Volume 18, Issue 4, December 1974
Index of content:
18(1974); http://dx.doi.org/10.1122/1.549360View Description Hide Description
Available experimental data of shearing flows are used to test the BKZ fluid model. The strain‐energy function is assumed in the form of where is obtained from the small‐amplitude oscillatory shearing data. The function is then calculated from simple shearing data (either shear stress or first normal stress difference). Nonuniqueness of F is seen in the results and it is suggested that the BKZ fluid model can be used only up to moderate shear rates. The stress growth after the start of simple shearing is also predicted and compared with experimental data. The prediction of stress relaxation after the cessation of simple shearing is also made and is qualitatively in agreement with experimental data.
18(1974); http://dx.doi.org/10.1122/1.549345View Description Hide Description
The stress‐growth phenomenon in the eccentric rotating disk (ERD) geometry is analyzed using a linearized Bird‐Carreau integral model. Good agreement is found between experimental observations and predicted responses for a low‐density polyethylene melt. Transient stress response is reported as time‐ and frequency‐dependent moduli. In start‐up, the approach of the viscous and elastic stresses to their steady‐state values at angular velocity Ω is found to be directly related to the decay of the storage modulus in stress relaxation after steady rotation.
18(1974); http://dx.doi.org/10.1122/1.549346View Description Hide Description
The classical energy method of Orr is used to investigate the stability of a plane Couette flow of a viscoelastic fluid obeying the constitutive equation of the so‐called second‐order fluid. For two‐dimensional disturbances of any magnitude, the presence of elasticity has been found to stabilize the flow. For small three‐dimensional disturbances invariant in the flow direction, the presence of elasticity has been found to affect the stability either way, depending on the relative values of the constants in the constitutive equation.
The Measurement of the Elongational Viscosity of Polymer Solutions Using a Viscometer of Novel Design18(1974); http://dx.doi.org/10.1122/1.549347View Description Hide Description
A prototype viscometer of novel design is described. Experiments using the viscometer with solutions of polybutadiene in decalin were carried out, and measurements were taken of thread tension and filament radius. Using a force‐balance equation, these results were used to evaluate the axial stresses in the filament. The effects of gravity, inertia, aerodynamicdrag, and stress history on the elongational viscosity are shown. The results are discussed in the light of previous experimental results and theoretical predictions of the elongational viscosity.
18(1974); http://dx.doi.org/10.1122/1.549361View Description Hide Description
Nonlinear creep under combinations of constant tensile and torsional stresses and recovery are reported for various constant temperatures ranging from 75 to 145°F. Results of the creep tests were describable by a power function of time whose exponent is independent of stress and temperature. These results, in conjunction with previous results from pure tension and pure torsion creep experiments on polyurethane, permitted using the multiple‐integral representation to describe the creep and recovery behavior of this material under different combinations of constant tensile stress, torsional stress, and temperature. Agreement with the creep‐test data is good, and prediction of creep under other states of stress and recovery is satisfactory. Most of the nonlinearity was found in the coefficient of the time‐dependent term.
18(1974); http://dx.doi.org/10.1122/1.549348View Description Hide Description
It had been shown previously that the dynamic viscositiesmeasured by superposing in‐line and transverse small‐amplitude oscillations on steady simple shearing were independent of the base rate of shear at ultrasonic frequencies in the BKZ fluid. This result was derived on the assumption that the shear relaxation modulus had a bounded right‐hand derivative at the origin. The present investigation proves this same result without this assumption. A similar conclusion is derived for the derivative of the storage modulus at high frequencies. In addition, it is shown that these ultrasonicmeasurements cast light on the question of the boundedness of the first two derivatives of the relaxation modulus at the origin.
18(1974); http://dx.doi.org/10.1122/1.549349View Description Hide Description
The deformation response of paving asphalts to small‐amplitude sinusoidal loading in shear is linear and thermorheologically simple so that master curves relating the dynamic shear modulus to the (reduced) frequency can be constructed. A simple analytical expression which gives a good fit to these master curves is proposed. Data were obtained for the response of 14 different asphalts over a range of frequencies and temperatures, and master curves relating the absolute value of the modulus to the reduced frequency were constructed. These were found to fit closely to an equation which is one arm of an hyperbola whose asymptotes represent the purely viscous and purely elastic behavior expected at infinitely low and infinitely high frequencies, respectively. The rapidity with which an asphalt changes from a viscous to an elastic response as the frequency of loading increases (shear susceptibility parameter) is indicated by the distance between the point at which the hyperbola crosses its “modulus” axis and its origin. The phase angle is approximately proportional to the slope of the hyperbola, and the equation relating the phase angle with reduced frequency obtained using this relationship gave an adequate fit to the data. From this equation, and that of the hyperbola, the relaxation spectra of the materials were calculated. Shear susceptibility parameters, limiting viscosities, and moduli at a very high frequency of the materials are given and the increase of these parameters when a Kuwait asphalt was air blown in the refinery is indicated. The method used to fit the hyperbola equation to the data and an indication of the precision of fit are given in the Appendix.
A Phenomenological Study of the Coincidence of Stress, Strain, and Birefringence Tensors in Rheologically Simple Materials18(1974); http://dx.doi.org/10.1122/1.549350View Description Hide Description
The time‐dependent transient values of the stress, strain, and dielectric susceptibility tensors were measured in a circular disk made of a rheologically simple material and subjected to two equal pairs of diametric loads oriented at right angles. The instantaneous application or release of each pair of loads was programmed at different time intervals so that the loading configuration was suddenly transferred from a four‐load rheologic equilibrium situation to a transition state with only one pair of diametric loads. In this way the isotropic point (stress, strain, or birefringent) existing at the center of the disk for the four‐equal‐load configuration split into a pair of isotropic points moving along the diameter of the disk towards its circular boundary as the recovery process in the viscoelastic material developed. The velocities of movement of this pair of isotropic points along the diameter of the disk in the recovery process allowed the study of the phase lag between the stress, strain, and optical principal axes. The material chosen for the experiments was a strongly plasticized epoxy polymer, designated as C‐100‐60‐8, which presented a strong viscoelastic behavior at room temperature. However, the study extended along the whole viscoelastic spectrum of the material from its glassy to its rubbery state, by applying the principle of reduced variables. Important results were revealed for the mechanical and optical viscoelastic behavior of rheologically simple materials extensively used in photoelasticity.
18(1974); http://dx.doi.org/10.1122/1.549351View Description Hide Description