Role of recovery in high temperature constant strain rate deformation

A model based on the three-dimensional distribution of dislocations is used to delineate the role of recovery during high temperature constant strain rate deformation. The model provides a good semi-quantitative explanation for classical work-hardening as well as for high temperature work-softening resulting from rapid recovery. It predicts linear work-hardening, whereby the ratio of the work-hardening rate,H, to the shear modulus,G, is constant when a crystal is tested in the absence of recovery. The slope of the stress-strain curve, θ, for high temperature deformation is related to the low temperature work-hardening rateH; the dislocation annihilation rate , the flow stress a, the free dislocation density ρ, the strain rate , and a parameter which is sensitive to the dislocation distribution. A modified version of the Bailey-Orowan equation for simultaneous work-hardening and recovery during constant strain rate deformation which is derived from the model takes the form

Rigid body translation in the (\bar 211) twin boundary in silicon

The rigid body translation accompanying a ( 11) twin boundary in silicon has been studied by transmission electron microscopy. From a detailed analysis of theα-type fringe systems in the 111, 311 and 2 0 common reflections, the following translation vector is deduced: [011], which is equivalent to [411] in the other crystal element. A slight deviation of this orientation is possible.     

Effects of back pressure on the superplastic forming of domes

The stress state during “simple” superplastic bulge forming (without a back pressure) is different from that when a back pressure is applied. In the former procedure, specimens or components are deformed under a biaxial tensile stress state, while in the latter, the deformation is achieved under the combination of a biaxial tensile stress and a uniaxial compressive stress state. Both theoretical and experimental studies have shown that when a back pressure is present, the deformation cannot be treated as simply governed by the difference between the forming pressure and the back pressure. The analytical expressions for the forming relationships and the influence of back pressure on experimental m-log (where m is the strain-rate sensitivity and is the equivalent tensile strain rate for bulge forming) relationships for Zn-22 wt% Al and Zn-4 wt% Al-1% Cu are given. Results show that with increasing back pressure, the m-log curve shifted towards higher strain rates, but the maximum m values were not affected.     

Non-linear response of internal friction to tensile strain rate and frequency during plastic deformation of high-purity aluminium

The internal friction of high-purity aluminium during the process of plastic deformation was measured by a middle torsion pendulum on a modified tensile testing machine. The effects of tensile strain rate, , in the range of 0.73×10^–6 to 50×10^–6s^–1, and frequency of internal friction measurement, f, in the range of 0.38 to 2.6 Hz were studied. The results showed a non-linear dependence of internal friction, Q ^–1, on and f ^–1 or on (=2 f). The interrelationship between internal friction during the process of plastic deformation and dislocation motion, and the effect of non-linearity on the dynamic behaviour of dislocations are discussed.     

Anisotropic flow and fracture in beryl [Be3Al2(SiO3)6]

Flow and fracture resulting from Vickers indentation testing on {0 0 0 1} and {10 0 } planar orientations have been examined. Flow characterized by indent shape differentiation was analysed to belong to the slip system with planes of the types { 10 0} and {11 0}. The ensuing fracture paths were resolved to propagate along {1 0 0} and {1 1 } cleavage planes whileK _c values obtained for them were 0.196 and 0.248 MPam^1/2, respectively.     

Effect of superplastic deformation on the grain size and tensile properties of Al-6.2Zn-2.5Mg-1.7Cu (7010) alloy sheet

An Al-Zn-Mg alloy (7010) was cold-rolled and annealed to produce a small recrystallized grain size, and superplastically deformed in the temperature range 475 to 520° C at strain rates to 2.8×10^–3 sec^–1. At 500° C and sec^–1 superplastic elongations up to 350% were obtained, but above about 60% elongation the residual room-temperature tensile properties after heat treatment decreased due to increasing grain-boundary cavitation. Grain growth rates were increased by superplastic strain.     

Failure crack orientation at ductile shear fracture of Fe80−x Ni x B20 metallic glass ribbons

Orientation of failure cracks of oblique mode at ductile shear fracture are measured for Fe_80–x Ni _x B₂₀ (x=10, 20, 30, 40, 50, 60) metallic glass ribbons (MGR) uniaxially extended with strain rate from 3.3×10^–6 to 1.25×10^–3 s^–1 at temperatures 300, 77 and 4.2 K. An angle between the failure crack and tension axis is found to depend non-monotonously on nickel concentrationx and strain rate . These dependences are probably due to the presence of dilatancy in shear bands and its variation as a function of concentration, strain rate and temperature.Mean values of quenching stresses in ribbons are estimated by comparing experimentally measured values and those predicted by T. Thomas in 1953.     

Load relaxation studies of germanium

A series of compressive load relaxation experiments were conducted on germanium single crystals in the temperature range 400 to 885° C. The curvature of the log-log data obtained from load relaxation tests changes from concave upward to concave downward as the test temperature increases at fixed stress level, or as the strain level increases at fixed temperature. At intermediate temperatures, 600° C, the transition from concave upward to concave downward curvature happens on a single relaxation curve. These observations are consistent with the two-branch rheological model proposed by Hart to explain the deformation behaviour of metals and were analysed in terms of this model. The transition from concave upward to concave downward curvature could be moved to higher temperature by doping germanium with gallium, which decreases the dislocation glide velocity relative to that in pure germanium. The transition could be shifted to lower temperature by compressing samples along [1 1] rather than [1 0] because the [1 1] orientation favours cross-slip while the [1 0] orientation does not. Dislocation dipoles and straight dislocations dominated the microstructure of samples which had concave upward log-log curves, while well-developed dislocation cell structures dominated the microstructure of samples which yielded concave downward curves. The observed changes in the curvature of the load relaxation curves and the dislocation structure both indicate the increased importance of dislocation climb with increasing temperature. When compared through the Orowan equation, the load relaxation results are in good agreement with published stress-dislocation velocity data.     

HREM study of atomic image of single crystal indium phosphide

This paper reports some experimental results of high resolution electron microscopy (HREM) studies on single crystal indium phosphide (InP) along the [0 0 1] zone axis. Using 400 kV electrons, with defocus value about 46.0 nm, the optimum conditions for structure imaging for both In and P atoms were found to be about 26.0 nm. Decreasing the specimen thickness to about 15.0 nm, only atomic images of P remain; increasing the specimen thickness to about 37.0 nm, only atomic images of In remain. These experimental results are in good agreement with computer simulation. It was also observed that for bent crystal deviating from the [0 0 1] axis, the bright spots, corresponding to In and P atomic columns in high resolution structure imaging, are elongated at a deviation angle equal to 0.18 degrees, the two bright spots are connected together along the direction of the [1 1 0] zone axis. This phenomenon is also confirmed by computer simulation. In the experiment, a pair of dislocation waves were observed with apparent Burgers vectors of and while the actual Burgers vectors may be and .     

Creep behaviour of polyethylene and polypropylene

Tensile creep tests and stress reduction studies during creep have been carried out for polyethylene and polypropylene. The results obtained suggest that a consistent approach for the presentation of creep data for these polymeric materials can be obtained since the creep curves at 293K for polyethylene and polypropylene over a wide stress range can be superimposed by describing the variation of creep strain,, with time,t, as= ₀ + _p [1 – exp (–K t)] + t, where ₀ is the initial strain on loading, _p is the primary creep strain, is the secondary creep rate, andK is a constant.     

The constant stress tensile creep behaviour of a superplastic zirconia-alumina composite

A detailed study was conducted to evaluate the constant stress tensile creep behaviour of a superplastic 3 mol% yttria-stabilized zirconia-20 wt% alumina composite. The comprehensive experimental results indicate that creep deformation may be expressed in the form exp(–585 000/8.3T), where is the steady-state creep rate, is the imposed stress, is the linear intercept grain size andT is the absolute temperature. Microstructural observations revealed that there is very little dislocation activity, or change in grain size or shape. A detailed analysis was conducted to evaluate the possible rate-controlling mechanisms in terms of the experimentally determined mechanical properties and the microstructural observations. Based on the maintenance of an equiaxed microstructure and the strong grain size and stress dependence, it is concluded that creep occurs by a grain-boundary sliding/grain rearrangement process.     

On the theory of plasticity with smooth surfaces of loading

The well-known theories of plastic yield with smooth surfaces of loading are developed and generalized on the basis of a model of a nonlinear anisotropically hardened medium based on the concept of slip. Unlike the commonly used procedure of application ofa priori known laws of hardening (variation of the surface of loading in the process of plastic deformation), we suggest a method for the experimental evaluation of a universal function of the material appearing in the constitutive equations for arbitrary complex loading processes including elastic unloading and plastic deformation in the direction opposite to the initial one. The constitutive equations are relatively simple and, hence, can easily be used for the statement and solution of boundary-value problems in the theory of plastic yield. Dnepropetrovsk State University, Dnepropetrovsk. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 33, No. 6, pp. 63–70, November–December, 1997.     

Tunneling with very long relaxation times in glasses,organic materials,and Nb-Ti-H (D)

The long-time (t=10–200 h) heat release from glasses, from organic materials, and from Nb-Ti-H (D) was measured at 30T70 mK. For Suprasil W glass, Dimethyl-Siloxan, Stycast 1266, Stycast 2850 FT, Vespel, and for Nb-Ti-H (D) with various Ti and D concentrations, we found . Typical values are = 0.05 nW/g for the organic materials and for Nb-Ti-H (D) and = 0.005 nW/g for the glass att=100 h after cooldown from room temperature. For charging temperaturesT _i <5 K, we find the predicted dependence (investigated for Suprasil W glass and for Nb-Ti-D). The observed time and temperature dependences agree with predictions of the conventional two-level tunneling model for amorphous materials even at these very long times. No heat release was observed for Teflon, graphite, and Al₂O₃.     

Creep and densification during anisotropic sintering of glass powders

The isothermal sintering behaviour of a barium magnesium aluminosilicate glass powder at 930°C was investigated using a heating microscope. The cylindrical samples exhibited a variable shrinkage anisotropy during sintering. The shrinkage anisotropy ratio, defined as the ratio of the relative change of height and diameter, varied linearly between 0.3 and 0.98 with the relative volume shrinkage during densification. Shrinkage anisotropy caused creep deformation of the samples. The creep rate varied exponentially with the densification rate and the ratio of creep to densification rates, , decreased as densification proceeded. This is in disagreement with most previous studies, which show a constant value of during the densification. Overall, the study points out the relevance of variable shrinkage anisotropy and how it affects the densification behaviour of glass powders.     

Metrological certification of current transformers under service conditions

Conclusions Theoretical analysis and experimental data confirm the statement that Eq. (16) permits the of a CT to be determined under fixed load and current conditions with an error that is smaller by a factor of two or three than the controlled accuracy grade of the standards [1, 2].During operation of a CT in the rated range of currents it is advisable to measure and at several points of the range for a determination of from Eq. (16) or of from Eq. (14).Besides this, when checking a CT in accord with [3] it is permissible to make corrections for the standard CTs. In this case the actual CT load should not differ by more than 20% from the one being corrected. Equation (16) permits a correction for any permissible load to be taken into account without a significant error buildup.Translated from Izmeritel'naya Tekhnika, No. 8, pp. 53–55, August, 1980.     

Three-dimensional shape of the Y2BaCuO5 pattern in melt-textured Y–Ba–Cu–O oxide

Crystallographic orientations of the Y211 tracks that were trapped within the melt-textured Y123 domains were determined from the orientation relationship among the Y211 pattern, twin traces and a microcrack. Analysing the orientation of the two-dimensional Y211 patterns that were observed on various crystallographic planes of the Y123, the three-dimensional shape of the Y211 pattern was inferred as follows: only one x-type Y211 pattern was included within one Y123 domain and three sets of diagonal Y211 tracks met with the corners of the Y123 domain. The diagonal Y211 tracks lie on the (1 1 0), ( 1 0), (0 1 1), (0 1), (1 0 1) and (1 0 ) planes of the Y123 domain. The planes where the Y211 tracks are located are considered to be the boundary planes where local growing parts of the Y123 domain impinge upon each other. The formation mechanism of the Y211 pattern is discussed on the basis of anisotropic growth behaviour and the shape of the Y123 domain. This revised version was published online in November 2006 with corrections to the Cover Date.     

Factors influencing ductility during cyclic torsional deformation of high purity aluminium

Cyclic torsion (twisting in a forward clockwise direction followed by twisting in the reverse direction) of high purity Al wires under the simultaneous application of a small tensile load (P) was found to increase the torsional ductility considerably. The number of twists in each direction (N) varied between 5 and 50 andP ranged between 0.1 and 0.78 kg mm⁻². The average shear strain increased considerably asN and/orP decreased. Specimens with a fine grain size showed higher ductility than those with a coarse grain size. By suitable combination ofN, P and grain size, exceeding 3000%, indicating superplastic behaviour, was obtained. The accompanying electrical resistivity changes were small and did not exceed 1%. The results are discussed in terms of recovery mechanisms and possible dislocation interactions occurring during this complex mode of deformation.     

Détermination des contraintes maximale et minimale en valeur algébrique résultant d'un effort normal et d'un moment de flexion dans une section quelconque d'un profil, à partir de trois mesures de déformations superficielles

Résumé Les contraintes maximale et minimale en valeur algébrique engendrées dans une section quelconque d'un profil, par un effort normal et un moment de flexion quelconque , peuvent être déterminées à partir de trois mesures de déformations superficielles effectuées au niveau de cette section. De plus, il est possible de calculer l'effort normal et le moment de flexion ainsi que ses composantesM _GY ,M _GZ sur les axes principaux d'inertie , et de définir la position de l'axe neutre de flexion ainsi que celle de l'axe neutre de flexion et d'effort normal.

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Summary The determination of the maximum and minimum stresses in algebraic value generated in an arbitrary section of a profile by a normal force and an arbitrary bending moment is an important problem that frequently arises. Before showing that 3 measurements of surface deformations effected on the level of the section studied suffice completely to solve this problem some theoretical considerations are recalled. These concern the establishment of the formula giving the bending stress. For this we can attach to the section either arbitrary central axes or the main central inertia axes; this latter possibility leading to a simpler formula. The formulae needed for the determination of the maximum and minimum stresses due to and are then established, for arbitrary coordinates of measurement points. Simpler formulae may be obtained when it is possible practically to choose simple ratios between the coordinates. Next it is shown that one can compute not only but and its componentsM _GY ,M _GZ , on the main intertia axes , and determine the position of the neutral bending axis as well as that of the neutral bending and normal force axis. Finally, the practical utilization of the method is indicated and a concrete case treated.

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Transmission electron microscope study of a directionally solidified Cu-MgCu2 eutectic

The crystallography and the interface structure of a unidirectionally solidified Cu-MgCu₂ eutectic alloy have been examined by transmission electron microscopy. The microstructure of the eutectic was found to be lamellar and regularly interrupted by faults. The preference of the particular orientation relationship could not be explained by relative atomic densities of the planes comprising the interface. Based on the defect contrast observed and extinction distance calculations, it is suggested that the fine array of defects observed at the interface may be characterized as steps with step vectors parallel to or Dislocations were also observed at the interface but they were rarely regular.     

A comparison of strengthening mechanisms in rolled and axisymmetrically deformed Ti-20Y composites

Two Ti-20%Y metal-metal composites were deformation processed: one axisymmetrically and the other by rolling. The microstructures, preferred crystallographic orientations, and tensile strengths of each were measured periodically as the deformation progressed. The axisymmetrically deformed Ti matrix developed a [10 0] fiber texture, and the rolled composite acquired a texture with the <0001> tilted 31° from the sheet normal toward the transverse direction with [10 0] parallel to the rolling direction. The orientations of the {10 0}<11 0> and (0002)<11 0> slip systems in Ti with these textures were used in conjunction with the maximum possible slip distances for dislocation travel in each specimen to demonstrate that the axisymmetrically deformed material should be stronger than the rolled material for composites of equal phase thickness and spacing. The strengths of the two composites measured in this study were compared at similar microstructural phase sizes and spacings, and the axisymmetrically deformed composite was indeed found to be somewhat stronger, although the difference in strengths was not large.