Volume 14, Issue 2, July 1970
Index of content:
14(1970); http://dx.doi.org/10.1122/1.549182View Description Hide Description
A constitutive equation is proposed for incompressible materials under isothermal conditions which gives very satisfactory results for the styrene‐butadiene rubber that was investigated. The material functions in this equation are evaluated from the results of uniaxial and equal biaxial stress relaxation tests. Theoretical expressions are developed for a number of deformation histories and compared to experimental results. The uniaxial histories which are investigated are the constant stretch‐rate loading, the exponential loading, and the constant stretch‐rate unloading.
14(1970); http://dx.doi.org/10.1122/1.549184View Description Hide Description
A series solution with terms depending on the curvature of the pipe is presented for the coiling effect. Because of its slow convergence the series is most useful only at Dean numbers below about 16. However, this is the normal range for viscometry with coiled capillaries. Theoretical analysis is also appropriate in this range because as the excess pressure drop due to coiling decreases it is more difficult to measure accurately by experiment. A previously unreported finding is made, that at very low flows all coiled capillaries yield a lower pressure drop than a straight capillary of the same axial length. However, this does not detract from the utility of coiled capillaries for high precision viscometry.
14(1970); http://dx.doi.org/10.1122/1.549183View Description Hide Description
A method is proposed for the solution of boundary value problems in finite elasticity. In this method successive small increments of the prescribed surface displacements and/or stresses and/or body forces are applied until the final prescribed values of these quantities are reached. The method lends itself to straightforward numerical analysis because the differential equations and boundary conditions that must be satisfied, at each increment, are linear in the incremental displacements. The problem is formulated in cartesian as well as curvilinear coordinates and in the material as well as in the spatial coordinate system. No restrictions are placed on the form of the strain energy function, but specific forms of the equations are given for a Neo‐Hookean material.
14(1970); http://dx.doi.org/10.1122/1.549185View Description Hide Description
This investigation represents the application of the theory of large deformation of elastic membranes to the problem of the inflation of an axially symmetric membrane by a linearly varying hydrostatic pressure. The membrane considered here is made of neo‐Hookean material. Under the assumption of very large deformation, it is shown that the stress resultants on the middle surface of the membrane are everywhere equal and constant. The problem is then reduced to a purely kinematic one. The governing equation is found to be nonlinear integral equation of the Volterra type. Further study of the problem shows that, irrespective of their initial configurations, axially symmetric membranes tend to deform to an identical shape under the present system of deforming forces. The exact analytical solution of the nonlinear integral equation has not been found. A computer program has therefore been developed to generate a numerical solution describing the deformed shape when the pressure is exerted by various types of fluids with different weight densities.
14(1970); http://dx.doi.org/10.1122/1.549186View Description Hide Description
Viscous and elastic rheological properties of three very dilute solutions (100 to 500 parts per million) of a commercial drag reducing high molecular weight Polyacrylamid in distilled water are presented. Shear stress (apparent viscosity) was determined over a shear rate range of about by a combination of cone and plate, couette, and capillary tube viscometers, and the first normal stress difference was determined versus shear rate in the cone and plate geometry. Transient response (rebound) characteristics were determined in a unique, specially designed, transient rheometer. A “pseudo‐linear” interpretation of the results of these tests is made in which three fluid parameters, defined in terms of a linear viscoelastic model, are determined as a function of strain.
14(1970); http://dx.doi.org/10.1122/1.549187View Description Hide Description
14(1970); http://dx.doi.org/10.1122/1.549188View Description Hide Description
The effective viscosity of a polar fluid is a measure of the amount of traditional shear viscosity the polar fluid will appear to possess in a particular flow situation. Four classical flow configurations are considered here; Couette flow, plane Poiseuille flow, pipe flow, and flow between concentric rotating cylinders. The principal non‐Newtonian characteristic of polar fluids in these flow configurations is an increased effective viscosity which is dependent upon the relative size and configuration of the flow situation. It is shown that the non‐Newtonian characteristics of polar fluids are more pronounced, and thus probably more easily measured, in pipe flow than in any of the other flow configurations considered here.
14(1970); http://dx.doi.org/10.1122/1.549193View Description Hide Description
We consider a mixed boundary initial value problem for the one‐dimensional damped wave equation At , is assumed to vanish. Here is a parameter which is small when the damping is large. Boundary layer and ray methods are employed to study the solution of this problem. For “quiescent” initial data, the motion is diffusive with diffusion occurring with two time scales. For “oscillatory” initial data, strongly damped, rapidly oscillating waves occur. The problem is a generalization of the damped linear oscillator.
14(1970); http://dx.doi.org/10.1122/1.549189View Description Hide Description
An experimental program was performed to determine the limit of linear viscoelastic response, the onset of yielding, and the condition of gross yielding for a pure and quartz particle filled epoxy resin. The onset of yielding was investigated by a number of different tests, e.g., examination of hysteresis loops, photoelasticity. The tests were performed in both tension and compression over a range of loading times. The limit stresses were found to depend strongly on the loading times.
Non‐Linear Behavior of Viscoelastic Materials. I. Disperse Systems of Polystyrene Solution and Carbon Black14(1970); http://dx.doi.org/10.1122/1.549190View Description Hide Description
To determine non‐linear viscoelasticity parameters for disperse and high‐polymeric systems, some fundamental relations have been derived between these parameters and the experimental quantities by viscoelastometry, particularly with a torsionally oscillating rheometer, on the basis of the general theory presented by Green and Rivlin. The non‐linear viscoelasticity of several disperse systems consisting of polystyrene solutions and carbon black has been measured by means of the torsionally oscillating rheometer at various temperatures ranging from 100 to 170°C, and in a frequency range from to 0.5 cycle per sec. As a result of harmonic analysis of the experimental results, it has been revealed that the resultant torque consists of the fundamental component and odd harmonics, and that the energy dissipated during one cycle is the same as that calculated from the fundamental component alone. Frequency dependence curves at various temperatures for and , which correspond to and for linear viscoelasticmaterials, can be superposed into master curves by horizontal and vertical shifts. The master curves manifest a plateau lower than the ordinary rubbery plateau on the low frequency side.