Deformation Of Copper Single 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 An evaluation of largely unpublished experimental rocking-curve data obtained on different crystallographic sections of deformed copper single crystals yielded a linear relationship between the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.

Determination of Long-Range Internal Stresses in Cyclically Deformed Copper Single Crystals Using Convergent Beam Electron Diffraction

Understanding long range internal stresses (LRIS) may be crucial for elucidating the basis of the Bauschinger effect, plastic deformation in fatigued metals, and plastic deformation in general. Few studies have evaluated LRIS using convergent beam electron diffraction (CBED) in cyclically deformed single crystals oriented in single slip and there are no such studies carried out on cyclically deformed single crystals in multiple slip. In our earlier and recent study, we assessed the LRIS in a cyclically deformed copper single crystal in multiple slip via measuring the maximum dislocation dipole heights. Nearly equal maximum dipole heights in the high dislocation density walls and low dislocation density channels suggested a uniform stress state across the labyrinth microstructure. Here, we evaluate the LRIS by determining the lattice parameter in the channels and walls of the labyrinth dislocation structure using CBED. Findings of this work show that lattice parameters obtained were almost equal near the walls and within the channels. Thus, a homogenous stress state within the heterogeneous dislocation microstructure is again suggested. Although the changes in the lattice parameter in the channels are minimal (less than 10−4 nm), CBED chi-squared analysis suggests that the difference between the lattice parameter values of the cyclically deformed and unstrained copper are slightly higher in the proximity of the walls in comparison with the channel interior. These values are less than 6.5% of the applied stress. It can be concluded that the dominant characteristics of the Bauschinger effect may need to include the Orowan-Sleeswyk mechanism type of explanation since both the maximum dipole height measurements and the lattice parameter assessment through CBED analysis suggest a homogenous stress state. This work complements our earlier work that determined LRIS based on dipole heights by assessing LRIS through a different methodology, carried out on a cyclically deformed copper single crystal oriented for multiple slip.

Deformation of copper single crystals: Comparison of experimental results with crystal plasticity simulations

A combined experimental and numerical study on deformation behaviour of single crystal copper is presented in this paper. High purity copper single crystals were fabricated and subjected to uniaxial compression loading at quasi-static strain rate. The stress-strain responses along four different crystallographic orientations were then extracted after determining the initial orientation by Laue Back-Refection technique. In order to study and compare the responses, a phenomenological crystal plasticity model was described and implemented in a crystal plasticity finite element based code. The key description of the model follows a generalized yield criterion that incorporates non-Schmid effects assuming cross-slip plays an important role on orientation dependence of the material. Using the model, the stress-strain responses of four different crystallographic orientations were investigated. Investigations were also carried out on the shape change of the deformed crystals along with lattice orientation mapping. Finally, details of slip activities of the deformed crystals were determined by comparing the orientation of slip lines with the theoretical traces of possible crystallographic planes. The identity of the experimentally determined active slip modes was matched with those determined by the simulations.

Identification of Dislocation Reactions and their Role in Uni-axial Deformation of Copper Single Crystals

This work shows the analysis of dislocation dynamics analyses of copper single crystal. A copper single crystal with uniaxial tensile loading axis along [1 1 1] crystallographic axis is considered. Each dislocation dynamics simulation cell is populated with Frank-Read sources randomly distributed on octahedral slip-systems. The strain-hardening behavior of a single crystal is controlled by interaction between dislocations which may result into formation of junctions. The interactions occurring between the dislocations, formation of junctions, occurrence of cross-slip and dislocation density evolution were analyzed. The contribution of individual reactions on the evolution of stress was then analyzed and strain-hardening coefficient representing each reaction was determined.

不均一変形した銅単結晶における初期段階の再結晶粒方位

The objective of the present study was to find the orientation relationship between a recrystallized grain at its initial stage and a deformation microstructure in a non-uniformly deformed copper single crystal. A tensile strain of 25% was applied to a 〈110〉 copper single crystal sample in which shallow grooves were made at both side faces before the tensile test to promote non-uniform deformation. A thin disc specimen prepared from the deformed sample was annealed in a high vacuum. A scanning electron microscope (SEM)/electron backscatter diffraction (EBSD) method was used to analyze the orientations of deformed and annealed states. There are two primary slip planes of the largest Schmid factor in a face-centered-cubic metal single crystal deformed along a 〈110〉 direction. In the present copper single crystal sample, both right-up and right-down band-like regions are formed in which either of the primary slips was activated. The arrangement of band-like regions on the overall sample surface was almost symmetrical. Between band-like regions, there were regions of patchy slip appearance, consisting of double-slip and single-slip areas. The band-like regions were rotated so that the slip directions moved towards the tensile axis. On the other hand, the rotation of patchy regions was relatively small. In the disc specimen annealed at 833 K, a recrystallized region was formed at the boundary between band-like and patchy regions. The recrystallized region consisted of two types of recrystallized grains having a twin relationship each other. Both types of recrystallized grains had an 〈111〉-rotated orientation relationship with the band-like region.

Molecular dynamics simulation of Bauschinger’s effect in deformed copper single crystal in different strain ranges

Plastic pre-strain may decrease the yield strength of metallic materials when stressed in the opposite direction, known as Bauschinger’s effect, which could considerably influence the performance of the materials. However, various processes on microscopic level associated with the Bauschinger’s effect are still not clear. In this study, defect generation, movement and annihilation in single crystal copper during cyclic tension-compression loading processes were simulated using the molecular dynamics method. It was observed that Bauschinger’s effect was asymmetrical and the strain hardening was more profound during compression. After plastic compression, the tensile fracture strain was increased. The absorbed energy was self-adjusted during the tension-compression cycles and kept relatively stable during the loading cycles. Efforts were made to understand the mechanisms responsible for these phenomena.

Investigation of the internal substructure of microbands in a deformed copper single crystal: experiments and dislocation dynamics simulation

We investigate the internal structure of microbands in a shear-deformed copper single crystal. The microstructure is characterized using high-resolution electron backscatter diffraction. The occurrence of microbands is due to the alternation of local orientation, which is characteristic of a deformation laminate. These microbands contain a substructure consisting of further local 1°-orientation alternations. A two-dimensional discrete dislocation dynamics model is used to describe the orientation substructure within the microbands. The boundary conditions for the simulation were estimated from the distribution of the geometrically necessary dislocation density obtained from the orientation map. The dislocation arrangement in the dynamic simulation explains the formation of the experimentally observed substructure.

Lamination microstructure in shear deformed copper single crystals

We investigate the formation of microscopic patterns in a copper single crystal deformed in a shear experiment. Using high-resolution electron backscatter diffraction imaging, we find a band-like microstructure consisting of confined areas in the sample with rotated lattice. Digital image correlation allows us to exactly determine the macroscopic state of deformation of the sample. This data can be used as a side condition to calculate the lamination parameters from the theory of kinematically compatible lamination of separate material regions, each deforming in single slip. The parameters given by the theory agree with the measured properties, i.e. a lattice rotation of 3° and a lamination normal rotated 7° counterclockwise from a 〈111〉 direction.

Shear localization in dynamic deformation of copper single crystals

Dynamic deformation of copper single crystals, especially of fatigued copper single crystals with different orientations, was conducted on a split-Hopkinson pressure bar apparatus. The strain rates were in the range 2 − 9 × 103 s−1. After dynamic deformation, the adiabatic shear bands (ASBs) were examined in a light microscope and SEM. The width and spacing of ASBs formed under different strain rates in a fatigued copper single crystal were measured and the spacing of ASBs is one-order of magnitude smaller than the theoretical predictions. The possible reasons for the discrepancy were discussed. The critical strains for the ASB formation in four different orientated single crystals at stain rate of about 4 × 103 s−1 were determined by examining the post-deformation specimens and dynamic stress–strain curves. It is clearly indicated that the critical strains for the ASB formation are orientation-dependent in copper single crystals. A simple microscopic mechanism for ASB formation in fatigued single crystals was proposed.

Orientation correlation in tensile deformed [0 1 1] Cu single crystals

Local crystallographic orientation of tensile deformed copper single crystals was investigated by the electron backscattering technique. Statistical evaluation of the data reveals the presence of an increased crystallographic correlation at the transition point between stages II and III of work-hardening. The transition state has the lowest probability of finding geometrically necessary dislocations in circular regions of radius smaller than 8 μm. According to the present results and other data showing that the relative fluctuation of the dislocation density has a maximum at the transition point, we conclude that the transition from stages II to III of work-hardening is similar to a second-order phase transformation of the statistical dislocation system.

The recrystallization of copper single crystals deformed at 4.2 K

The deformation of copper single crystals at 4.2 K occurs by a sequence of slip, twinning and slip in the twinned structure. Subsequent annealing of the deformed structures obtained at various points at this sequence of deformation permits the detailed nature of the deformed and recrystallized states to be related in a unique fashion. Material recrystallized from structures obtained prior to the occurrence of twinning yields randomly oriented grains. However, the recrystallization textures obtained from the twinned material show two sharp components both of which are obtained from a 40° rotation around the normal to the twinning plane. The two components grow along the original matrix–twin interfaces resulting in a new layered structure, which is coarser than that formed by plastic deformation. The origin of the two recrystallization texture components is interpreted in terms of the enhanced mobility of the 40° 〈1 1 1〉 tilt grain boundaries, which in the present layered twin–matrix structure lies parallel to the twin–matrix lamellae.

Simulation of high speed deformation of copper single crystals

Plastic deformation of copper single crystals was simulated by molecular dynamics using an embedded atom potential. The time step of molecular dynamics is on the order of 1 fs which corresponds to ultra high speed deformation. This paper reports the results of tension, bending, and compression tests. On notched tension surfaces, Heidenreich-Shockley partial dislocations formed near the tip of the notch as expected. In the absence of notch, creation of dislocations was quite difficult under tension. On compression surfaces, partial dislocations were generated near the wrinkle of the possibly redundant slip plane.

Plastic deformation of copper single crystals by simulation using X-ray Lang method and molecular dynamics

Copper rectangular parallelepiped single crystals with a notch have been extended or compressed. In a crystal with a notch, partial dislocations were created near the tip of the notch in elongation as we expected. It is hard to see where the dislocations were created just looking the displaced positions of atoms, but by a simulation of X-ray Lang topography, the creation of dislocations was easily observed. Before creation of dislocations, some indication was quite clearly shown. For compression dislocations did not start near the tip of the notch but started uniformly on the surface, the effect of notch was minor.

The early stages of fatigue and evolution of persistent slip bands in a copper single crystal

Low-amplitude constant plastic cyclic deformation of copper single crystals oriented for single slip [(1) over bar 23] was carried out at room temperature in air. The plastic shear strain amplitude was 1 x 10(-3). The observation of dislocation structure evolution in the early stages of fatigue and the investigation of the formation of persistent slip bands (PSBs) in the latter stage were conducted using the scanning electron microscopy electron channelling contrast technique. Inspecting the variations in shape and distribution of matrix walls for different numbers of cycles, dislocation evolution in the early cyclic deformation was roughly divided into two stages. During the evolution process, the primary edge dislocations on the primary slip planes and the screw segments between matrix walls may play a key role in the two successive stages respectively. From the observation of PSB initiation and of its morphology and dislocation structure, a possible mechanism for PSB formation was proposed. It was suggested that, once the spacing between matrix walls and the width of the matrix walls reached critical values, the collapse of a matrix wall which was caused by the unbalance of the forces exerted by crew segments could induce collapse of an adjacent matrix wall. Therefore a persistent slip line (PSL) was formed consequently. Along the PSL, the neighbour screw segments would strongly activate and finally induce the formation of the ladder structure of a PSB.

The early stages of fatigue and evolution of persistent slip bands in a copper single crystal

Abstract Low-amplitude constant plastic cyclic deformation of copper single crystals oriented for single slip [123] was carried out at room temperature in air. The plastic shear strain amplitude was 1 × 10−3. The observation of dislocation structure evolution in the early stages of fatigue and the investigation of the formation of persistent slip bands (PSBs) in the latter stage were conducted using the scanning electron microscopy electron channelling contrast technique. Inspecting the variations in shape and distribution of matrix walls for different numbers of cycles, dislocation evolution in the early cyclic deformation was roughly divided into two stages. During the evolution process, the primary edge dislocations on the primary slip planes and the screw segments between matrix walls may play a key role in the two successive stages respectively. From the observation of PSB initiation and of its morphology and dislocation structure, a possible mechanism for PSB formation was proposed. It was suggested that, once the spacing between matrix walls and the width of the matrix walls reached critical values, the collapse of a matrix wall which was caused by the unbalance of the forces exerted by crew segments could induce collapse of an adjacent matrix wall. Therefore a persistent slip line (PSL) was formed consequently. Along the PSL, the neighbour screw segments would strongly activate and finally induce the formation of the ladder structure of a PSB.

Characterization of self-similar dislocation structures by X-ray diffraction

The development of the statistical parameters of the dislocation structure during plastic deformation of copper single crystals (average dislocation density, and average dislocation density fluctuation) was investigated by the method of X-ray diffraction peak profile analysis. It is found that during the deformation process, while the dislocation density increases monotonically, the average fluctuation exhibits a maximum corresponding to the transition from stage II to stage III of work hardening. The fractal dimension of the dislocation structure was also investigated. A strong correlation was found between the fractal dimension and the relative dislocation density fluctuation.

Transmission electron microscopy observations of debris structure in deformed copper single crystals

Transmission electron microscopy observations of debris structure in deformed copper single crystals

Transmission electron microscopy observations of debris structure in deformed copper single crystals

Abstract The debris component of the dislocation substructure in copper single crystals deformed at 78 K was studied by weak-beam transmission electron microscopy. The following defects were identified: primary unfaulted dipoles, faulted dipoles, stacking-fault tetrahedra and defect clusters. It is shown that all these defects can be derived from primary dislocations. The distribution of dipole sizes as a function of flow stress suggests that they are refined by chopping as deformation proceeds; so just before fracture their lengths vary from 30 nm down to vanishingly small loops. The size distribution of stacking-fault tetrahedra shows a small dependence upon the degree of deformation and suggests that some equilibrium size of these defects is established in the presence of the other elements of the substructure. Small dot-like clusters of dimension below 2nm are most probably the remains of larger entities that have shrunk during warm-up to room temperature. Rearrangement of the structure, which occurs between 78 K and room temperature, may to a large degree explain the observed changes in electrical resistivity described in previous work by Niewczas et al.

Primary and secondary dislocation dipole heights in cyclically deformed copper single crystals

Copper single crystals were cyclically deformed in single slip to pre-saturation at ambient temperature. The microstructure consisted of dense dipole bundles separated by channels with low dislocation densities. The dipole height in the presaturation microstructure is approximately independent of location, being equal in the dipole bundles (or veins) as within the channels, for both primary and secondary dipoles. The maximum dipole heights suggest strengths that are about a factor of two higher than the flow stress. The above observations and the consideration of thermal activation to assist the separation of dipoles under stress suggest a homogenous stress distribution without internal stresses, although other interpretations are expressed in the literature.

Spectral analysis of acoustic emission during cyclic deformation of copper single crystals

Abstract Acoustic emission (AE) is investigated during fatigue at constant-plasticstrain control of copper single crystals oriented for easy glide, aiming at AE monitoring of structural transformation and dislocation self-organization during cyclic deformation. The results of AE analysis are compared with the cyclic response and hysteresis loop shape on different stages of fatigue. It is shown that the modern AE technique employing spectral analysis is sensitive to all essential structural changes in dislocation ensembles during fatigue such as matrix hardening, formation of veins and channels, persistent slip band (PSB) nucleation and development until crack initiation. The evidence is given for early identification of strain localization by means of AE. It is shown that the maximum of median frequency of the AE power spectral density at the intermediate stage of rapid hardening can be considered as an indicator of local softening followed by strain localization in PSBs. The moment of crack nucleation is...