Torsion of a cylinder

The sample, usually in the form of a cylinder, can be subjected to uniaxial compression (the simplest and most common test), uniaxial tension, shear, bending or torsion. In compression, the sample rests on the base-plate and is compressed by a horizontal flat plate attached to the crosshead when... 

The relations discussed above can be applied directly to homogeneous deformations of a body in which the strains are the same everywhere in the sample and the macroscopic deformation of the sample is essentially the same as that of any infinitesimal element of it. In many deformation geometries commonly used for experimental measurements, however, such as torsion between coaxial cylinders, torsion of a cylindrical rod, flow through a tube, flexure, etc., the magnitudes of the strains and rates of strain vary from point to point. Application of the equations of continuity and motion and integration over the sample geometry are then necessary to relate external forces and displacements to the viscoelastic functions. For some cases, if the deformations are small, the geometry is no real complication ... 

An example of a free oscillation device whose deformation geometry is torsion of a circular cylinder is shown in Fig. 6-7. The apparatus of Plazek, Vrancken, and Berge mentioned above under creep is equipped here with a moment arm to provide an adjustable moment of inertia. The oscillations are followed by reflection of a light beam from a mirror attached to the rotating unit onto a photocell, whose output is automatically recorded. From the trace (Fig. 6-8), the characteristic frequency cOc and the decrement A can be obtained it is convenient to match with an adjustable enlarger to standard exponential envelopes. The decrement is proportional to the slope of a plot of the logarithm of the maximum amplitude... 

In recent years a few authors have obtained analytical solutions for the aforementioned equations in multiply connected regions. These authors include Ling [1], Kuo and Conway [2], [3], and Kraus [4]. Ling, Kuo and Conway problems of torsion of multihole cylinders, and solved the problem of two dimensional heat circular region with a ring of holes. These authors employed functions defined by Howland [5] in order to obtain their solutions in the form of multiple series. Kraus also used the same functions to obtain a solution for a perforated... 

Coaxial (Concentric Cylinder) Viscometer, The eadiest and most common type of rotational viscometer is the coaxial or concentric cylinder instmment. It consists of two cylinders, one within the other (cup and bob), keeping the specimen between them, as shown in Figure 27. The first practical rotational viscometer consisted of a rotating cup with an inner cylinder supported by a torsion wire. In variations of this design the inner cylinder rotates. Instmments of both types ate useful for a variety of apphcations. 

When the liquid, solution or lyophobic colloidal suspension contains asymmetric particles or when it is too concentrated, other methods must be applied to measure the viscosity. This is for instance the case with clay suspensions. In the past the viscosity of clay suspensions was measured by means of a bucket with a hole in it. The bucket was filled with clay suspension and after the stopper had been removed from the hole, the time required by the volume to drain was measured as a function of e.g. the volume and composition. Later mechanical methods were applied. One of them is based on the principle that a metal cylinder or disc, suspended from a torsion thread, is exposed to a certain resistance when you rotate it in the solution or suspension. Before the measurement the cylinder or disc is turned 360° anti-clockwise and then released. After having revolved over a certain angle, the cylinder or disc will change its direction of rotation. The rotation angle is a measure for the viscosity. 

Viscosity and Plasticity—Viscosity and plasticity are closely related. Viscosity may be defined as the force required to move a unit-area of plane surface with unit-speed relative to another parallel plane surface, from which it is separated by a layer of the liquid of unit-thickness. Other definitions have been applied to viscosity, an equivalent one being the ratio of shearing stress to rate of shear. When a mud or slurry is moved in a pipe in more or less plastic condition the viscosity is not the same for all rates of shear, as in the case of ordinary fluids. A material may be called plastic if the apparent viscosity varies with the rate of shear. The physical behavior of muds and slurries is markedly affected by viscosity. However, consistency of muds and slurries is not necessarily the same as viscosity but is dependent upon a number of factors, many of which are not yet clearly understood. The viscosity of a plastic material cannot be measured in the manner used for liquids. The usual instrument consists of a cup in which the plastic material is placed and rotated at constant speed, causing the deflection of a torsional pendulum whose bob is immersed in the liquid. The Stormer viscosimeter, for example, consists of a fixed outer cylinder and an inner cylinder which is revolved by means of a weight or weights. 

In a rotational viscometer the solution is filled in the annulus between two concentric cylinders of which either the external (Couette-Hatschek type) or the internal (Searle type) cylinder rotates and the other, which is connected to a torsion-measuring device, is kept in position. Let R, and Ro be the radii of the inner and outer cylinders, h the height of the cylinder which is immersed in the solution or its equivalent height if end effects are present, a> the angular velocity of the rotating cylinder, and T the torque (or moment of force) required to keep the velocity constant against the viscous resistance of the solution. It can be shown that the shearing stress (see, for example, Reiner, 1960) ... 

Three techniques related to oscillating-body methods can be mentioned. One involves measuring the torsional oscillations of a piezoelectric crystal immersed in a fluid it can achieve accuracies of about 2% and has been used in a variety of conditions. A second involves measuring the drag on a rotating cylinder magnetically suspended in the fluid it can achieve uncertainties as low as... 

In the user interface, provision must be made for the user to identify the cylinder or connection on which the operation is to act, and for the user to specify the desired changes. The click-select and menu specification which is characteristic of the Macintosh or of Microsoft Windows (TM) is suited to at least crude specification of these operations. With such direct manipulation of the cylinders the user would find it extremely easy to fold a molecule. For example, rather than painstakingly altering individual torsion angles as is required in software provided with the IRIS graphics station, the user could move an entire sidechain "as an object" in itself. 

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