Oriented Copper Single Crystals Research Articles

Formation of dislocation structures during cyclic deformation in near-[001] multiple-slip-oriented copper single crystals

Dislocation structures in [001]-oriented copper single crystals have historically been studied at relatively low plastic shear strain amplitudes (γpl). Herein, the dislocation structure is investigated across a wide γpl range of 1.7 ∙ 10−4–1.7 ∙ 10−2. When γpl < 1.5 ∙ 10−2, the dislocation structure comprised a labyrinth with a set of parallel (100) and (001) walls. However, as γpl approached 1.5 ∙ 10−2, the dislocation structure changed to a cell structure to accommodate the higher plastic strain. The formation plane of the cell boundary depends on which slip system is activated as the primary slip system.

Analysis of deformation bands and cell structure in cyclically deformed near-[formula omitted]-oriented copper single crystals

In this study, we investigate the deformation bands (DBs), viz. DBI and DBII, and cell bands (CBs) in the near-1¯11-multiple-slip-oriented single crystals during cyclic deformation. Three different types each of DBIs [(111), (1¯1¯1), and (1¯11¯)] and DBIIs [(2¯11), (1¯21), and (1¯12)] can be summarized as the primarily activated slip plane and the combination of activated primary and coplanar slip systems, respectively. The formation planes of CBs [(121), (1¯1¯2), and (2¯11¯)] are perpendicular to the cross-slip plane and parallel to the primary slip direction. The highly symmetrical characteristics of multiple-slip-oriented single crystals can produce inconsistent correspondences between DBs and CBs.

Assessment of Internal Stresses Using Dislocation Dipole Heights in Cyclically Deformed [001] Copper Single Crystals

There have been a number of studies on dipole separations in cyclically deformed FCC single crystals in single slip while there are no such studies in multiple slip. The dipole heights provide insight into the presence of long-range internal stresses (LRIS). In this study, we investigated how LRIS compare with the single slip studies through measuring the dislocation of dipole heights. [001] oriented copper single crystals were cyclically deformed in strain-control to saturation at ambient temperature. Transmission electron microscopy (TEM) confirms a labyrinth dislocation microstructure with high dislocation density walls and low dislocation density channels. The maximum dipole heights under the saturation stress were approximately independent of location, being nearly equal in the walls and within the channels. This, by itself, supports a uniform stress across the microstructure and low long-range internal stresses. The maximum value for dipole heights suggests dipole strengths (local stresses) that are about a factor of 2.4 higher than the applied stress based on the usual athermal equations. Considering the small “extra” stress that may be provided by tripoles or small dislocation pile-ups, a nearly homogenous stress distribution with only small internal stresses may be present, which is consistent with the observation of uniform dipole height across the heterogeneous dislocation microstructure. This observation that the stress state appears to be homogenous and higher than the applied stress has also been reported in the case of cyclically deformed metals in single slip.

Development of Deformation Bands During Cyclic Deformation of Multiple Slip Oriented Copper Single Crystals with multiple slip orientation

Development of Deformation Bands During Cyclic Deformation of Multiple Slip Oriented Copper Single Crystals with multiple slip orientation

Observation of Fatigue Dislocation Structures Formed in [001] Multi-slip Oriented Copper Single Crystals by High-voltage Scanning Transmission Electron Microscopy

Observation of Fatigue Dislocation Structures Formed in [001] Multi-slip Oriented Copper Single Crystals by High-voltage Scanning Transmission Electron Microscopy

Formation mechanisms of cyclic saturation dislocation patterns in [0 0 1], [0 1 1] and [formula omitted] copper single crystals

This work reveals the formation mechanisms of saturation dislocation patterns in three typical multiple-slip oriented [0 0 1], [0 1 1] and [ 1 ¯ 1 1 ] copper single crystals. Compared with the single-slip oriented copper single crystals, the three multiple-slip oriented ones show very different dislocation patterns. It was found that the dislocation patterns in cyclically saturated copper single crystals are the Labyrinth structure for [0 0 1], wall structure for [0 1 1] and cell structure for [ 1 ¯ 1 1 ] , respectively. Based on a two-phase structure consisting of persistent slip bands and veins for single-slip orientation, the formation mechanisms of the dislocation patterns in multiple-slip oriented crystals are proposed as follows: the formation of the complex dislocation patterns depends on the activating slip system. The easy operation of the critical secondary slip system will contribute to the formation of the Labyrinth structure. The activation of the coplanar secondary slip system will be beneficial to formation of the cell structure. If no secondary slip system is activated, the wall structure is more prone to appear. Finally, the intrinsic relationship between various dislocation patterns and face centered cubic crystal structure was established.

Long-range internal stresses in monotonically and cyclically deformed metallic single crystals

Abstract Selected experimental measurements and theoretical predictions for the magnitude of long-range internal stress in monotonically and cyclically deformed metals are assessed and recently developed, spatially-resolved X-ray micro-beam techniques for direct measurements of long-range internal stress are discussed. The results of previously reported differential-aperture X-ray microscopy spatially-resolved measurements of long-range internal stress in dislocation-cell interiors in monotonically deformed copper are compared with predictions and analyses associated with the composite model of deformation. In addition, the results of volume-integrating X-ray line-profile measurements and spatially-resolved differential-aperture X-ray microscopy measurements of strains in &lt;100&gt; oriented copper single crystals that were cyclically deformed to pre-saturation (without persistent slip bands) are presented.

Deformation banding and shear banding in single crystals

A theory of rigid-plastic single-crystal deformation based on the hypothesis that the crystal follows a mode of deformation that minimizes the plastic power is developed. In addition to the usual homogeneous slip modes, plastic power minimization in the present theory also extends over inhomogeneous deformation modes in the form of deformation bands or shear bands. Bands are assumed to originate from unstable perturbations of the lattice orientation. The evolution of the banded substructure with continued deformation depends on the mobility of the interband dislocation boundaries. The theory predicts the evolution of substructural morphology and lattice orientation with deformation. These predictions agree quantitatively with experimental observations in initially ( 1 1 2 ) / [ 1 1 1 ¯ ] - and (0 0 1)/[1 1 0]-oriented copper single crystals that undergo shear banding and deformation banding, respectively, when subjected to plane strain deformation.

Onset of abnormal subgrain growth in cold rolled {1 1 0}〈0 0 1〉 oriented copper single crystals

Copper single crystals of {1 1 0}〈0 0 1〉 orientation were cold rolled and annealed at 300 °C to study both the deformed state and early stages of static recovery. A homogeneous cellular substructure was generated during rolling with normal direction/rolling direction (ND–RD) sections revealing intersecting bands aligned at an acute angle to RD. These bands exhibit cyclic orientation changes about ND with amplitudes and wavelengths up to 10° and 10 μm, respectively. During annealing, cells situated at the extreme of these orientation perturbations undergo the most rapid coarsening; such a process is similar to the abnormal subgrain growth previously observed in {1 1 0}〈0 0 1〉 oriented aluminium single crystals.

Implications of linear relationships between local and macroscopic flow stresses in the composite model

Abstract Earlier results obtained by X-ray diffraction studies on tensile-deformed [001]-orientated copper single crystals have recently been re-assessed with respect to the evolution of the long-range internal stresses and the local flow stresses of the dislocation cell walls and the cell interiors. It was noted that the magnitudes of the long-range internal stresses and of the local flow stresses increase in good approximation linearly with the applied macroscopic flow stress. In the present work, the results of a similar analysis of earlier published X-ray data, which were obtained on tensile-deformed [001]-orientated Cu–Mn single crystals, are reported. When the friction stress of the alloy is taken into account, similar linear relationships to the case of deformed [001]-orientated copper single crystals were obtained. The implications of these results are analyzed in the framework of the composite model of crystal plasticity. It is shown that linear relationships of the type considered imply, in terms of the composite model, that the ratio between the local dislocation densities in the dislocation cell walls and the cell interiors must remain constant during deformation. This result is discussed with respect to the experimentally obtained data on local dislocation densities.

A Study of the Early Stages of Recovery in Cold Rolled {110}&lt;001&gt; Oriented Copper Single Crystals

Copper single crystals of {110}&lt;001&gt; crystallographic orientation were cold rolled to a true strain of 1.4. Specimens were cut from the as-deformed crystals with all surfaces mechanically ground and deep-etched in concentrated nitric acid to minimise the likelihood of surface nucleation of recrystallized grains during subsequent annealing. The early stages of static recovery were studied by annealing specimens at 300 oC. The crystallographic features of the deformed and annealed microstructures were determined by high resolution electron backscatter diffraction. It was observed that deformation was homogeneous with the microstructure in ND-RD plane exhibiting two complementary sets of intersecting bands at ~+ 35o to ND. Along these bands and in the microstructure, in general, there was an overall spread in orientation about ND towards {110}&lt;112&gt;. However, the orientation spread along these bands was cyclic, that is, sinusoidal orientation gradients were generated about ND with amplitude of up to 20o and wavelength 5-10 µm. Annealing resulted in the preferred growth of cells that have orientations at the edge of the orientation spread of the deformation substructure. This localized coarsening of the microstructure is similar to the discontinuous subgrain growth observed in {110}&lt;001&gt; oriented Al single crystals and indicates that discontinuous subgrain (cellular) growth can also occur in metals of lower stacking fault energy.

Local and Global Effects in Texture and Microstructure Observed after Channel-Die Compression of Copper Single Crystals and after Cross-Rolling of Copper Sheets

The change of the deformation path leads to destabilization of the substructure and affects the texture of the deformed metal. The observed changes of texture and microstructure are, as a rule, significant and their characteristics depend on the geometry of the deformation process. Previous investigations on copper (and copper alloy) samples after deformation by rolling and channel-die compression were based on X-ray pole figure measurements and on observations in the light microscope. Hereby only global texture and structural characteristics have been obtained. The present study is mainly based on measurements of individual crystal orientations performed by ACOM (Automated Crystal Orientation Measurement, “Automated EBSD”) in the SEM which enables a precise local analysis of the investigated phenomena. For the channel-die experiments, (1 1 2)[1 1 -1] and (1 1 2)[1 -1 0] oriented copper single crystals have been used. After pre-deformation, a second deformation step has been carried out in transverse direction. The {1 1 2}&lt;1 1 0&gt; orientations are destabilized by channel-die compression, and clusters of layers develop which are composed of complementary {1 1 0}&lt;1 1 2&gt; components. The deformation process in polycrystalline sheets after rotating the rolling direction leads again to a distinct disintegration of the microstructure and destabilization of the b fiber. This process of microstructure reorganization after pre-deformation is fast and of high dynamics.

Brass-type shear bands and their influence on texture formation

The issues of brass-type shear band formation and the evolution of band microtexture components are addressed. The analysis is based on bands developed by plane strain compression in twinned {112}〈111〉 oriented copper single crystals deformed at 77 K. Substantial progress in understanding the formation of the bands was possible thanks to systematic local orientation measurements using transmission electron microscopy (TEM). The TEM orientation maps allowed investigation of the way in which unstable behavior of twin-matrix layers leads to the brass-type shear bands. It has been found that several important transitions of the deformation textures are correlated with shear banding. Early stages of shear band formation are the result of the equally effective operation of two coplanar slip systems on the {111} slip planes. This process leads to the lattice rotation about the 〈110〉 axis and to the rise of Goss orientation. For well-developed shear bands, a second rotation about the 〈112〉 direction is observed. It is accompanied by activation of new slip systems. The observed disappearance of matrix components from the shear band microtexture is the result of twinning within reoriented matrix lamellae. In the twin-oriented areas, the dominance of one of two coplanar slip systems ultimately leads to the formation of the brass texture component.

A second-order phase-transformation of the dislocation structure during plastic deformation determined by in situ synchrotron X-ray diffraction

In situ X-ray diffraction peak profile analysis during plastic deformation in [0 0 1] oriented copper single crystals was carried out using synchrotron radiation. Characteristic changes of the hardening coefficient indicate that a transition occurs from stage III to stage IV which has been observed for the first time in a single crystal under low temperature deformation conditions. The long-range internal stresses, the dislocation arrangement parameters and the fluctuations of the dislocation density show non-monotonous changes at this transition suggesting that the dislocation structure, especially within the cell-wall regions, reveals a second-order phase transition. A microscopic dislocation model is introduced which not only illustrates the break of symmetry, but also describes well the development of new grains (“fragmentation”) during plastic deformation.

TEM Orientation Mapping Applied to the Study of Shear Band Formation

The formation of brass-type shear bands (SBs) in twinned microstructures of \({\rm C} \{ 112 \} \langle 111 \rangle \) oriented copper single crystals, has been investigated after channel-die deformation at 77 K. Setting up a system for making high-resolution orientation maps using transmission electron microscopy (TEM) has opened new advantageous circumstances for the analysis of orientation changes within SBs. This method with spatial resolution higher than 10 nm allows an examination of microstructure images composed of nanoscale sub-cells forming SBs structure. The early stages of SBs formation are the result of equally effective operation of two slip systems operating on the {111} slip planes which could be represented by a ‘resultant super-system’ of \(\{ 111 \} \langle 112 \rangle\) type. This process leads to the lattice rotation about \(\langle 110 \rangle \) axis and to the rise of Goss orientation within the band. A minor group of components is observed near \(\{ 114 \} \langle 221 \rangle \), arising from the near primary matrix orientation. For well-developed SBs, a second rotation about \( \langle 112 \rangle \) direction is observed. This tendency, resulting from the \(\{ 111 \} \langle 110 \rangle \) type slip systems operation, is usually accompanied by activation of new slip systems. Hence the process of SBs formation is regarded as a strictly crystallographic one.

The fatigue limits of copper single crystals cyclically deformed at constant plastic strain amplitudes

Based on systematic surface observations, experimental measurements on the fatigue limits of differently oriented copper single crystals cyclically deformed at constant plastic strain amplitudes are summarized, and an orientation dependence of the fatigue limit is sketched. It was found that the fatigue limits of crystals depend mainly upon the low-strain-amplitude dislocation structures, which are characteristic of the particular crystal orientations. When multiple-slip deformation is the main mode of deformation and ultimately produces stable lowenergy dislocation structures such as labyrinth and cell structures, the fatigue limit can be improved notably.

SEM-ECC Investigation of Dislocation Arrangements in Cyclically Deformed Copper Single Crystals with Different Crystallographic Orientations

The dislocation arrangements induced by cyclic deformation in some differently oriented copper single crystals were investigated using electron channelling contrast (ECC) technique in scanning electron microscopy (SEM). It is shown that the ECC technique can well be used to examine dislocation arrangements in fatigued copper single crystals, especially at higher imposed plastic strain amplitudes. The typical dislocation structures in the cyclically deformed copper single crystals detected by this technique are in good agreement with those found by transmission electron microscopy (TEM). Furthermore, the SEM-ECC technique shows some attractive advantages compared to TEM. For instance, ECC observation clearly reveals an evolutional process of dislocation structure from the vein structure of matrix formed at lower strain amplitude to the labyrinth structure formed st higher strain amplitude. Moreover, the exact observations of dislocation arrangements within cyclic deformation bands (DBs), which are rather difficult to achieve by TEM, are successfully accomplished using the ECC method. The DBs formed in cyclically strained copper single crystals may exhibit quite different microstructures, depending upon their crystallographic orientation and accumulated plastic strain, such as PSB ladder, wall and labyrinth structures. Finally combining the existing TEM results with the present SEM-ECC observations, we can state with certainty that the crystallographic orientation has a strong effect on the saturation dislocation features of copper single crystals.

Influence of crystallographic orientation on cyclic strain-hardening behaviour of copper single crystals

The cyclic strain-hardening behaviour of copper single crystals with various slip orientations is considered systematically. It is shown that the crystallographic orientation has a strong effect on the cyclic hardening behaviours of double- and multiple-slip-oriented copper single crystals. The initial cyclic hardening of differently oriented copper single crystals is mainly dependent on the modes and intensities of dislocation interactions between slip systems operating in the crystal, as well as on the possibility of cross-slip. A distinctive strain burst phenomenon has been frequently observed in the very early stage of cyclic hardening for critical double-slip-oriented crystals. A secondary cyclic hardening stage occurs readily late in cyclic deformation of coplanar doubleslip-oriented crystals.

Texture and Hardness in Wire Drawn [001] Copper Single Crystals

The crystallographic texture and Vickers hardness which develop during wire‐drawing of [001] oriented copper single crystals have been studied experimentally as well by simulations. The experiments revealed orientation changes producing cross‐shaped patterns in the {200} pole figures and important variations in the Vickers hardness across the diameter. Metallographic investigations showed the presence of deformation bands perpendicular to the initial 〈100〉 directions. By adopting a model for the velocity field inside the die, simulations have been carried out by using a Taylor type rate sensitive crystal plasticity model, including microscopic hardening. The simulated pole figures show the features of the experimental ones and the predicted stress levels correlate well with the measured hardness data.

Fatigue crack initiation and propagation in [210] oriented copper single crystals in vacuum and in air

The effect of environment on the fatigue life, crack initiation and propagation have been a subject of extensive investigations and numerous discussions for a long time. The purpose of the present work is to examine the environmental effect on fatigue crack propagation in copper compact tension (CT) specimens which allow them to control the crack initiation site and to observe crack growth on a relatively large area. A special attention is given to the crack propagation behavior and to the crack growth rate.