Deformed Copper Crystals Research Articles

Misorientations and geometrically necessary dislocations in deformed copper crystals: A microstructural analysis of X-ray rocking curves

AbstractIn this study, the deformation-induced misorientations that are typically found in face-centred cubic single crystals deformed in single slip into stage II (and early stage III) of the work-hardening curve are discussed with respect to the experimentally observed broadening of X-ray rocking curves. By making use of well-established empirical relationships between characteristic features of the microstructure and the flow stress, some of the ambiguities of earlier interpretations of rocking curves could be avoided, and relationships between the half-widths of the rocking curves, the density of geometrically necessary dislocations, and the flow stress could be derived for both the tilt misorientations due to the kink bands lying perpendicular to the primary Burgers vector and the twist misorientations originating from the dislocation networks (grids, sheets) lying parallel to the primary glide plane. An evaluation of largely unpublished experimental rocking-curve data obtained on different crystallographic sections of deformed copper single crystals yielded a linear relationship between the broadening of the rocking curves and the flow stress. In terms of the predictions of the model developed, this implies that the ratio of the density of the geometrically necessary dislocations (that are responsible for the misorientations) to the total dislocation density remains constant during deformation, at least up to flow stresses of about 50 MPa. The absolute densities of the geometrically necessary dislocations are found to be a small fraction (at most ca. 5%) of the total dislocation densities. In terms of the evolution laws of deformation-induced dislocation boundaries proposed in the literature, it is concluded that both kink bands and grids/ sheets follow the characteristics of so-called geometrically necessary boundaries.

Misorientations and geometrically necessary dislocations in deformed copper crystals: A microstructural analysis of X-ray rocking curves

Abstract In this study, the deformation-induced misorientations that are typically found in face-centred cubic single crystals deformed in single slip into stage II (and early stage III) of the work-hardening curve are discussed with respect to the experimentally observed broadening of X-ray rocking curves. By making use of well-established empirical relationships between characteristic features of the microstructure and the flow stress, some of the ambiguities of earlier interpretations of rocking curves could be avoided, and relationships between the half-widths of the rocking curves, the density of geometrically necessary dislocations, and the flow stress could be derived for both the tilt misorientations due to the kink bands lying perpendicular to the primary Burgers vector and the twist misorientations originating from the dislocation networks (grids, sheets) lying parallel to the primary glide plane. An evaluation of largely unpublished experimental rocking-curve data obtained on different crystall...

Self-consistent experimental determination of the dislocation line tension and long-range internal stresses in deformed copper crystals by analysis of dislocation curvatures

The present TEM study on deformed copper single crystals had several objectives. In a first step, the line tensions of near-edge and near-screw dislocations were determined directly by a statistical analysis of the radii of curvature of dislocation segments that had been pinned in the stress-applied state. Next, using the experimentally determined values of the line tensions, the locally acting shear stresses and their spatial variations were evaluated. Finally, the local values of the deformation-induced long-range internal stresses and their spatial variation were analysed in terms of the differences between the applied stress and the local stresses. The whole analysis was done in a self-consistent manner. Based on the experimentally established values of the line tensions, equilibrium shapes of dislocation loops, approximated by ellipses, were constructed. It was found that the dislocation loops are much less elliptical, i.e. rounder, than in the classical “line tension” model of de Wit and Koehler. Comparison of the results with those of later theoretical studies in the so-called “relaxation” model yielded significantly better agreement. The magnitudes of the long-range internal stresses were generally found to be of the order of the applied stress with stress enhancement in the dense dislocation walls and back stresses in the areas with lower dislocation densities in between. These results are in line with the predictions of the composite model.

Cyclic behaviour and surface slip features in 〈111〉 oriented copper single crystals

New information about cyclic behaviour and surface deformation features have been obtained on 〈111〉 oriented copper crystals cycled in air and in vacuum at different stages of fatigue life. In this way a secondary hardening stage has been observed and different types of slip events have been distinguished; in particular, evidence of {100} glide has been obtained which had never been observed before at room temperature in cyclically deformed copper crystals.

Formation of dislocation structures during cyclic deformation of F.C.C. crystals—I. Formation of PSBs in crystals oriented for single-slip

The formation of persistent slip bands (PSBs) in cyclicly deformed copper crystals oriented for single slip has been investigated. Both macroscopic data, the stress-strain responses, the change of the shape of hysteresis loops and the nucleation stresses for PSB formation, and the direct TEM observations of dislocation structures at structural transition and saturation stages suggest that the formation of dislocation walls of PSBs takes place either through breach of dislocation veins in their centers along (111) planes or through a gradual development of walls alongside veins. While the former mechanism is dominant for low plastic strain amplitude cases, where the dislocation veins are well developed before structural transition; the latter is more important for high plastic strain amplitude cases, where the dislocation veins are incomplete at transition stage. The pre-existing dislocation structure is supposed to be an important factor affecting the structural transition. Various observations reported in the literature have also been discussed.

Nucleation of persistent slip bands in cyclically deformed copper crystals

Abstract It is suggested that the formation of persistent slip bands during cyclic deformation of copper single crystals occurs as the result of a transformation in an irregular dislocation microstructure (found after saturation in the harder parts of the crystal) to produce the so-called ‘wall structure’ characteristic of the slip bands. Micrographs of a specimen containing both wall and matrix structures show a definite relationship between the two on the basis of which a tentative mechanism for the transformation is proposed. The evidence presented also suggests that any theory intended to account for the wall spacing will have to be based on events occurring at, or shortly after, saturation rather than on the conditions found in the slip bands later in the test.

Stored energy of 78 K tensile deformed copper crystals

Copper single crystals (99.999% purity) of six different orientations and polycrystals (mean grain diameter d = 0.35 mm) were deformed in tension at 78 K. The energy release from 40 up to 400°C was measured by means of an annealing calorimeter (electron beam calorimeter). All specimens were observed to release energy only during recrystallization. The measured values of stored energy E s , are proportional to the flow stress squared but at constant flow stress the amount of energy stored depends on crystal orientation. Is Θ II the work hardening coefficient in stage II. the product E s · Θ II is found to be independent of orientation. The ratio of stored to expended energy of stage 11 amounts to about 7 per cent. These results are discussed on the basis of current work-hardening theories. It is concluded that only primary dislocations contribute essentially to the stored energy. General characteristics of the orientation dependence of recrystallization temperature and temperature interval are described.

Stored energy in deformed copper crystals

Stored energy in deformed copper crystals

Dislocation energy in deformed copper crystals: V M Polovov et al, Phys Stat Sol (a), 11 (2), June 1972, 421–431

Dislocation energy in deformed copper crystals: V M Polovov et al, Phys Stat Sol (a), 11 (2), June 1972, 421–431

Dislocations energy in deformed copper crystals

Measurements of the dislocation density and the energy released during recovery and recrystallization were used to calculate the specific dislocation energy in deformed copper crystals. The experimental data have been compared with the theoretical estimates on the energy stored by crystals with different spatial distributions of dislocations. The total energy of dislocations in deformed copper crystals has been shown to include the statistically averaged contributions from the short-range stresses due to the configurations similar to isolated dipoles or dispersed dislocations of opposite signs, as well as the long-range stresses from dislocation pile-ups or other dislocation groups. [Russian Text Ignored.]

The anisotropic hardness of plastically deformed copper crystals

The anisotropic hardness of plastically deformed copper crystals

Dislocation Distribution near the Surface of Weakly Deformed Copper Crystals

Dislocation Distribution near the Surface of Weakly Deformed Copper Crystals

The effect of dispersed phases upon the annealing behaviour of plastically deformed copper crystals

Abstract An electron microscopic investigation is described of the effect of high temperature annealing on deformed copper single crystals containing dispersed second phases of either cobalt or silica. Sections of selected orientation cut from the deformed crystals were annealed at 700°C. It was found that specimens deformed into Stage I recovered to the low dislocation densities present before deformation, whereas the crystals deformed to Stage II recovered to form structures consisting of sheets of dislocation networks on the primary slip planes. Several of the basic networks were analysed, and their formation and distribution are discussed in terms of a modification of the deformation structures. Annealing at temperatures at which the cobalt precipitate redissolved resulted in little further structural change. The ability of these crystals to resist recrystallization is ascribed to the stability of the recovered structures and the absence of suitable recrystallization nuclei, arising from the increased...

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.

Mechanical Hysteresis in Deformed Copper Crystals

Half-cycle loops measured at room temperature in copper crystals of an easy glide strained into stage I represented decrements of the order of 10−1 at strain amplitudes in the 10−5 range. Coating the crystals with chromium was useful in extending the amplitude range over which closed loops could be studied. The energy loss was attributed to unpinning of primary-dislocation-forest-dislocation interactions. The large modulus reduction could be accounted for by using the density of excess primary dislocations inferred from pertinent etch-pit studies.

The effect of dispersed silica particles on the recovery and recrystallization of deformed copper crystals

Single crystals of internally oxidized copper-silicon alloys were deformed by cold rolling and the changes occurring on annealing at 700°C have been followed by hardness testing and optical and electron microscopy. It was found that the dispersed phase could either cause an acceleration or retardation of recrystallization depending upon the interparticle spacing. Nucleation rate and growth rate of recrystallization nuclei are affected by comparable amounts with change of interparticle spacing and not a retardation of nucleation rate alone as observed in aluminium alloys.

The density and distribution of dislocations in deformed copper crystals

The density and distribution of dislocations in copper crystals deformed in tension have been studied using etch-pitting techniques. The dislocation density is found to be roughly proportional to the square of the flow stress and in quantitative agreement with other experimental and theoretical results. The dislocations are distributed in a rough cell structure after sufficient strain. Interaction between primary and secondary dislocations leads to the formation of dense dislocation networks, which grow and coalesce to form the boundaries of the cell structure. Glide polygonization occurs in large regions of lattice curvature where dislocations of one sign accumulate. The kink bands that separate regions of reverse curvature appear to originate at subboundaries that are effective dislocation barriers.