* exp[−D/τ] to express the quasi-viscous behavior of dislocation velocities. Here, v=dislocation velocity, v*= terminal velocity, D=characteristic drag stress, and τ=resolved shear stress. Also, a physical relation between dislocation density and plastic strain is derived. The nonlinear differential equation that results from combining the strain-rate equation with an equation that describes the loading machine is integrated. Approximate analytic solutions, and numerical calculations, are given for the upper yield stress and the initial portion of the stress-strain curve. The effects of initial dislocation density, characteristic drag stress, crosshead speed, machine stiffness, and dislocation multiplication rate on the upper yield stress are calculated. It is shown that the upper yield stress exceeds the cohesive stress at a critical crosshead speed. Delay times are also calculated for rapid load application followed by constancy of the load and compared with experiments for LiF. The effects of strain hardening are considered in a companion paper.

Three-stage hardening in tantalum single crystals

Three-stage hardening has been found to occur in tantalum single crystals deformed in tension over a limited range of orientations, temperatures and strain-rates. The orientation range is for crystals oriented favorably for single glide. The temperature range corresponds to T T m − 0.10 to 0.18. Above this temperature range stages I and II tend to disappear; below this temperature range the initial flow stress starts to increase rapidly and there is also an abrupt decrease in the uniform elongation. Increasing the strain-rate was found to be entirely analogous to decreasing the temperature. The slip direction is 〈111〉 and the slip planes approximate to those carrying the highest resolved shear stress, except at 4.2°K where {110} slip planes were observed. Twinning was also observed at 4.2°K; the twin system, which is of the type 〈111〉 {112}, was found to be the expected one for tensile deformation. Fracture occurred by cleavage at these low temperatures and by chisel edge necking at higher temperatures. The work-hardening rate in stage II is ~ G/600.

Die bildung von verformungszwillingen in kupfer-einkristallen

Tensile tests were performed on copper single crystals of various orientations at low temperatures. It was observed that the formation of twins was always preceded by the overshooting of the crystal axis. Also it was observed that just before twinning conjugate slip occurred. In both unirradiated and neutron irradiated crystals the twin plane was always parallel to the conjugate slip plane. Electron microscope transmission studies show prior to the twinning a dislocation distribution which is typical for single glide. This dislocation arrangement is not altered appreciably by the twinning. At least in the case of copper, all observations seem to confirm the twinning model proposed by Venables which is discussed in detail.

The detection of secondary slip during the deformation of copper and α-brass single crystals

Abstract Deviations from single glide during the deformation of Cu single crystals have been detected by following the orientation of the tensile axis using x-ray techniques. The deviations for room temperature deformation of some crystals can be explained if it is assumed that 5–10% of the elongation is produced by slip on the secondary systems and the remainder on the primary system. The deviations from single glide are much smaller in α-brass crystals which also show more overshoot, so that secondary slip is inhibited. It is suggested that secondary slip is produced near the heads of piled-up groups of primary dislocations at the ends of newly formed slip lines where the resolved shear stress on the secondary systems is high. Secondary slip is thus very localized, producing little strain, but it can give rise to a high forest density.

Dislocation distributions in deformed copper single crystals

Abstract Dislocation etch pit distributions and slip lines were studied on copper single crystals oriented for single glide and deformed in tension at 4·2°K. Slip lines on the cross slip plane were observed from the earliest stages of deformation and their character changed during the transition to stage II. The distribution of forest dislocations is much more isotropic and less homogeneous than that of dislocations crossing other planes. The ratio of the forest to other dislocation densities in stage I is about 1:15 but tends to 1 in stage II. The flow stress correlates better with the forest than with main glide dislocation density; twist experiments support this conclusion.

Dislocations and Glide in Lead Sulfide as a Function of Deviations from Stoichiometry and Doping Additions

Point defects induced in PbS by slight deviations in chemical composition about the stoichiometric ratio were shown in a qualitative experimental study to affect dislocation density and strength. A very small but reproducible increase in dislocation density was observed by an etch-pit method in single crystals of PbS and in silver-doped PbS having excess sulfur or excess lead as compared with the stoichiometric composition. With a prismatic punching technique to obtain a measure of the yield strength, a slight increase in strength was found to correlate with an increase in point defect concentration in PbS. An etch-pit and slip-line analysis of glide in stoichiometric PbS verified the single primary glide system {100}〈110〉.

Continuous distributions of dislocations. V. Twisting under conditions of single glide

The theory of continuous distributions of dislocations is applied to discuss the geometrical features of the twisting of a cylindrical crystal deforming by single glide. It is first assumed that the strains are small, and that the dislocations arrange themselves so as to produce no far-reaching stress, and explicit expressions for the shape changes, lattice rotations and dislocation distribution are derived. The theory is in reasonable agreement with the observations of Whapham & Wilman (1956) when the angle of twist per unit length is not too large. The expression for the shape of the glide surfaces is much simpler than that derived by Whapham & Wilman, who also applied a small strain approximation, but not consistently. It is shown that the consistent reduction of the complicated expression of these authors leads to the simple one of the present theory. Further, the correct shape of the glide surfaces for large strains is also derived using the boundary conditions employed by Whapham & Wilman. This predicts an asymmetry of the type observed in a severely twisted crystal before correction of the observations for macroscopic bending, although the predicted asymmetry is rather too large.

Continuous distributions of dislocations IV. Single glide and plane strain

The theory of the continuously dislocated crystal is applied to discuss the behaviour of a crystal which has deformed by single glide. When the single glide is also in one crystallographic direction only the deformation is two-dimensional, and this situation is treated in detail. The analysis assumes that the dislocations arrange themselves so that they cause no far-reaching stress. In single glide, the lattice lines originally normal to the slip plane are the orthogonal trajectories of a family of surfaces, the glide surfaces. It is shown that these surfaces are developable, and that this imposes additional restrictions on the dislocation density, which are not considered by Nye (1953) and which provide a basis for the classification of the possible states of dislocation. A convenient analytical solution is given of the general equations for single glide when the lattice rotations are everywhere small. The discussion of plane strain begins by treating the lattice deformation. The general equation governing the lattice rotation is given, and the necessary boundary conditions and methods of solution are discussed. The analysis is compared with that of Nye and illustrated by some examples of practical interest. More realistic problems are posed when the boundary conditions specify changes of shape of the specimens. To discuss these the relationship between the lattice, shape and dislocation deformations is considered, and it is shown how all these deformations can be found from the necessary boundary conditions on the shape deformation. The general solution, which is valid for large strains, is applied to a general class of bending problem, and equations relating the geometrical features of the lattice, and of lines scribed on the crystal are derived. The general analysis is illustrated by examples emphasizing certain confusing degeneracies arising in the very symmetrical situation of uniform plane bending (Nye 1953), and revealing the meaning of many valued solutions for the lattice rotation.