Determination of normal stress differences in steady shear flow

Summary Using the cone- and-plate apparatus ofAdams andLodge, values of pressure gradient,r-d¯p/dr in a range 300 to 3000 dyn/cm², have been measured to an accuracy of 1% at shear rates near 10 sec^–1 in liquids of viscosity less than 200 poise. Using the constancy of pressure gradient at a given shear rate as an indicator of liquid stability, it was found that a polyisobutene liquid containing 2% of Oppanol B 200 in Oppanol B I, when stored at rest at 25 °C, was stable during a certain 7-day period after dissolution and unstable during the subsequent 30 days.     

The effects of boundary to the ECRH and the energy absorption of ICRH

Electron-cyclotron resonant heating (ECRH) of Tokamak plasma is examined. When plasma is heated by waves, we must consider the distribution of incident wave energy toO andX modes as the wave is incident from vacuum to the surface of plasma as well as the absorption efficiency ofO mode andX mode. Numerical calculation shows that for small incident angle, the incident energy transfers principally intoO mode when the electric fieldE ⁱ of incident wave is parallel to the incident plane, therefore it is efficient to heat the plasma byO mode. WhenE ⁱ is perpendicular to the incident plane, the energy transfers principally intoX mode and heating the plasma byX mode is efficient. Ion-cyclotron resonant heating (ICRH) is also considered, the formula of the energy of ion-cyclotron wave absorbed by plasma is obtained.     

Comparison of viscometer geometries for non-steady shear flows

Summary Suitability of cone- and-plate, parallel disk and concentric cylinder viscometric geometries for nonsteady shear flow of non-Newtonian fluids was analyzed. Both the cone- and plate and the parallel disk viscometers possess the undesirable property that the equations of motion do not permit simple solutions, i. e., solutions for which only one pair of components of the shear stress tensor is non-zero. No such difficulty appears in the analysis of the concentric cylinder viscometer, and therefore this instrument is to be preferred for this type of study.

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Zusammenfassung Die Geometrien des Kegel-Platte-, des Parallelscheiben- und des konzentrischen Zylinderviskosimeters werden auf ihre Eignung für Messungen bei nichtstationärer Scherströmung nicht-Newtonscher Flüssigkeiten untersucht. Die Kegel-Platte und die Parallelscheiben-Viskometer haben beide die unerwünschte Eigenschaft, daß die Bewegungsgleichungen keine einfachen Lösungen haben, das heißt, Lösungen für die alle außer einem einzigen Paar der Komponenten des Schubspannungstensors verschwinden. Diese Schwierigkeit erscheint nicht in den Ergebnissen für das konzentrische Zylinderviskosimeter, und damit ist dieses Gerät für diese Versuche bevorzugt.

     

A study of simple shearing flows in polar fluids

Summary In the present paper we have made a study of simple shearing flows in three polar fluids — (i) the model ofCondiff andDahler, (ii) the model ofEringen, and (iii) the model ofStokes. We have investigated in detail the components of stress, equations governing the motion and boundary conditions in the above fluids in flows induced by motion of boundaries or a pressure gradient. By means of tables, we have studied the common features of these fluids and related the fluid parameters involved in each case.     

Revisit to the determination of stress-intensity factors and J-integrals using the caustics method

Applications of the optical (shadow) method of reflective caustics to measurement of the stress-intensity factor andJ integral in various specimens are investigated. The necessary experimental requirements to help determine accurate stress-intensity factor andJ integral are described. The ratios ofr _o (radius of initial curve)/r _p (plastic-zone size) andr _o/t(thickness of specimen) are found to be very important experimental parameters to obtain meaningful stress and/or strain intensities surrounding crack tips. The appropriate ranges to determine accurate values of stress-intensity factor andJ integral for polycarbonate (compact tension) and aluminum (c-shaped tension) specimens are presented. Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 8–11.     

On viscous flow and effective viscosity of concentrated suspensions and emulsions

Summary Previous analysis byHappel (3) of viscous flow in concentrated solid suspensions has been extended to include concentrated emulsions of slightly deformable fluid particles in the presence or absence of surfactant impurities.General expressions were obtained for viscous flow in multi-particle systems when arbitrary shear fields are imposed. Specific relations were then derived for uniform,Couette and hyperbolic fields. The behavior is found to be strongly dependent upon particle concentration and surfactant concentration. The theoretical expressions obtained for effective viscosity of emulsions compare favorably with experimental data ofNeogy andGhosh (18),Sibree (15),Sherman (17), andBroughton andWindebank (16). These results support other studies on ensemble velocities [(10), (12), and in particular (22)], which strongly indicate the practical value and factual reliability of cell models in predicting the behavior of suspensions and emulsions.     

Théorie des effets rhéo-optiques dans un continu polarisable et magnétisable

Summary The total momentum-energy tensor describing the interaction of a polarizable and magnetizable continuum with an electromagnetic field is constructed on the basis ofLorentz invariance. The equations of balance of energy and momentum are deduced and applied to the study of the magnetooptical, electrooptical and photoelastic behavior of an elastic polarizable and magnetizable isotropic continuum. This model exhibits theCotton-Mouton andKerr effects but thePockels andFaraday rotations don't appear.     

The geometry of the „cones“ used in cone- and-plate viscometers

Summary The geometry of eighteen cones used in two commercial cone- and-plate viscometers has been determined by measuring the profiles along four radii at right angles to each other. It is found that the cones are not truly conical and that there is considerable uncertainty in assigning a value to the cone angle and to the position of the apex. Large differences were also found between the calculated mean values and those quoted by the manufacturers. Thus the latter values should not be used without confirmation. The effect of these results on viscosity determination is discussed.     

Perturbation solutions for non-linear crack problems

Approximate solutions ofJ integrals under plane loadings (modes I and II combined) and antiplane shear loadings (mode III) are obtained for bodies with central through cracks of power hardening materials, by using a perturbation method. The obtained calculating formula is very simple and a comparison with available results shows that the formula enjoys quite good accuracy and is suitable for engineering uses.     

Adaptive eigenfrequency analysis by improvedr- andh-adaptive finite element method based on perturbation and element energy ratio

A new adaptive technique ofr- andh-version for vibration problems utilizing the matrix perturbation theory and element energy ratio is proposed. In structural vibration analysis, through ther-convergence adaptive finite element process, mesh optimization can be realized. In the light of the judgement on the changes in the magnitude of the element energy ratio, local refinement can be achieved in the process ofh-convergence adaptive finite element so that more accurate finite element solutions can be obtained with as few meshes as possible. Many numerical examples are given and the proposed approach is shown to be feasible and effective. Project supported by the National Natural Science Foundation of China (No. 19872029).     

The oscillation of a spheroid along its axis in a non-Newtonian fluid

Summary The present paper investigates the nature of the fluid flow when a spheroid is suspended in an infinitely extending elastico-viscous fluid defined by the constitutive equations given byOldroyd orRivlin andEricksen, and is made to perform small amplitude oscillations along its axis. The solution of the vector wave equation is expressed in terms of the solution of the corresponding scalar wave equation, without the use ofHeine's function or spheroidal wave functions. Two special cases (i) a sphere and (ii) a spheroid of small ellipticity, are studied in detail.Née MissRenuka Rajagopalan.     

Discretized ordinary differential equations and the Conley index

LetN be a compact isolating neighborhood of an isolated invariant setK with respect to an ODEx=f(x) (C) and(h) x=x + h(x, h) be a consistent one-step-discretization of (C). It is proved in this paper that for someh ₀ > 0 and allh ]0, h₀[, the setN isolates an invariant setK(h) of(h) and the discrete Conley index ofK(h) coincides with the continuous Conley index ofK.     

Optimal estimates for the uncoupling of differential equations

Our aim in this note is to give optimal conditions on the spectral gap for the existence of an uncoupling of a differential equation of the form = Cz + H(=) into a system ofuncoupled equations of the form (x, y) = (Ax, By) + (F(x, (x)), G((y),y)), whereC=A×B is a bounded linear operator on a Banach spaceZ=X×Y satisfying a spectral gap condition, andH=(F,G) is a Lipschitz function withH(0) = 0. We also give optimal conditions for the regularity of the manifoldsgraph andgraph , and optimal conditions for the regularity of the leaves of two foliations of the phase space associated to the uncoupling. Sharp estimates for the Lipschitz constant of and and for the Hölder exponent of the uncoupling homeomorphism and its inverse are also given.     

Nature of strain recovery in polyvinyl chloride following steady laminar shearing

Summary It is well known that viscoelastic materials, subjected to steady laminar shearing, develop a tension in the direction of shear, and it is of both practical and theoretical, interest to determine whether, this can give rise to normal components of strain recovery parallel and perpendicular to this direction, in addition to the tangential component corresponding to the applied shear. This has been investigated for the condition where there is opportunity for stress relaxation after shearing, plasticised polyvinyl chloride being used for the purpose. The hot material was sheared in a cone- and-plate rheometer at 1.0 sec^–1, and then allowed to cool without recovery being permitted. It was then removed, and suitable specimens were cut and re-heated above the shearing temperature, the resultant recovery being measured. In addition to partial shear recovery there was considerable retraction in the direction of shear. Moreover the accompanying expansion in the transverse plane was greater perpendicular to the shear planes than parallel to them. The strain recovery increased with applied shear till the latter reached 10–15, and then diminished, in agreement with previous tests on shear recovery immediately after shearing.

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Zusammenfassung Bekanntlich entwickelt viskoelastisches Material, einer stationären laminaren Scherung unterworfen, eine Spannung in Scherrichtung, und es ist von Interesse, ob bei Verschwinden der Zugspannung diese Anlaß zu Normalkomponenten der Dehnungserholung führen kann, zusätzlich zur Tangentialkomponente. Dies wurde unter Bedingungen untersucht, bei denen nach der Scherung Gelegenheit für Spannungsrelaxation gegeben war, bei plastifiziertem PC. Das heiße Material wurde in einen Konsus-Platten Rheometer bei 1.0 sec^–1 geschert und konnte dann ohne Rückfederung abkühlen. Es wurden geeignete Proben ausgeschnitten und über die Temperatur bei der Scherung hinauf aufgeheizt und anschließend die Rückfederung gemessen. Zusätzlich zu einer teilweisen Rückbildung der Scherung traten beträchtliche Schrumpfungen in der Scherrichtung auf. Außerdem war die Verdickung senkrecht zu den Scherebenen stärker als parallel. Die Deformationserholung stieg bis zu 10–15 an und verminderte sich dann in Übereinstimmung mit früheren Versuchen über Schererholung unmittelbar nach dem Scheren.

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The author wishes to record his thanks to Mr.W. C. Barry B. Sc. (Eng.) M.I.E.E., Manager of the Research Laboratories, to Mr.S. E. Goodall M. Sc. (Eng.) M. I. E. E., Chief Engineer of W. T. Henley's Telegraph Works Co., Ltd., and to the Company, for permission to publish this paper.     

Comparison of two methods for stress relaxation data presentation of solid foods

Published exponential relaxation equations, derived from Maxwellian models, were used to generate data for linear representation in the form ofP(0) ·t/(P(0) —P(t)) =k ₁ +k ₂t whereP(t) is the decaying parameter (force, stress or modulus),P(0) its initial value (att = 0) andk ₁ andk ₂ constants. The computer plots indicated that the fit of this normalized and linearized form was excellent for equations containing at least three exponential decay terms. The fit was not as good for some of the two-term exponential equations mainly due to the lack of accurate account for the initial stage of the relaxation process. In all the cases, however, the linear representation could clearly reveal the general rheological character of the analysed materials in terms of the relative degree of solidity.     

Numerical study of natural convection flow in a vertical slot

The stability of convective motion, generated by a lateral temperature difference across a vertical slot, is studied numerically over a range ofGr=5000 to 1.5 × 10⁵,Pr=0.01 to 10, andA=8,16 and 20. Various cellular flow structures and temperature patterns are illustrated. Several branches of solutions characterized by different numbers of the cells in the flow patterns as well as by both steady and unsteady multicellular patterns are found for low-Prandtl-number fluid in the vertical slot. Meanwhile, the behaviors of the temperature variation and heat transfer are also discussed. The project supported by the National Natural Science Foundation of China (59776011) and by the Returnee from Abroad Funding of Academia Sinica.     

A note on streaming double refraction in a dilute suspension of rigid spheroids subject to weak Brownian rotations

Summary The phenomenon of streaming double refraction is examined theoretically for simple shear flow of a dilute suspension of rigid spheroids which are subject to weak Brownian rotations. In particular, we employ recently derived expressions for the statistical distribution of particle orientations in the limit of weak rotaryBrown-ian motion to calculate the corresponding limiting behavior of the extinction angle and the birefringencen. These are compared with the earlier results ofScheraga, Edsall, andGadd (17), who utilized a slowly convergent series solution due toPeterlin andStuart for the orientation distribution. The familiar stressoptical relations which have been proposed for various polymeric materials are found to be inapplicable for a suspension of the type considered.     

Spin tests to determine brittle fracture under plane strain

The feasibility of using cyclic thermal stress or hydrostatic pressure to generate a fatigue crack in a large test-rotor blank is demonstrated. Test rotors, having test notches with fatigue-crack terminations, were spun to fracture to determine optimum test-notch design. It was found that, for the other test-notch dimensions held, it was necessary to extend the fatigue crack a minimum of 0.1 in. from the machined portion of the test notch to obtain a most effectively notched test rotor. In another series of tests, the influence of temperature on brittle-fracture strength of a Cr-Mo-V steel under plane strain was evaluated. It was found that, although there is a significant increase in fracture strength with increasing temperature, no knee in the curve is apparent in the vicinity of the conventionally measured transition temperatures ofNDT andT ₅₀. Also, design against brittle fracture is still required at temperatures aboveNDT andT ₅₀.Paper was presented at 1968 SESA Spring Meeting held in Albany, N. Y., on May 7–10.     

Particle statistics in x-ray diffractometry

Summary Expressions are derived for the relative r.m.s. error of diffractometer intensity measurements. The result for stationary specimens:=4R[sin/m w h N _eff]^1/2, withh=1/2(h _F+h_S) andN _eff=cAv/v², is identical with the result of Alexander c.s.¹, except for a slight difference in the numerical constant and in the definition ofw. The value of this parameter is found to lie betweenR+(w_F, w_S)_min (the last term indicating the smallest of the widthsw _F andw _S) andR+1/2(w _F+w_S); it reaches the latter limit in the case of integrated intensities being measured by totalizing counts while scanning through a line. For rotating specimens the particle statistics error turns out to be almost independent ofw. The following approximative formula is established:=6.5R sin/h(mN _eff)^1/2, showing that the factor of improvement resulting from specimen rotation is of the order of (h/w)^1/2.Part. II: Experiments, by P. M. de Wolff, Jeanne M. Taylor and W. Parrish, is in the course of preparation.Work done when on leave of absence (Nov. 1954–May 1955) from Technisch Physische Dienst T.N.O. and T.H., Delft, Netherlands.     

The balance of entropy on earth

Entropy is absorbed and emitted in the. atmosphere and in the litho- and hydrosphere of the earth by absorption and emission of radiation. The value of the total production rate of entropy may be decomposed into the production rates ofradiative entropy andof material entropy. Although the latter amounts to only 3,4 % of the total, the material entropy production rate is the one that is relevant to meteorology, life science and ecology. Civilization accounts for less than 1 % of the material entropy production.