Energy release rates in a constrained epoxy disc with Hookean and Mooney–Rivlin materials

Assuming that the disc material can be modeled either as Mooney–Rivlin or as Hookean and the steel ring enclosing the disc as Hookean, the energy release rates as a function of the crack length are evaluated and compared. Two loadings are considered––one in which the surface of the star shape hole in the disc is loaded by a uniform pressure and the other in which the temperature of the composite body is uniformly raised. It is found that the linear and the nonlinear analyses give qualitatively similar results for the two loadings. For each load, the energy release rate increases with an increase in the starter crack length, reaches a maximum value and then decreases gradually.     

A study of the freezing of binary solutions saturating a porous matrix

The freezing of a binary solution saturating a porous matrix is investigated experimentally and numerically. An aqueous solution of sodium chloride constituted the binary solution. Spherical glass beads constituted the porous matrix. The freezing was initiated at one of the vertical walls of a rectangular cavity. The temperature distribution in the solid, liquid and mush regions were recorded. A mathematical model that considered conduction as the only mode of heat transfer was developed. The predictions of the model were compared with experimental data. In general, as the model were compared with experimental data. In general, as the model ignored natural convection, the predicted temperatures agreed well with the data during early times in the freezing when conduction was the dominant mode of heat transfer. But as freezing progressed the predictions departed from the data and this departure was larger when the initial superheat was high i.e., when the natural convective flow was vigorous and its influence strong on the freezing process.

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Untersuchung des Gefriervorgangs in einem mit binärer Flüssigkeit getränkten porösen Körper

Zusammenfassung Der Gefriervorgang in einem mit einer binären Flüssigkeit getränkten porösen Körper wurde experimentell und numerisch untersucht. Eine wässerige Lösung von Natriumchlorid bildete die Binärlösung, während eine Glaskugelschüttung den porösen Körper repräsentierte. Der Gefriervorgang wurde an einer der senkrechten Wände einer rechteckigen Vertiefung eingeleitet und die Temperaturverteilung in der Fest-, Flüssig- und Mischphase gemessen. Das zur Überprüfung der experimentell gefundenen Ergebnisse dienende mathematische Modell unterstellte Wärmeleitung als einzigen Wärmetransportmechanisms. Da zu Beginn des Gefriervorgangs die im Modell vernachlässigte natürliche Konvektion gegenüber der Wärmeleitung von geringem Einfluß ist, zeigte sich in diesem Bereich gute Übereinstimmung zwischen Theorie und Experiment. Mit fortschreitendem Gefriervorgang traten immer größere Abweichungen auf, besonders wenn die Anfangsüberhitzung hoch war und folglich die natürliche Konvektionsströmung starken Einfluß auf den Gefriervorgang nahm.

     

On network models of molten polymers: Loss of junctions due to stretching of material planes

Summary In a deforming continuum, material surfaces change their area. If material points are members of a surface which stretches during the deformation, these material points increase their relative distances. The continuum is modeled by a network of macromolecules which form temporary junctions between each other. Junctions on a stretching material surface increase their distance. As a consequence, the probability ofjunction breakage is increased.The stretching of material planes through a material point is described by means of an embedded coordinate system. The metric of this coordinate system is the Cauchy tensorC. Astretch measure _p is defined for arbitrary flows. The stretch measure is used to formulate a memory function in a rheological constitutive equation for large strain. Specific applications are made to unidirectional simple shear, uniaxial extension and biaxial extension.In a consecutive study, comparison with experiments will demonstrate to what degree the selected memory function can describe the actual behavior of the polymer.

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Zusammenfassung Materie-Flächen in einem Kontinuum ändern ihren Flächeninhalt, wenn sich das Kontinuum deformiert. Punkte auf einer Materie-Fläche vergrößern ihre Abstände, wenn die Fläche gedehnt wird. Das Kontinuum stellt man sich als ein Netzwerk von Makromolekülen mit temporären Knotenpunkten vor. Knotenpunkte in einer sich vergrößernden Fläche vergrößern während der Deformation ihren Abstand. Als Folge davon erhöht sich die Wahrscheinlichkeit, daß sich dieseKnoten lösen. Mit einem eingeprägten Koordinatensystem wird beschrieben, wie sich ebene Materie-Flächen, die durch einen Punkt der Materie gehen, vergrößern oder verkleinern. Mit der Metrik des Koordinatensystems, dem Cauchy-TensorC, wird ein Dehnungsmaß _p für Strömungen beliebiger Art definiert. Dieses Dehnungsmaß wird dazu verwendet, die Gedächtnisfunktion einer rheologischen Stoffgleichung für große Deformationen zu formulieren. Das Dehnungsmaß wird für besondere Strömungen wie die einfache Scherung, die einachsige Dehnung und die zweiachsige Dehnung berechnet.In einer späteren Arbeit soll durch Vergleich mit Experimenten gezeigt werden, inwieweit die gewählte Gedächtnisfunktion das Verhalten von Polymerschmelzen wiedergibt.

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On leave from the University of Stuttgart.

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With 2 figures     

Flow of second-order fluids over an enclosed rotating disc

Summary This paper is devoted to a study of the flow of a second-order fluid (flowing with a small mass rate of symmetrical radial outflow m, taken negative for a net radial inflow) over a finite rotating disc enclosed within a coaxial cylinderical casing. The effects of the second-order terms are observed to depend upon two dimensionless parameters ₁ and ₂. Maximum values ₁ and ₂ of the dimensionless radial distances at which there is no recirculation, for the cases of net radial outflow (m>0) and net radial inflow (m<0) respectively, decrease with an increase in the second-order effects [represented by T(=₁+₂)]. The velocities at ₁ and ₂ as well as at some other fixed radii have been calculated for different T and the associated phenomena of no-recirculation/recirculation discussed. The change in flow phenomena due to a reversal of the direction of net radial flow has also been studied. The moment on the rotating disc increases with T.Nomenclature , , z coordinates in a cylindrical polar system - z ₀ distance between rotor and stator (gap length) - =/z ₀, dimensionless radial distance - =z/z ₀, dimensionless axial distance - _s = _s/z₀, dimensionless disc radius - V =(u, v, w), velocity vector - dimensionless velocity components - uniform angular velocity of the rotor - , p fluid density and pressure - P =p/(₂ z ₀₂ ² , dimensionless pressure - ₁, ₂, ₃ kinematic coefficients of Newtonian viscosity, elastico-viscosity and cross-viscosity respectively - ₁, _{2 2}/z ₀ ² , resp. ₃/z ₀ ² , dimensionless parameters representing the ratio of second-order and inertial effects - m = , mass rate of symmetrical radial outflow - l a number associated with induced circulatory flow - Rm =m/(z ₀₁), Reynolds number of radial outflow - R _l =l/(z ₀₁), Reynolds number of induced circulatory flow - Rz =z ₀ ² /₁, Reynolds number based on the gap - ₁, ₂ maximum radii at which there is no recirculation for the cases Rm>0 and Rm<0 respectively - ₁(T), ₂(T) ₁ and ₂ for different T - U _1(T) ⁽⁺⁾ = dimensionless radial velocity, Rm>0 - V _1(T) ⁽⁺⁾ = , dimensionless transverse velocity, Rm>0 - U _2(T) ^(–) = , dimensionless radial velocity, Rm=–Rn<0, m=–n - V _2(T) ^(–) = , dimensionless transverse velocity, Rm<0 - C _m moment coefficient     

Study on Deformation of Polycrystalline Aluminum Alloy Using Moiré Interferometry

Polycrystalline aluminum alloy is manufactured by annealing, compared to the width of the specimen, the size of the grains can not be omitted, which makes the specimen anisotropic. Under uniaxial tension, the deformation field is inhomogeneous. In this study, moiré interferometry is successfully applied to measure the deformation of the polycrystalline specimen. The experimental results presented the stress versus strain responses of the marked grains in different orientations and different shapes. By using fringe centering method, the strain distributions under certain load in the centers and on the boundaries of the grains are analyzed.     

Surface deformation measurements of a cylindrical specimen by digital image correlation

Planar digital image correlation has been extended to measure surface deformations of cylindrical specimens without physical contact for high-temperature situations. A single CCD camera acquires the surface image patterns of a section of a specimen in the undeformed and deformed states to determine two-dimensional displacements on a projection plane. Axial, circumferential and shear deformations are determined through curvature transformation on the two-dimensional projection displacement field. The resolution of this technique was determined for a cylinder of 22.23-mm diameter to be 3.5 μm for the axial displacement, 0.05 percent for the axial and shear strains and 0.08 percent for the circumferential strain when correlation computations are carried out over a field of 5 mm×5 mm.     

Acoustics and dynamics of coaxial interacting vortex rings

Using a contour dynamics method for inviscid axisymmetric flow we examine the effects of core deformation on the dynamics and acoustic signatures of coaxial interacting vortex rings. Both “passage” and “collision” (head-on) interactions are studied for initially identical vortices. Good correspondence with experiments is obtained. A simple model which retains only the elliptic degree of freedom in the core shape is used to explain some of the calculated features.     

Design and stress evaluation of a nonsymmetric pressure vessel

Presently, the large variation in demand for electrical power at different periods of the day imposes new considerations in the evaluation of pressure components in large steam-generating equipment. In the past, pressure components such as valve bodies have been designed for static pressure conditions against bursting with sufficient stiffness to assure operation ability. In today's plant operation, the response of the valve body to thermal transients will have a major influence on the life of the valve. Since the valve body is a compact nonsymmetric body, the direct calculation of stresses is very complex. The evaluation of the behavior of nonsymmetric pressure components under the loads imposed by various operational modes requires information from both analytical and experimental methods of analysis. The contributions from modern computer-calculation programs and three-dimensional photoelasticity are discussed as applied to the evaluation of a valve body used in a large, supercritical steam generator. In the analysis, computer procedures are used to develop the preliminary geometry for pressure loading. Because of the close proximity of the nonsymmetrical openings, a three-dimensional photoelastic analysis is used to calibrate the computer model. Once a satisfactory computer model has been developed for pressure loading, it is used to calculate the thermal stresses. Since stresses have little meaning in themselves, a design basis is necessary to evaluate the significance of the calculated stresses. The design basis must consider the types of failures which are possible and is thus dependent on the temperature at which the valve must operate. A design basis is discussed for the evaluation of pressure components in a boiler system.