Volume 18, Issue 1, March 1974
Index of content:
Rheological Properties of Viscoelastic Fluids from Continuous Flow Through a Channel Approximating Infinite Parallel Plates18(1974); http://dx.doi.org/10.1122/1.549352View Description Hide Description
Important rheological properties of viscoelastic fluids can be obtained by studying continuous flow through a channel approximating infinite parallel plates. This flat plate rheometer eliminates or reduces some problems of conventional ones and extends the region of useful measurements to high shear rates. Four pressure transducers are flush mounted on the top plate to measure the normal stress From these measurements the shear stress can also be obtained. The normal stress in the direction of flow is obtained from the measurement of the impact of the exit stream. A Weissenberg rheogoniometer (WRG) is used to measure the shear stress and the primary normal stress difference Data are presented for polyethylene oxide solutions of 0.25%, 0.9%, 2.0%, and 3.0% in water. Newtonian fluids were used to test and compare the apparatus. Fluid viscosities from 0.01 to 6000 poise and normal stresses from 100 to were determined for shear rates from 0.03 to The rotational geometry of the WRG limits its use to shear rates under Further, the precision of normal stress measurement with the parallel plates is better than obtained with the WRG. The shear stress values obtained with the plates are of equivalent precision and higher accuracy. Normal stress dependence upon shear rate is fit by the molecular dumbbell model of Bird et al. over a wide range of conditions. In the upper region the model predicts a slope of 2/3 and is obtained by regression analysis of the data. In the lower region a slope of 2 is predicted and obtained. Extrapolation of and data using this model allows to be obtained at shear rates far higher than with the WRG. The magnitude of the ratio decreases as Polyox concentration increases and the fluid becomes more elastic. The complete state of stress is determined for all Polyox solutions, and pressures at the exit surface and exit centerline are found to contribute substantially to the total stress tensor.
18(1974); http://dx.doi.org/10.1122/1.549328View Description Hide Description
The stress relaxation of viscoelastic material after cessation of steady‐state flow has been investigated. A method is proposed that allows fairly accurate prediction of the shear stress component, as well as the first normal stress component, for a relatively wide range of time and shear rates. The main advantage of the method is in its simplicity, which could make it suitable for engineering calculations.
18(1974); http://dx.doi.org/10.1122/1.549329View Description Hide Description
The failure‐envelope description for tensile failure of viscoelastic materials under uniaxial stress was generalized to multiaxial stresses in a previous paper by the author. In the current paper, the theory is refined and the temperature of application extended from 70°F to the range −35° to 165°F. The material studied was LX‐04‐1, a high explosive composed of 85% HMX crystalline particles and 15% Viton polymer. Data for experimental verification were obtained with biaxial tests on hollow cylindrical specimens. Parameters describing multiaxial failure are determined as a function of temperature. In the strict sense, the theory should be applied only to stress states not far from biaxial since experimental verification is carried out only for biaxial stresses. Experimental limitations prevented a more general verification at this time.
18(1974); http://dx.doi.org/10.1122/1.549327View Description Hide Description
Viscosities, first and second normal‐stress differences, and related materialfunctions were determined for steady‐state and oscillatory shearing of polyethylene oxide and polyacrylamide solutions by use of a Weissenberg R‐17 Rheogoniometer with cone‐and‐plate shearing geometry. Pressure transducers—located along the radius of the plate, with their 0.04‐in‐O.D. pressure‐sensing membranes flush with the plate surface—were used to determine local values of the normal stress. The sensitivity of the transducers was 20–30 for steady‐state and 10–15 for unsteady‐state measurements. The ratio of the secondary to the primary normal‐stress difference was negative, was as large as −0.2 for the solutions studied, and appeared to decrease with increasing shear rates over the shear‐rate range investigated. Complex viscosity and displacement and amplitude functions for both the primary and secondary oscillatory normal‐stress differences were determined as functions of the frequency. A significant improvement in the agreement predicted by the “analogies” between the oscillatory primary‐normal‐stress‐difference functions and the complex viscosityfunctions was achieved in comparison with previous results by reduction of instrument compliance. The Spriggs four‐constant and similar models, as well as the Carreau and Bogue‐Chen models, were compared with our steady‐state and oscillatory data, and these fit the data fairly well; but overall, the Bogue‐Chen model appears to represent the data somewhat better.
18(1974); http://dx.doi.org/10.1122/1.549330View Description Hide Description
Elongational and shear viscosities of bead‐filled styrene acrylonitrile composites were measured in the rubbery flow region at very low strain rates. Composites contained 9–37% spherical glass beads by volume. Within experimental error, elongational viscosity was found to be constant and equal to three times shear viscosity at very low strain rates for the composites containing less than 20 vol % glass beads. The experimental data were used to evaluate a number of the classical theories for the viscosity of suspensions. In general, the theories were more appropriate for the elongational than for the shear data. Both elongational and shear viscosities were discovered to have the same dependence on the filler concentration up to 20 vol % glass beads. Dewetting is very noticeable in high strain tensile testing for all nonzero filler concentrations. In the data presented here, simultaneous measurements of longitudinal extension and lateral contraction established that the samples did not dewet during the viscosity measurements.
18(1974); http://dx.doi.org/10.1122/1.549331View Description Hide Description
Capillary extrusionflow curves of four anionic and five polydisperse polystyrenes have been measured at five temperatures between 170 and 237°C. The non‐Newtonian flow curves of the narrow distribution polymers can be represented by a common master curve in terms of the viscosity ratio and the product of shear rate and a relaxation time. The polydisperse polymers do not yield a single flow curve. Current molecular and semiempirical models do not yield master curves which fit the experimental plots. Exceptions are Pao's model for monodisperse polymers and an empirical relation presented in this article which fits the data of the five commercial polymers studied. The existence of a general theory which represents experimental polymer flow curves satisfactorily has yet to be demonstrated. An acceptable model should predict rheological parameters correctly and should also show why experimental data for polymer melts scatter rather severely. Such scatter often reflects lack of control of an important experimental parameter and it is suggested that this parameter may be connected with differences in the physical significance of various estimates of zero shear viscosity, Shear history of the samples may also be an important factor.
Approximation of Irregular Loading by Intervals of Constant Stress Rate to Predict Creep and Relaxation of Polyurethane by Three Integral Representations18(1974); http://dx.doi.org/10.1122/1.549332View Description Hide Description
Three integral representations for nonlinear creep were employed to predict from constant‐stress creep data the strain resulting from two irregular loading experiments. The stress history for these experiments was approximated by intervals of constant stress rate. By employing this method of approximation and a numerical procedure, the creep representations were inverted to permit predicting from the same constant‐stress creep data the stress resulting from prescribed time‐varying strains. This procedure was used to predict the tensile stress relaxation of two multiple‐step tensile strain tests.
18(1974); http://dx.doi.org/10.1122/1.549353View Description Hide Description
A strain energy density function is proposed which is based on a generalized measure of strain. The function has the form where G, B, n, and m are material constants, and is the first invariant of the (generalized) Lagrangean strain The function fits data on natural rubber and on a synthetic rubber in various homogeneous stress fields up to the point of break. The powers n and m are sensibly independent of temperature, while the two moduli G and B depend linearly on temperature, over the range investigated.
18(1974); http://dx.doi.org/10.1122/1.549354View Description Hide Description
A revised theory is presented of slit‐ and capillary‐die rheometry, which, contrary to the earlier ones, predicts that the ratio of the second normal stress difference to the first, is negative in sign and its magnitudes is always less than unity. In order to test the theory, use is made of exit‐pressure measurements for five polymer melts and six polymer solutions. Exit pressures of polymer melts were obtained from both slit and capillary dies, and exit pressures of polymer solutions were obtained from slit dies with flush‐mounted pressure transducers. The values of first normal stress differences determined from exit‐pressure measurements show good agreement with the ones measured with a Weissenberg rheogoniometer. It has been found that lies between −0.4 and −0.6 under the conditions investigated for five polymer melts. This is in line with recent measurements of the normal stress ratio of various polymer solutions.