Volume 30, Issue 2, April 1986
Index of content:
30(1986); http://dx.doi.org/10.1122/1.549891View Description Hide Description
An analytical solution, based on the lubrication approximation, is given for the flow associated with the consolidation of circular cylinders in a Newtonian liquid. The solution has been obtained from the combined requirements of momentum conservation in the fluid and of overall mechanical equilibrium. The results are presented in terms of both the fluid flow characteristics and the time‐dependent translation pattern prevailing in the cylinder array. The analysis is supplemented by a numerical example illustrating the nature of the solution. This work is relevant to flow problems generally found when forming reactive or nonreactive polymeric composites containing oriented continuous cylindrical fibers.
30(1986); http://dx.doi.org/10.1122/1.549848View Description Hide Description
Novel designs and procedures have been developed which greatly reduce the end effects in a concentric cylinder viscometer. The essential features of the most versatile design are a hollow inner cylinder, open at both ends, conterminous inner and outer cylinders, and a pool of mercury at the bottom of the cup which essentially eliminates the torque exerted on the bottom of the inner cylinder and on the sample in the gap. Preliminary experiments with a Newtonian liquid and a suboptimal design demonstrate that absolute measurements can be made, provided the curved sample/air and sample/mercury interfaces are “symmetrical” across the top and bottom of the gap. The method promises to be particularly suitable for rather viscous, non‐Newtonian fluids, including those with an appreciable yield stress. Existing viscometers can be readily modified to implement these ideas. The limitations are that the fluid to be tested must be considerably more viscous than mercury, and the angular velocity of the cup must be kept below levels where centrifugal forces or normal stress effects start to significantly affect the shape of the sample/air and sample/mercury interfaces.
30(1986); http://dx.doi.org/10.1122/1.549849View Description Hide Description
The dynamics of viscoelastic liquids in a thixotropic shear loop is examined. Shear start‐up and thixotropic loop experiments with an aqueous poly(acrylamide) solution were conducted under a wide range of Deborah and Weissenberg numbers. The transient stresses generated by the liquid were measured and compared with predictions of the Wagner model. An efficient linear regression algorithm, utilizing a singular‐value decomposition routine, was developed and used to extract the linear parameters of the model from dynamic‐mechanical data. The nonlinear parameter was obtained from start‐up data by Wagner's method. The dynamic response of the liquid in a thixotropic loop is characterized by several distinct features, including stress overshoot and residual stress, which are well reproduced by the Wagner model. The general form of the dynamic response function is governed by the specific combination of the Deborah and Weissenberg numbers. Overall, the results indicate that viscoelastic effects may lead to distinct hysteresis in the response function in a thixotropic loop experiment, which may be erroneously interpreted as a rheological thixotropic effect.
Nonlinear Viscoelastic Analysis of Uniaxial Stress‐Strain Measurements of Elastomers at Constant Stretching Rates30(1986); http://dx.doi.org/10.1122/1.549850View Description Hide Description
Two mathematical methods are presented to analyze uniaxial stress‐strain measurements of amorphous polymericmaterials at constant stretching rates. Both methods are based on a well‐known single integral constitutive equation in which the time and strain effects are separated. The first approach results in an analytical equation and is only valid for materials of which the relaxation rate and nonlinearity are restricted. The second method is based on a numerical evaluation of the integral, and is exact for infinitesimal summation steps. Both methods enable the nonlinearity of the strain tensor to be determined if the linear viscoelastic behavior of the material is known.
30(1986); http://dx.doi.org/10.1122/1.549851View Description Hide Description
An experimental study has been carried out to specify the nonlinear viscoelastic behavior of noncrystalline peroxide‐cured EPDM networks covering a range in elongation ratios between one and seven. Stress‐strain curves, measured at constant rates of elongation at 300, 345, and 390 K, are analyzed with two recently published methods. Time and strain effects are shown to be separable. The nonlinear strain measure, determined at various stretching rates, is studied as a function of temperature, cross‐link density, and prepolymer type. These results are compared with the strain measures of two phenomenological theories, namely with the Mooney‐Rivlin equation and a constitutive equation which contains the nonlinear nmeasure of strain, and with the predictions of the molecular theory of elasticity of polymer networks developed by Flory.
30(1986); http://dx.doi.org/10.1122/1.549852View Description Hide Description
The question of slip and the influence of materials of construction on the observed extrudate irregularities are examined for high viscosity molten polyethylenes. Capillary rheometer studies were conducted for several linear (LLDPE and HDPE) and branched (HP‐LDPE) polyethylenes, Viton A, and Barex‐210. Extensive blown filmfabrication studies were conducted for narrow MWD UNIPOL process LLDPE resins. The results indicate that the assumption of “no‐slip at the rigid boundary” is generally not valid for polyethylenes above a critical shear stress of approximately 0.1–0.14 MPa, when either surface or gross irregularities are present in the extrudate. Loss of extrudate gloss at the critical shear stress defines the onset of melt fracture. Within the range of variables examined, the critical stress is relatively insensitive to molecular characteristics (molecular weight, MWD, and chain branching), melt temperature, and the detailed design of the capillary. Contrary to capillary rheometer observations, blown filmfabrication results for LLDPE indicate that materials of construction for the die land region have a significant influence on melt fracture, and suggest breakdown of adhesion at the polymer/metal interface as a primary cause of slip and melt fracture. The results demonstrate that methods to improve adhesion, by proper choice of materials of construction for the die land region and/or use of adhesion promoters in the resin, virtually eliminate the rate‐limiting effects of melt fracture in commercial blown filmfabrication. The results highlight a deficiency of standard capillary rheometer methods to delineate the influence of materials of construction and/or adhesion promoters on observed melt fracturecharacteristics with molten polyethylenes.
30(1986); http://dx.doi.org/10.1122/1.549902View Description Hide Description
The frequency dependences of the storage and loss shear moduli, and of dilute solutions of three cellulose tricarbanilate fractions in tetraethylene glycol dimethyl ether were measured at 25.0°C by the Birnboim‐Schrag multiple‐lumped resonator. The frequency range was 100 to 5800 Hz and the concentration range 0.5 to 3 g/L. The weight‐average molecular weights were 0.4, 0.8, and Intrinsic viscosities were determined by capillary viscosimetry. For interpretation of the results, the bead‐spring coil model and the Yamakawa‐Yoshizaki theory for the intrinsic viscosity of helical wormlike chains were modified to take into account a moderate degree of molecular weight heterogeneity with assumption of a Schulz‐Flory distribution. The viscoelastic data could be fitted by the bead‐spring model with the hydrodynamic interaction parameter or 0.05 and From the intrinsic viscosities, the persistence length was calculated from the Yamakawa‐Yoshizaki theory as 10 nm for all three samples, much smaller than those of semiflexible rodlike molecules previously studied.
30(1986); http://dx.doi.org/10.1122/1.549853View Description Hide Description
We suggest a very simple memory integral constitutive equation for the stress in crosslinking polymers at their transition from liquid to solid state (gel point). The equation allows for only a single (!) material parameter, the strength and it is able to describe every known viscoelastic phenomenon at the gel point. Measurements were performed on polydimethylsiloxane model networks with balanced stoichiometry for which the crosslinking reaction has been stopped at different degrees of conversion. At the gel point, the loss and storage moduli were found to be congruent and proportional to over a wide range of temperature (−50°C to +180°C) and five decades of frequency ω. The hypothesis is made that this behavior is valid in the entire range This congruence hypothesis is consistent with the Kramers‐Kronig relation and leads to a constitutive equation which shows that, for our polymer, congruent functions are as much a rheological property at the gel point as are infinite viscosity and zero equilibrium modulus. This makes it now possible to measure exactly the instant of gelation of a crosslinking polymer without having to stop the crosslinking reaction.
Stress Relaxation as a Method of Analyzing Stress Growth, Stress Overshoot and Steady‐State Flow of Elastomers30(1986); http://dx.doi.org/10.1122/1.549854View Description Hide Description
Stress relaxation behavior is a manifestation of stored memory which existed just prior to the relaxation.Stress relaxation after instantaneous deformation and stress relaxation after constant rate of deformation have already been treated theoretically for the case of linear viscoelastic behavior. This paper extends the interpretation to the large deformation, where the viscoelastic behavior includes nonlinear cases. Of particular interest is the stress relaxation after cessation of steady‐state flow. We have succeeded in estimating the magnitude of deformation, whereby the relaxing stress was converted to a modulus‐time curve. Consequently, the relaxation after cessation of flow can be interpreted in a consistent manner with other types of relaxation, where the magnitude of deformation is known. The interpretation is based on the storage and dissipation of memory in the preceding deformational process. A quantitative comparison of the gain and loss of memory may be made by comparing relaxation modulus‐time curves to see which part of the time‐distribution of memory was affected.