Volume 14, Issue 4, December 1970
Index of content:
14(1970); http://dx.doi.org/10.1122/1.549173View Description Hide Description
In this paper we present the results of uniaxial, equal biaxial, and unequal homogeneous biaxial tension of viscoelastic materials under isothermal conditions and compare them with predictions based on the approximate constitutive equations of Refs. 1 and 2. Theoretical expressions for uniaxial and equal biaxial constant and logarithmic stretch‐rates and for unequal homogeneous biaxial single‐step and double‐step relaxation and constant stretch‐rate are developed and compared with experimental results for a styrene‐butadiene rubber (SBR); agreement is found to be satisfactory. The uniaxial and equal biaxial constant stretch results for very short ramp times are used to predict the behavior of actual single‐step relaxation tests and to study the effects of fast motion on the constitutive equations of Refs. 1 and 2.
14(1970); http://dx.doi.org/10.1122/1.549174View Description Hide Description
The concept of the generalized Newtonian fluid (GNF) provides a useful basis for the formulation of constitutive equations for real materials. The purpose of this paper is to review the rational foundations of the generalized Newtonian fluid, and to discuss the problems involved in its practical application to real materials. Of special interest are the types of material constants which must appear and the dimensionless groups which govern the solutions of boundary value problems. It is demonstrated that, if the material function of a GNF contains one material constant with units of viscosity, it must also contain at least one material constant with units of time (or reciprocal time). The role of this characteristic time for both purely‐viscous and elastic fluids is discussed.
14(1970); http://dx.doi.org/10.1122/1.549175View Description Hide Description
Two new methods for finding the second normal stress difference are proposed; one depends on an analysis of edge effects in a cone‐plate device, the other depends on the shape of the free surface in an open‐channel flow. Additionally, the effect of the edge conditions on the total thrust in a cone‐plate device is considered carefully. Some possible errors in the interpretation of these measurements is found. For two solutions (polyisobutylene/cetane, polyethylene‐oxide/water) the viscometric functions are presented. In both cases the second normal stress difference was found to be negative, in contrast to some earlier conclusions.
14(1970); http://dx.doi.org/10.1122/1.549176View Description Hide Description
The volume changes accompanying extension of peroxide vulcanizates of natural gum rubber were measured using a dilatometer technique. Measurements of the force‐extension behavior and compressibilities were made on the same samples for the range of extension and volume change covered in the volume experiments. A constant compressibility was found; however, the volume changes accompanying extension were not proportional to the isotropic part of the stress. Thus, the strain energy cannot be separated into a sum of two parts, one due to the shear and one due to the dilatation.
14(1970); http://dx.doi.org/10.1122/1.549177View Description Hide Description
The capillary flowproperties of two commercial samples of polystyrene and three narrow distribution samples have been examined. Viscosity and extrudate diameter were measured as functions of temperature, shear rate, capillary diameter, and capillary length. Shear stress was found to be the primary flow variable controlling the swelling ratio (extrudate diameter/capillary diameter); polydispersity was the primary molecular variable. At low shear stresses the swelling ratio in all samples approached a constant value of approximately 1.10, concomitant with the approach of the viscosity to its Newtonian value. At high shear stresses the first normal stress difference, was calculated from the swelling ratio by the momentum balance method of Metzner et al. The values obtained were too small by several orders of magnitude. An alternative approach, in which the increase in diameter at the exit was attributed to stored elastic energy in the fluid, led to normal stresses of the correct magnitude.
14(1970); http://dx.doi.org/10.1122/1.549178View Description Hide Description
Following essentially the analysis of Nakajima and Shida but using a one‐constant stored energy function a simplified relationship is given between recoverable shear strain imposed on a flowing melt during capillary flow and the magnitude of the extrudate swelling on emerging from the capillary. Where experiments on capillaries of several different values cannot be carried out there are some advantages to studies using a zero‐length (orifice) die rather than a long capillary.
14(1970); http://dx.doi.org/10.1122/1.549196View Description Hide Description
In the course of our work on the characterization of materials by our kinetic interpretation of non‐Newtonian flow, it had become desirable to make measurements other than at steady state constant shear rate and the sudden application of a steady shear. The present paper describes four modifications we have made and used: (1) a torque detection system to eliminate upper cone motion during transient and oscillatory measurements; (2) measurements under both unsteady and steady state condition in a constant stress field; (3) a versatile and inexpensive oscillatory capability to allow both amplitude and frequency variation of nearly any wave form desired; and, finally, (4) the measurement of the primary normal force difference under any conditions, with essentially no change in gap setting. Examples of typical results on a concentrated polymer solution are presented.
14(1970); http://dx.doi.org/10.1122/1.549179View Description Hide Description
A new method for description of viscoelastic functions with Prony series of exponentials is presented and compared with existing methods. This method places constraints on the coefficients of the series which guarantees smoothness of the functions and a discrete spectral representation. An optimization technique is used to obtain the solution. The resulting series permit the use of Whittaker's method of solution of integral equations which is specialized to the case of viscoelastic analysis, and an exact relationship is obtained between creep and relaxation functions.
14(1970); http://dx.doi.org/10.1122/1.549180View Description Hide Description
A linearized stability analysis has been applied to a fluid flowing in a gravity field between horizontal planes in Couette flow under conditions such that the temperature of the bottom plane exceeds that of the top. The analysis was carried out for two different forms of constitutive equations: (1) a “generalized second‐order equation,” which is a differential model usually associated with continuum theories, and (2) an integral equation which has its basis in a molecular model and accounts for network junctions which rupture at a certain critical strain. Both models lead, after application of a number of simplifying assumptions, to the same set of differential equations which must be satisfied at a condition of nonoscillatory marginal stability. In contrast to the case for Newtonian fluids, there is coupling between the equations describing momentum and energy disturbances. This fact leads, for viscoelastic fluids, to a critical Rayleigh number which is dependent upon flow properties. In particular, the critical Rayleigh number is highly sensitive to the sign and magnitude of the second normal stress difference, a result shared with earlier studies of some other stability problems. Significance of the results is discussed.
Shear Rate Dependent Relaxation Spectrum: Conversion from Dynamic Viscosity to Steady Flow Viscosity for Polyethylene Melts14(1970); http://dx.doi.org/10.1122/1.549181View Description Hide Description
The steady flowviscosity η and the dynamic viscosity η′ of several linear polyethylene melts (190°C) were measured using the Weissenberg rheogoniometer and the Instron rheometer. In correlating the two viscosities, the use of Graessley's theory of viscosity in steady shearing flow in combination with the box distribution of relaxation times as suggested by Maruyama et al. has been critically examined. The new approach discussed in this paper uses Graessley's functions and in conjunction with the relaxation spectrum derived from linear viscoelastic data using an iterative method. The required relation is where γ̇ is the shear rate and τ is the relaxation time. Here and A good agreement was obtained in all cases without involving any coordinate shift. The approach illustrated in this article enabled us to estimate quantitatively the effect of shear rate on the relaxation spectrum and also to estimate fractional contribution to the viscosity at a given relaxation time and shear rate.