Extra Strain Research Articles

Strain in microcrystals and in superlattices

A new general theory of the dependence of strain on crystal size L for defect-free cubic materials bounded by {100} faces is presented. While current theories predict a ('y/L) dependence, this work suggests a (F/L)½ dependence by considering both surface tension (rny) and surface free energy (6FL2) effects. Since small crystals, especially if very fresh or not annealed, may contain a large fraction of point defects, the sizedependent strain must be separated from the defect-induced strain. The theory is verified by reinterpreting three experimental studies reported in the literature and based on the techniques of electron microscopy, x-ray diffraction, and nuclear magnetic resonance. The theory offers a straightforward explanation for the extra longitudinal strain in superlattices, as detected by Raman spectroscopy.

Perturbation by and recovery from bend curvature of a fully developed turbulent pipe flow

An experimental investigation was carried out to study the perturbation by and recovery from bend curvature of a fully developed turbulent pipe flow. The pipe Reynolds number and the pipe-to-bend radius ratio were 50 000 and 0.077, respectively. Hot-wire techniques were used to measure the three components of mean velocity and the six components of the Reynolds stress along a horizontal as well as along a normal plane in streamwise locations extending from 18 diameters upstream to 18 diameters downstream of the U-bend. Results show that a Dean-type secondary motion is established in the bend and is confirmed by a numerical modeling of the flow based on a two-equation closure. Evidence of a second cell is obtained within the bend and again verified by numerical results and previous total pressure measurements. Therefore it is postulated that the pressure field is also responsible for the second cell. The second cell disappears at about one diameter downstream of the curved bend. Turbulent kinetic energy is greatly enhanced by additional production due to extra strain rates created by bend curvature. Since viscous dissipation is the only way in which this extra energy can be destroyed, recovery from bend curvature takes a long distance.

Evidence for deformation‐induced K‐feldspar replacement by myrmekite

ABSTRACT Several examples of deformation‐induced myrmekite have been found in two amphibolite facies mylonites derived from granitic protoliths, namely a muscovite‐poor S‐C mylonite and a single foliation, muscovite‐poor mylonitic gneiss. Back‐scattered SEM and conventional optical microscopy show that in both rock types, syntectonic myrmekitic intergrowths of oligoclase and quartz formed on the two sides of K‐feldspar grains that faced the local inferred incremental shortening direction for the mylonite. Myrmekite does not occur on the two ends of the grain that faced the incremental stretching direction.The replacement of K‐feldspar by plagioclase and quartz results in a volume decrease and is favoured on high normal stress sites around the grains. We suggest that the ambient temperature, pressure and chemical activities were such that the replacement reaction was favoured, but the addition of extra strain energy along the high‐pressure sides of the grains localized the reaction at these sites. This energy could arise from elastic strain, or strain associated with tangled dislocations or twin boundaries. The relative roles of stress and strain energy concentrations in driving the replacement reaction are not known, but both were probably important.

Turbulent flow in a conical diffuser: Overview and implications

Turbulent flow in a conical diffuser has been examined through determination of the mean pressures, mean strain rates, energy, shear stress, triple products, length scale, and balances of energy and shear stress. Some quantities are more revealing than others in pointing out the complexity of a flow subjected to an adverse pressure gradient. Sudden application of extra strain rate to the flow seems to affect conditions so drastically that a final picture of the flow in terms of mean and turbulent fields becomes unrecognizable in relation to the initial condition. Initially all the measured parameters show rapid changes in their values and thus characterize a region of importance. Dynamics of the flow reflected by some parameters such as kinetic energy attain asymptotic values in the outlet region of the diffuser and, in turn, show a type of equilibrium of the flow. Additionally, the expanding wall region toward the exit has a low mean velocity and very high turbulence intensity. Finally, there is a growth of core region in the last one-third of the diffuser; this layer shows exceptionally high values of the higher moments.

Selective feeding programmes in Ethiopia and East Sudan–1985/1986

A survey of thirty‐four feeding programmes in Ethiopia and East Sudan was undertaken. Wie differences were found between the two countries and also within Ethiopia. Irrelugar general ration distribution was commonplace in Ethiopia, thus placing an extra strain on selective feeding programmes. The principal admission criteria to Selected Feeding Programmes (SFPs) were weight for height categories. The cut‐off stages of the emergency. Useful compasirions between programmes were hampered by such differences, as well as by the different methods of reporting data.The types of food usd in programmes depended on availability and included high energyu drinks, poridges, take‐home pre‐mixes and sometimes indigenous foods. A large number of foods e.g. cornedbedef, chicken paté, noodles, da4tes etc. Some added interesting variety and added nutritional value to the diet, while others caused more problems than they solved due to their low acceptability, inappropriate packaging, limited accompanying information and complex an costly preparation. The imlementation of food dination policies by donors and consignees regarding appropriate foodstuffs and their recommended use was considered to be the major solution to this problem.

Curvature and pressure-gradient effects on a small-defect wake

A fully developed two-dimensional turbulent wake was deflected by an airfoil-like thin plate placed at small angles in the external flow. The response of the mean-flow and turbulence properties of the wake to the ‘mild’ pressure gradient and the ‘mild’ streamline curvature caused by the deflection is studied. Owing to the small defect velocity, the extra strain rates are large compared with the main shear strain and the Reynolds stresses are strongly influenced by both the pressure gradient and the streamline curvature. The defect velocity relative to an appropriately chosen ‘potential-flow velocity’, and the mean vorticity, however, are not as strongly influenced by the curvature. Changes in the magnitudes of the Reynolds-stress components are much larger than would be caused by the simple rotation of coordinates aligned with the wake path. Most turbulence-model parameters are influenced significantly, while some pure turbulence parameters, such as the Taylor microscale, are relatively uninfluenced. The rapid and lagged responses are apparent and the terms in the transport equation for turbulent kinetic energy indicate that the response of the production terms is almost instantaneous, while the diffusion and dissipation terms are delayed.

A simple method for including shear deformations in thin plate elements

AbstractA method is described for including the effect of shear deformations in existing thin plate finite elements, and thereby extending their range of application to include moderately thick plates. The method does not add extra degrees of freedom to the final element, so the thick and thin plate elements can be used interchangeably, and the thick plate solution is not appreciably more expensive than the thin plate solution.It is assumed that the shear deformations are constant over the element and, to account for this, two extra internal shear strain variables are added to the element. Various methods for eliminating these internal variables are examined but it is shown to be impossible to simultaneously satisfy both the constant bending moment and constant shear patch tests, except for parallelograms. However, one method gives elements which pass the constant shear patch test and, although failing the constant bending moment patch test for arbitrary geometries, gives errors which are small enough to be neglected in most engineering applications.This method has been applied to a triangular plate element and it is shown that the results obtained with this element converge (for all practical purposes) to the correct thick plate results.

A theoretical and numerical approach to the plastic behaviour of steels during phase transformations—I. Derivation of general relations

Empirical models have been proposed for the anomalous plastic behaviour of steels during phase transformations; they distinguish between classical plasticity (response of the material to variations of the stresses or the temperature) and transformation plasticity (response of the material to variations of the proportion of the phases). This paper uses the Hill-Mandel homogenization method to provide theoretical foundations for such models. Without postulating arbitrarily the existence of an extra plastic strain of a new unknown type on a microscopic scale, it is shown that the distinction between (macroscopic) classical and transformation plasticity is a consequence of the homogenization process; furthermore the transformation plastic strain rate decomposes naturally into two terms which can be interpreted as corresponding to the well-known Greenwood-Johnson and Magee mechanisms. An interesting property of dilatometric diagrams is also proved in the course of the treatment.

Turbulence Measurements in a Compressible Reattaching Shear Layer

Detailed hot-wire measurements of the longitudinal component of the mass-flow fluctuations have been made in an approximately self-preserving free shear layer reattaching on a 20-deg ramp at Mach number 2.9. The experimental configuration is especially designed to provide a well-defined initial condition for the reattachment process. The absolute mass-flow turbulence intensity increases dramatically through the compression in the reattachment region, which is in sharp contrast to similar subsonic reattachments. It is clear that the mean dilatation contributes significantly to the turbulence amplification. In addition, the length scale is affected strongly by the presence of extra strain rates. Prediction of this flow will require some sophisticated modeling, and the challenge to the predictor is clear.

The chemical reactivity of penicillins and other β-lactam antibiotics

The rates of the acid catalysed hydrolysis of penicillins and cephalosporins are linear in Ho and, unlike other amides, show no rate maximum with increasing acidity. Electron-withdrawing substituents at C-6 in penicillins decrease the rate of hydrolysis with a ρI of ca.4 and they decrease the rate when attached to the amine leaving group. The acylamido-group at C-6 in penicillins, but not at C-7 in cephalosporins, exhibits neighbouring group participation with a rate enhancement of ca. 103. The absence of penicillenic acid formation from benzylpenicillin in acidic solution is not due to the ionisation of the carboxy-group. These observations are rationalised by a scheme, involving N-protonation and formation of an acylium ion intermediate. The alkaline hydrolysis of penicillins proceeds 102 faster than a β-lactam after correction for substituent effects. There is no evidence for substantial inhibition of amide resonance in the bicyclic β-lactam antibiotics, little evidence to indicate extra strain in these systems and no evidence that expulsion of the leaving group at C-3 in cephalosporins occurs in the transition state.

Poisoning with Tricyclic and Related Antidepressants—A Ten-Year Review

Self-poisoning with tricyclic and related anti-depressant drugs has increased in frequency over the last few years so that, at present, some 20 per cent of patients admitted to hospital following self-poisoning have ingested a drug of this group, either alone or, more commonly, in association with alcohol, a benzodiazepine and/or other drugs. We present the results of a retrospective analysis of 316 admissions to a general medical hospital dealing with patients over 12 years, following self-poisoning with tricylic or related drugs. Although serious toxic effects may sometimes occur, their frequency has probably been over-estimated, at least in older children and adults; in this series the incidence of significant hypotension was 13 per cent, grand mal convulsions 4 per cent, respiratory depression to the degree of requiring mechanical ventilation 2 per cent and severe cardiac arrhythmias or conduction disturbances 1.5 per cent. It is suggested that routine 'prophylactic' treatment against convulsions and cardiac arrhythmias, advocated by some previous authors, is unnecessary and potentially dangerous; indeed, even the establishment of an intravenous infusion may put an extra strain on a depressed myocardium. In this series, supportive treatment alone was sufficient for the majority of patients (81.6 per cent) and additional treatment was given only in the presence of some specific indication. Using such conservative measures, the mortality rate in the 10-year study was only 0.6 per cent. Medical efforts in the future, it is suggested, would be more appropriately directed towards preventing unnecessary prescribing of these drugs for trivial mental upset, rather than the development of new drugs of this type or other 'prophylactic' measures, designed to prevent relatively rare toxic effects.

The physiological cost of carrying light and heavy loads.

Nine subjects walked on a treadmill with load weights equal to 10% and 40% of body weight carried on the back. Although the speed of the treadmill was selected so that the measured oxygen consumption (VO2) was the same for both load conditions, the heavier load placed an extra strain on the cardiopulmonary system and was perceived by all subjects as harder work than the lighter load. When the subjects worked at their own pace, walking on a level road or climbing stairs with load weights equal to 10% and 40% of body weight, they compensated for the heavier load by decreasing walking speed or climbing rate. Although the energy costs calculated from walking speed, body and load weight for self-paced walking and the external work of stair climbing were the same for both load conditions, the heavier load was again perceived as harder work. These findings are discussed as they relate to the definition of acceptable load weights.

The role of grain-boundary sliding in the creep of polycrystals

A theoretical analysis is performed to describe the development of overall strain in a polycrystal when internal deformation and sliding of its constituent grains occur concurrently. It is demonstrated that, although sliding is not an independent deformation mode, its occurrence does lead to increased overall strain and the effect is quantified. The extra strain associated with sliding cannot be derived from measured boundary displacements simply by geometrical arguments which do not involve the physical properties of the material.

The breeding of the Sooty tern Sterna fuscata in the Seychelles and the effects of experimental removal of its eggs

In the Seychelles the eggs of the Sooty tern Sterna fuscata are collected for human consumption. A reduction in the number of Sooty terns breeding in exploited colonies has been attributed to over‐exploitation of the eggs. However, the population decline has been over‐estimated and factors other than exploitation have led to a reduction in the land area available to breeding colonies.In the study colony, on Bird Island, egg laying was highly synchronous, and birds which laid at peak laying time had a higher reproductive success than those that laid early or late. The higher success of these birds was due to their being at the same stage of the reproductive cycle as their neighbours: this reduced losses of eggs to predators and losses of chicks due to pecking by adults and other chicks. Birds which laid late, which included young birds and birds which had lost their first egg and laid a replacement, were therefore penalized.The ability to lay a replacement egg after loss of the first, was found experimentally to be much greater than previous estimates had suggested, and some individuals were induced to lay a third egg. Both the ability to relay and the success of replacement eggs declined seasonally. The laying of a replacement egg did not seem to place extra strain on the parents, and the lower weights of most replacements compared with first eggs was due to seasonal factors rather than to the inability of adults to produce a large second egg.The food brought by the parents to the chicks consisted mainly of fish and squid, but frequent and abrupt changes in the species composition of the food suggested that food supplies were unpredictable. In 1973 chick growth was interrupted by two periods of food shortage, and although late hatched chicks experienced this food shortage early in their lives, starvation did not appear to be a major source of mortality.The regulation currently in force in the Seychelles imposing a close season for egg collecting protects only late‐laid eggs, and since these have a very low success rate and can contribute little to future generations, there is no biological foundation for continuing this restriction. Adult mortality and age at first breeding are not known for Seychelles Sooty tern populations, and exploitation should be restricted to 10–20% of the birds that lay during the main laying period.

The effect of mean compression or dilatation on the turbulence structure of supersonic boundary layers

It is now well known that the turbulence structure of thin shear layers can be strongly affected by the application of extra rates of strain in addition to the shear velocity gradient. Examples of such extra strain rates include lateral divergence or convergence, and streamline curvature in the plane of the mean shear. The changes in Reynolds stress are an order of magnitude larger than would be expected from the explicit extra terms in the Reynolds-stress transport equations, and therefore an order of magnitude larger than predicted by conventional calculation methods. In the present paper, one of a series on ‘complex’ turbulent flows, we show that bulk compression or dilatation (i.e. an extra strain rate div U) also appears to affect turbulent shear layers, typical values of Reynolds stress being increased by compression and decreased by dilatation. The fractional change in Reynolds stress is an order of magnitude larger than the fractional change in volume of a fluid element. The physical mechanism is probably analogous to that responsible for the large effects of divergence or convergence in incompressible flow. Because the phenomenon seems to be of great practical importance we discuss it in the context of engineering calculation methods. An empirical correction formula, analogous to those used to allow for divergence or curvature effects, greatly reduces the large discrepancies found between recent experiments on supersonic boundary layers and calculations by conventional extensions of successful incompressible-flow methods.

Creep under Varying Load

The creep behaviour of nickel under cyclic loading has been studied, the aim being to relate the creep strain to the metallurgical recovery that occurs during each load reduction. Square-wave loading between stresses σ1 (40 or 80 N/mm2) and σ2 (0–σ1) for times t 1 (0.01–0.1 h) and t 2 (0.1–20 h) was applied at 650 or 750° C, and a point of principle was to apply the full stress σ1 initially until the metal was fully work-hardened so that all subsequent changes could be ascribed to recovery. The strain per cycle consists of three components, which could be expressed in terms of experimental conditions: (1) ∆ε1, the normal strain in time t 1 at a stress σ1; (2) ∆ε2, the strain in time t 2 at stress σ2; ε2/ε1 = (σ2/σ1)m, where m = 10 at 650° C and 5.2 at 750° C; (3) ∆εr, the extra strain on reloading from σ2 to σ1; ∆εr = bt 2⅔ + c, where b and c have been determined. The factor c can be negative, probably because strain-ageing occurs. A consequence is that three functions are needed to describe accurately the state of nickel during creep.At high temperature and low stress, recovery did not accumulate from cycle to cycle. By fitting the acceleration factor (∆ε1 + ∆ε2 + ∆εr)/∆ε1 into a standard creep-strain/time equation, the envelope strain/time relation for cycling is described with satisfactory accuracy. At low temperature and high stress the creep rate steadily accelerated, presumably because recovery accumulated from cycle to cycle. Quite good predictions were made from the first few cycles. In both cases the predictive accuracy is more reassuring than it is with the conventional strain-hardening or time-hardening methods. The physical metallurgical approach enables this final result to be obtained with relatively little experimentation, though on this first occasion many extra experiments were performed to check various points.

The rate of the gas phase iodination of cyclobutane. The heat of formation of the cyclobutyl radical

AbstractThe gas phase iodination of cyclobutane was studied spectrophotometrically in a static system over the temperature range 589° to 662°K. The early stage of the reaction was found to correspond to the general mechanism where the Arrenius parameters describing k1 are given by log k1/M−1 sec−1 = 11.66 ± 0.11 – 26.83 ± .31/θ, θ = 2.303RT in kcal/mole. The measured value of E1, together with the fact that E−1 = 1 ± 1 kcal/mole, provides ΔH(c‐C4H7.) = 51.14 ± 1.0 kcal/mole, and the corresponding bond dissociation energy, D(c‐C4H7H) = 96.8 ± 1.0 kcal/mole. A bond dissociation energy of 1.8 kcal/mole higher than that for a normal secondary CH bond corresponds to one half of the extra strain energy in cyclobutene compared to cyclobutane and is in excellent agreement with the recent value of Whittle, determined in a completely different system. Estimates of ΔH and entropy of cyclobutyl iodide are in very good agreement with the equilibrium constant K12 deduced from the kinetic data. Also in good agreement with estimates of Arrhenius parameters is the rate of HI elimination from cyclobutyl iodide.

MODULUS CHANGES IN STRAIN-CYCLED COPPER

The shear modulus (G) of copper is heavily reduced by cold working at low temperatures as has been shown by Druyvesteyn et al. [1]. The effect, the so-called ƊG-effect, was attributed to dislocations introduced by the deformation as described by Mott [2] and Friedel [3]. When an elastic stress is applied, the dislocations bow out in their glide planes causing an extra elastic strain and thus a decrease of the modulus. This modulus defect was reduced by annealing at higher temperatures which was ascribed to the pinning of dislocations by point defects. Many investigators studied these effects after unidirectional deformation [4] but analogous studies on cyclically deformed materials are much less numerous. In the present work the decrease of the shear modulus due to strain controlled cyclic torsion was measured on rods of polycrystalline pure copper cycled at various amplitudes. After some 5 x 104 cycles at 78 °K, G reached a saturation value qualitatively in accordance with for instance the behaviour of the flow stress vs. number of cycles in fatigued metals. The saturation value of - ƊG/G increased with strain amplitude up to about 4 % for a strain amplitude of 4.2 x 10-4. The isochronal recovery behaviour was analogous to that observed after unidirectional deformation. Three discrete steps were present, called IIa, IIb, and III centered at 133 °K, 193 °K and 273 °K respectively. After cyclic deformation step III was considerably smaller. Cycling at room temperature and at 78 °K caused about the same ƊG-effect, if measured at 78 °K. As the point defects produced by the deformation are mobile at room temperature, this implies that point defect pinning does not occur when the dislocations move to and fro during cyclic deformation. The dependence of the modulus effect on the measuring temperature is in accordance with the observations of Druyvesteyn and Blaisse [5] after unidirectional deformation.

Modulus changes in strain-cycled copper

Measurements are presented on the behaviour of the shear modulus and the internal friction of polycrystalline copper during torsional fatigue at 78°K. During fatigue the total strain amplitude, adjustable between 5 × 10−4 and 1.5 × 10−2, is kept constant. Analyzed in terms of the dislocation string model, the resulting behaviour of dislocation density and line length, is in good agreement with measurements on the shear modulus during unidirectional deformation and with the behaviour of the flow stress during fatigue. A discrepancy with resistivity measurements is discussed briefly.Les auteurs présentent des mesures relatives au comportement du module de cisaillement et du frottement interne du cuivre polycristallin au cours d'essais de fatigue par torsion, à 78°K. L'amplitude totale de la déformation, réglable entre 5 · 10−3 et 1,5 · 10−4, est maintenue constante au cours des essais. Analysé à l'aide du modèle des chapelets de dislocations, le comportement résultant de la densité des dislocations et de la longueur des lignes est en bon accord avec les mesures du module de cisaillement au cours d'une déformation unidirectionnelle et avec le comportement de la contrainte plastique au cours de la fatigue. Une brève discussion au sujet d'un désaccord avec les mesures de résistivité est présentée.Es wird über Messungen des Schermoduls und der inneren Reibung in polykristallinem Kupfer während der Torsions-Ermüdung bei 78°K berichtet. Während der Ermüdung wurde die Gesamtdehnungsamplitude, die zwischen 5 × 10−4 und 1,5 × 10−2 einstellbar war, konstant gehalten. Die Analyse anhand des Saiten-Modells der Versetzung zeigte eine gute Übereinstimmung des Verhaltens der Versetzungsdichte und der Bogenlänge mit Messungen des Schermoduls während einsinniger Verformung und mit dem Verhalten der Flieβspannung während der Wechselverformung. Eine Diskrepanz zu elektrischen Widerstandsmessungen wird kurz diskutiert.

The implications of the out-of-field phenomenon for effective teaching, quality education and school management

The out-of-field phenomenon, that is the situation where teachers teach outside their field of expertise, adds complexity to the education environment and affects learners, colleagues, parents, governing bodies and school management. It puts extra strain on school management's responsibility to provide quality management and jeopardises effective teaching and quality learning. This article examines the implications of the out-of-field phenomenon for school management. An empirical investigation entailing the use of a qualitative approach was employed for the study. Data were gathered through semi-structured interviews with selected participants who shared their experiences of the phenomenon. Findings indicated that the out-of-field phenomenon and its implications should be recognised in order to provide effective and quality teaching, substantial teacher support and sufficient staff development programmes.