Polarity in Bending Deformation in InSb Crystals : II. Theory and Supplementary Experiments(Physics)

A geometrical consideration of the configuration of {111} tetrahedra in a bent crystal having the sphalerite structure shows that the type of bending is reversed between the primary slip plane and some of the secondary slip planes. This explains why the secondary slip is activated and the primary slip plane becomes forest-rich in β-bending. Two types of experiments establish the origin of the higher flow stress in β-bending compared with α-bending. It is concluded that the difference in the flow stress between the two types of bending in the deformation stage after the lower yield point originates mainly from the difference in the activity of the secondary slip system, while that in the early stage of deformation originates from the difference in the rate of increase in the density of screw dislocations due to the difference in the mobility between α-dislocations and β-dislocations moving on the primary slip plane

Work-hardening of Foil Crystals of Copper

An investigation has been made on the plastic properties of recrystallized copper foil crystals of which thicknesses are down to 6.6 microns. It has been found that stress-strain curves of single crystal and pseudo-single crystal (crystal having the cube-texture) specimens thicker than 50 microns consist of three deformation stages in a quite similar way to those of bulk single crystals and that the value of the work-hardening rate in the stage II of deformation decreases very sensitively with decreasing specimens thickness. Pseudo-single crystal specimens thinner than about 10 microns do not reveal the stage II of deformation, but the work-hardening rate takes a very high value when the tensile axis approaches to the [001] direction. The work-hardening rate of the well-developed stage II in 50.8 microns thick specimens elongated in directions near [011] is much lower than that observed in the specimens elongated in directions near [001]. A large fraction of slip lines observed on (100) surfaces of the foil crystals are clustered in early stages of deformation. This clustered distribution of slip lines becomes more remarkable with increasing strain when the tensile direction of the specimens is near [001]. On the contrary, when the specimens are elongated in directions near [011], the distribution of slip lines tends to be uniform as the deformation becomes larger. Some considerations are made on the mechanism of work-hardening on the basis of possible interactions between dislocations operating during deformation

Plastic Deformation of Foil Copper Crystals. II : Electron Microscopical Study

In order to study the relation between work-hardening characteristics of 10.0 and 50.8μ copper foil crystals and dislocation phenomena occurring in them, the distribution patterns of residual dislocations in the crystals have been observed as a function of strain, orientation, and specimen thickness. Dislocation tangles were found at an early stage in the deformation of a specimen that showed the lowest value of the work-hardening rate. Tangles developing only along one kind of slip planes were observed in specimens showing low work-hardening rates. On the other hand, in specimens with high hardening rates, the development of cell structure is found without exception. The structures of the cell boundaries become more complex and, at the same time, the sizes of cells decrease as the strain increases. Configurations which are thought to show the formation of sessile dislocations, and pile-ups against them were also observed. It is suggested that the cell structure is formed because of irregular and complex motions of dislocations determined by the complex internal stress field originating from dislocations accumulated during deformation

Distribution of Dislocations in Germanium Single Crystals during Plastic Deformation

Dislocation configurations in germanium single crystals developed during tensile deformation at 600℃ were frozen in by the rapid cooling of deformed crystals under load and investigated with etch pit technique. Distribution patterns of dislocation etch pits at various deformation stages were observed on two kinds of surfaces which were cut out parallel to the cross slip plane (111) and to the primary slip plane (111). Peculiar distribution patterns of etch pits were developed during stage I, namely, the stripe on the (111) surface and the dense zone on the (111) surface. Stripe patterns of dislocation etch pits were also observed on the surfaces cut out parallel to the critical slip plane (111) and to the conjugate slip plane (111). It was found that the stripes on (111), (111), and (111) surfaces and the dense zone on (111) surface were interrelated each other. Characteristics of the distribution pattern of etch pits were compared with those observed on f.c.c. metals

Strain-Rate and Temperature Dependence of Mechanical Behaviour in Germanium Crystals

The stress-strain characteristics and the development of the dislocation structure in germanium crystals are investigated as dependent on the strain rate and the temperature. The results are interpreted in the light of the dislocation behaviour which has been clarified by the foregoing paper. The shape of the stress-strain curve is similar for any set of the strain rate and the temperature chosen. It is concluded that the higher density or the higher velocity of moving dislocations in crystals results in the higher flow stress and the larger strain in each deformation stage. The essential difference between stage I and stage II lies in the difference in the dislocation arrangement and not in the dislocation density. The mobile fraction of dislocations at lower yield point is estimated to be of the order of several percent. It is found that, once forest dislocations begin to be active, stage I is never restored by any choice of the strain rate or the temperature in the subsequent deformation

Interaction of Dislocation with Atomic Order in Solid Solutions

A mechanism of the interaction between a dislocation and the atomic order, which is due to the coupling of the stress field of the dislocation with lattice distortion accompanied by ordering in superlattice alloys, is proposed. The interaction energy and the locking force against the motion of the dislocation are calculated for the superlattice of the β-brass type by using the quasi-chemical treatment developed by Iwata. The effect of thermal motion on the locking force is also considered on the basis of H. Suzuki\u27s treatment. The interaction energy and the locking force for an edge dislocation reveal a sharp peak at the Curie point of order-disorder transformation, while such a sharp peak is absent in a screw dislocation. The values for a screw dislocation are found to be 1～10 per cent of those for an edge dislocation. Furthermore, the short-range order hardening is expressed in terms of order parameters for the superlattice of the β-brass type

A Model for the Dynamical State of Dislocations in Crystals during Deformation(Physics)

The equilibrium state of moving dislocations in a crystal during the constant strain-rate deformation is discussed on the basis of three hypotheses. I. The configuration of immobile dislocations is such that static free energy of the crystal associated with existing immobile dislocations be as low as possible. II. There are certain equilibrium stationary values in the density and the velocity of moving dislocations which depend on the rate-controlling mechanism of dislocation motion and on the deformation condition. III. The equilibrium state of moving dislocations is determined so as to make the component of the flow stress associated with moving dislocations minimum to maintain the given strain rate. This model is shown to give a good description of the strain-rate dependence of the deformation behavior in germanium crystals at 600℃ observed experimentally

Dynamical State of Dislocations in Germanium Crystals during Deformation(Physics)

Experimental results in the strain-rate change tests on germanium single crystals done in a previous paper are analysed with the use of new velocity data for isolated dislocations. An equilibrium stationary state of moving dislocations appears in the deformation stage beyond the middle of stage 0 of the stress-strain curve. The velocity v and the density N_m of moving dislocations in the equilibrium state are observed to depend on the strain rate [ε] as v∝[ε]^ and N_m∝[ε]^, respectively, at 600℃. Transition of the state of dislocation motion from one equilibrium state to another by a sudden change of the strain rate during deformation is also investigated. It is concluded that the values of v and N_m in the equilibrium state at a certain temperature are determined completely by the strain rate and do not depend on the density of total dislocations in the crystal nor on the values of v and N_m which the crystal has assumed previously. A transient stage of about 0.5% in strain is found to exist when the state of dislocations motion is transferred from one equilibrium state to another by the change of strain rate