Stress relaxation of large amplitudes and long timescales in soft thermoplastic and filled elastomers

We propose a model for describing mesoscale relaxation mechanisms in soft thermoplastic elastomers and also in the high-temperature regime of filled rubbers. The model consists of hard spheres embedded in an elastic matrix. It is solved by dissipative particle dynamics. We study the response of the model to deformations of various amplitudes. We show that it displays slow relaxation processes of large amplitudes that are related to irreversible reorganizations at a mesoscopic scale. We characterize these reorganizations as buckling of instabilities that change the local environment of the hard inclusions. Paper presented at the 3rd Annual Rheology Conference, AERC 2006, April 27–29, 2006, Crete, Greece.     

Fracture data and stress-strain behavior of rocks in triaxial compression

Test results are reported for a recently completed experimental research program on rocks subjected to triaxial compression. Sandstone, marble, granite and shale specimens were tested at confining pressures as high as 90,000 psi corresponding to mean stresses of up to 143,000 psi. Recognizing that the largest potential experimental error in such tests results from making strain and load measurements external to the vessel, special load and strain-measuring devices were designed and fabricated for use inside the pressure vessel. The specimens were carefully machined cylinders with length-to-diameter ratios of two and with diameters ranging from 4/16 in. to 1 in. The confining pressure was held constant during each run, but varied from 0 to 90,000 psi over the tests. Results are reported in the form of:

1. Stress-strain curves for individual specimens
2. Maximum shear stress at fracture vs. mean-stress curves for each rock type tested
3. Tabulation of results for 59 specimens

A number of tests were run on granite specimens which had been previously fractured. Results from these tests showed good agreement with tests on intact granite, providing the confining pressure was above 30,000 psi.     

Über die Tilgung periodischer Störungen bei digitaler Meßwertverarbeitung

übersicht Beim Einsatz von Proze?rechnern mu? zur Unterdrückung von periodischen St?rungen im Me?signal bisweilen anstelle eines analogen Filters ein digitales Filter treten. Damit eine Abtasfrequenz unterhalb der doppelten zu filternden St?rfrequenz gew?hlt werden kann, werden die Gesetze zur digitalen Erfassung und Rekonstruktion von langsam ver?nderlichen periodischen Signalen dargestellt. Durch Einführung eines zus?tzlichen Me?punktes innerhalb der Abtastzeit ist eine Sch?tzung und Tilgung einer gegenüber der Abtastfrequenz h?herfrequenten St?rung m?glich. Die hierzu erforderlichen Differenzengleichungen werden diskutiert und der Tilgervorgang an einem Beispiel demonstriert. Benutzt man mehrere Tilgergleichungen, dann k?nnen Spektralanteile im Me?signal oberhalb der halben Abtastfrequenz unterdrückt werden.

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Summary In process computer application periodic disturbances are to be sometimes suppressed by digital filters. In order to choose a sampling frequency lower than the highest frequency of the disturbance, the paper describes the principle of digital measuring and reconstruction of slowly varying periodic signals. By introducing an additional measuring point within the sampling-period it is possible to estimate and to suppress a disturbance, whose frequency is above half the sampling frequency. The corresponding difference equations are discussed and an exemple illustrates the dynamic behaviour of suppression. Applying further equations, it is possible to suppress parts of spectral density being activ above half the sampling frequency.

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Meinem Lehrer, Herrn Professor Dr.-Ing. K. Klotter, zum 75. Geburtstag gewidment.     

Turbulent flow of non-Newtonian substances

Summary A unique shear stress-shear rate relationship exists for laminar flow of any time independent substance in a tube, whereas this is not the case for turbulent flow. In order to obtain a unique relationship for turbulent flow, a new approach based on the elementary theoretical interpretation of experimental data is adopted in the present paper. In particular, wall shear stress is found to be a unique function of a new turbulent pseudo shear rate term. In this relationship therè are two parameters which characterize a given substance — the limiting viscosity at high shear rateµ _m and a factor _m which takes into account modification of turbulent structure by the non-Newtonian properties. Both of these parameters must be determined experimentally. Methods of predicting pressure gradients and of scaling up are outlined. In applying the approach to suspensions in which the solid phase has a density greater than that of the liquid medium, it may be important to determine the increment in shear stress equivalent to the energy required to maintain the solid particles in suspension.The validity of this approach is confirmed by data for the flow of a variety of substances including kaolin suspensions and Carbopol solutions in tubes ranging in diameter from 1.5 to 20 mm. Nomenclature C volume fraction solid in suspension - D tube diameter - f Darcy-Weisbach friction factor - g gravitational acceleration - K _s proportionality constant defined by eq. [10] - L length of tube - P pressure - Re Reynolds number - t exponent defined by eq. [1] - V mean velocity - V ^* volume of particles in pipe lengthL - W settling velocity of particles - _m factor defined by eq. [1] - shear rate - turbulent pseudo shear rate defined by eqs. [8] and [9] - _w wall shear stress - ( _w) _s increment in wall shear stress due to presence of settling particles - µ _m limiting viscosity at high rate of shear - ₁ density of carrier liquid - _m density of mixture - _s density of solid Professor of Chemical Engineering, University of Toronto and scientific advisor to Worthington (Canada) Ltd.With 8 figures     

The experimental determination of velocity distribution in annular flow

In the study of the flow of a fluid through an annular gap, the outer surface of which is stationary while the inner surface may be rotated, it is necessary to be able to accurately determine the velocity profiles obtaining in the axial, tangential, and radial directions of flow.

A method is described for this purpose employing hot-wire anemometry techniques and typical profiles are presented for each of the above flow directions. In the case of pure axial flow, a comparison is made between experimental and theoretical results, showing a close correspondence.     

Superposition of finite deformations in Mooney-Rivlin materials

Six controllable states are known to exist for all homogeneous, isotropic, incompressible, elastic bodies. It is shown that certain pairs of these controllable states may be superposed in Mooney-Rivlin materials thereby constructing new controllable states for these materials.

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Zusammenfassung Es gibt sechs kontrollierbare Zustände für alle homogenen, isotropischen, inkompressiblen, elastischen Körper. Es ist gezeigt dass gewisse Paare dieser kontrollierbaren Zustände geschichtet werden können in Mooney-Rivlin Materialen und dadurch neue kontrollierbare Zustände für diese Materialen geschaffen werden.

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This work was carried out while both authors were associated with the Department of Aerospace Engineering and Engineering Mechanics at The University of Texas at Austin and was supported by U.S. National Science Foundation Grant GK-37367 to that institution.     

A torsional creep apparatus

Summary This paper describes a torsional creep apparatus for the determination of the creep compliance in shear as a function of time. The instrument is suitable for the measurement of compliances below 5·10^–8 m²/N, in the time range between 1 and 10⁵ seconds. Within five minutes and with an accuracy of 1 C, the temperature of the specimen can be adjusted to any value between –175 and –200 C. From the torsional creep measurements can be calculated the dynamic shear modulus and the corresponding damping. The lowest damping, determined in this way, is several times 10^–3.

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Zusammenfassung Ein Apparat zur Messung des Torsions-Kriechverhaltens wird beschrieben. Das Instrument ist zur Bestimmung von Nachgiebigkeiten kleiner als 5·10^–5 m²/N im Zeitbereich zwischen 1 und 10⁵ Sekunden geeignet. Die Temperatur der Probe läßt sich innerhalb 5 Minuten und mit einer Genauigkeit von 1 C auf jeden Wert zwischen –175 und –200 C einstellen. Aus der gemessenen Kriechfunktion können der dynamische Schubmodul und die dynamische Dämpfung berechnet werden. Eine untere Grenze für die Dämpfung, die man auf diese Weise noch bestimmen kann, ist einige Male 10^–3.

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The work was partly sponsored by the Office of Naval Research, Washington, D. C., under contract number N 62558-3884.     

Experimental and theoretical determination of frequencies of elastic toroids

Experiments are described which determine natural frequencies of five toroidal models whose major diameters are of 10 in. and whose minor diameters vary from 0.25 to 2 in. The experimentally determined frequencies are compared with the theoretical frequencies derived using the elementary theories for the in-plane and out-of-plane vibrations of circular rings of R. Hoppe and J. H. Michell, as well as the method of internal constraints. The comparative results for the frequencies are presented in tabular form.     

Magnetohydrodynamic mixed convection in a vertical channel

The problem of combined free and forced convective magnetohydrodynamic flow in a vertical channel is analysed by taking into account the effect of viscous and ohmic dissipations. The channel walls are maintained at equal or at different constant temperatures. The velocity field and the temperature field are obtained analytically by perturbation series method and numerically by finite difference technique. The results are presented for various values of the Brinkman number and the ratio of Grashof number to the Reynolds number for both equal and different wall temperatures. Nusselt number at the walls is determined. It is found that the viscous dissipation enhances the flow reversal in the case of downward flow while it counters the flow in the case of upward flow. It is also found that the analytical and numerical solutions agree very well for small values of ε.     

Phase split of liquid–liquid two-phase flow at a horizontal T-junction

This paper provides data on the split of liquid/liquid two-phase flow at a horizontal T-junction. Phase maldistribution was measured for kerosene–water flow at the T-junction with equal pipe diameters of 67.4 mm. Data were taken with both stratified flow with a mixture at interface and dispersed flows approaching the junction. The degree of phase maldistribution was not very great but preferential emergence of either phase from the side-arm was observed depending on the flow rates of the two-phases. There are similarities with the limited split data from liquid/solid flows and the degree of separation is seen to depend on the dispersed/continuous phase density ratio. The data were compared to predictions from the correlation by Seeger et al. The Seeger equation gives but reasonable agreement.