Volume 9, Issue 2, September 1965
Index of content:

Analysis of Flow Properties in Relation to Molecular Parameters for Polymer Melts
View Description Hide DescriptionReported data on polystyrene, polyethylene, and polydimethylsiloxanes are contradictory with respect to the shear rate at which the transition from Newtonian to non‐Newtonian flow occurs. Some data implies that the transition occurs at the same lower limiting shear rate and is independent of molecular weight above a critical molecular weight. On the other hand, other data shows that above a critical molecular weight the transition occurs at lower rates of shear as the molecular weight increases. The considerations of Bueche for melt polymer flow confirm the latter type of transition behavior. It is proposed that the discrepancies are due to molecular weight distribution, temperature effects, and methods of obtaining zero shear viscosities. Data are presented to support these views.

Steady‐State Melt Viscosity of Plasticized Hydrocarbon Elastomers
View Description Hide DescriptionThe steady‐state melt viscosity of several plasticised hydrocarbon elastomers is shown to be described by a reduced variable treatment which allows superposition of the viscosity‐shear rate curve for any polymer containing a diluent on the viscosity curve of the pure polymer. The shift factors which accomplish this superposition may in turn be broken up into two factors: (1) a function of the volume concentration of the diluent alone, which represents the loosening of the entanglement network, and (2) a factor representing the effect of the diluent on segmental friction and chain configuration. The latter is shown to be related to the temperature of measurement and the glass transitiontemperatures of both polymer and diluent. The relationships developed permit predictions of plasticizer efficacy for any diluent/polymer combination from glass transition and density data alone.

The Flow of a Molten Polymer
View Description Hide DescriptionThe Williamson empirical equation which fits polystyrene melt viscosity data is derived by considering the melt as a system of elastic springs which are entangling and disentangling. The theory allows one to trace changes in the number of extensible elements and the relaxation time for the rupture of intermolecular links. For uniform molecular weight samples, the number of extensible elements per molecule is proportional to the molecular weight. Widening the molecular weight distribution lowers the number of extensible elements per cc. The thermal relaxation time increase rapidly with increasing molecular weight. The effect of fillers on the number of extensible elements and the relaxation time is complex.

Viscosity Measurements near a Million
View Description Hide DescriptionViscosity measurements are reported for a variety of systems as a function of shear using a thin film, double‐thermostatted, concentric cylinder viscometer. The basic instrument design and the cylinders which are of unusually narrow clearance and fine machining permit accurate and precise viscosity measurements to be made at homogeneous shear rates up to two million Measurements are reported on a molecular weight series of pure normal paraffin hydrocarbons from to Viscositiesmeasured at the highest shear agree within a precision of 2% and better with known low shear hydrocarbon viscosities. This result indicates an absence of both heating effects and molecular degradation and reveals Newtonian flow over the entire shear rate range of the instrument. Similar tests were also performed on several pure cyclic compounds in a test for conformational shifts between rotational isomers which possibly could be induced by a high shear field. The improved high shear concentric cylinder viscometer was also used to double the shear rate range for the established viscosity of standard API Oil 104, which is the most widely studied and the most non‐Newtonian of current non‐Newtonian viscosity standards.

The Influence of Additional Orientation Mechanisms on the Theory of Streaming Birefringence
View Description Hide DescriptionThe problem of determining the orientation distribution function of rigid particles of arbitrary shape is formulated in a general stochastic approach to consider any acting orientation mechanism, stochastic or deterministic. The effect of the various orientation mechanisms on the partial differential equation of the problem is analysed. A particular orientation mechanism acting on rigid ellipsoidal macromolecules in addition to the hydrodynamic and the Brownian effects is considered in Couette flow: a force field in the radial direction x, varying linearly with x. It is shown that the effect of a uniform electric field in the radial direction on polarizable ellipsoidal particles is of this nature. The corresponding steady‐state orientation distribution function is determined to the third order for the case of predominant Brownian influence, and the theory of streaming birefringence of a dilute suspension of rigid ellipsoidal macromolecules in Couette flow is generalised to include the influence of the additional orientation mechanism: the direction of the isocline and the amount of birefringence are calculated to the second order.

Viscoelastic Behavior of a Filled Elastomer in the Linear and Nonlinear Range
View Description Hide DescriptionRheological behavior of a filled elastomer consisting of a polyurethane rubber and granular potassium chloride was investigated with both long‐ and short‐term loading producing conditions of torsion, uniaxial tension, and compression. The volumetric response and the thermo‐rheological behavior of the elastomer was also studied. To represent the observed behavior for moderate stresses and strains a linear viscoelastic model was developed. The results of torsion relaxation tests performed on the inert solid propellant are presented for three strain levels over the temperature range −60 to +200°F. The torsion relaxation moduls (at 5 sec for 4.31% initial shear strain) was changed by 2 orders of magnitude for a temperature variation of −60 to +200°F. Prolonged exposure to high temperatures and humidity degraded the rubber‐to‐filler bond so that the predominant relaxation response was that of a polyurethane rubberfoam.

Thermal Effects in Model Viscoelastic Solids
View Description Hide DescriptionAs part of a general study of the behavior of materials with temperature‐dependent properties, simple models of a viscoelastic solid are considered here. Ideal experiments at constant stress and constant rate of deformation are examined. The analysis leads to yield and fracture criteria which in the usual theory are regarded as experimentally determined quantities. Rate of strain and size effects are also deduced and a phenomenon resembling strain hardening can develop. The treatment is independent of, but complementary to, the atomic scale theories of the deformation of solids. The temperature coefficient of viscosity which is introduced into the continuum theory here, is related to the energy of activation for the flow process which is accessible to the atomic scale theory. Knowledge of the temperature field in which motions of the atoms occur could improve the predictions based on dislocation theory.

Time, Temperature, and Molecular Weight Effects in Environmental Stress Cracking
View Description Hide DescriptionA parametric study was made of the stress relaxation of linear polyethylene in air and a stress cracking environment, Igepal. Breaking time is shown to be a function of reduced variables of time, temperature, and molecular weight. Acreleration of tests for failure time can be achieved if the test temperature is raised, since for 0.96 density P.E. over the range of 50–110°C no mechanism change occurs. Stress relaxation measurements are shown to give results similar to the bent strip stress cracking test (ASTM D 1693‐60T). This latter test can also be accelerated 80 times for 0.96 density polyethylene and 1500 times for 0.95 density polyethylene. A slight modification of the test procedure is required to obtain meaningful results. Some effects of strain, thickness, and presoaking are also reported.

Peel Adhesion: Micro‐Fracture Mechanics of Interfacial Unbonding of Polymers
View Description Hide DescriptionA simple and precise means of measuring internal bond stresses in peel is now available. By the use of a newly designed “bond stress analyzer” the magnitude and positional distribution of internal normal stresses may be measured during peel. The design theory, construction, and operation of the instrument are reviewed in detail. The influence of the angle of peeling upon the cleavage stress distribution is investigated and analyzed. The results, interpreted in terms of present theory of peel adhesion, suggest that the peel test is a valid measure of interfacialadhesionproperties only at a peel angle of The detailed form of the cleavage stress function in the region of boundary fracture indicates that cavitation and orientation processes contribute importantly to high peel strengths in elastomeric adhesive interlayers.

Tear Phenomena around Solid Inclusions in Castable Elastomers
View Description Hide DescriptionAdhesion studies on spherical particles imbedded in elastomers have shown that cohesive failure of the binder phase always precedes dewetting. The latter is a sudden and irreversible process resulting in permanent damage to the system. Cohesive failure manifests itself in the formation of a number of small holes near the surface of the filler particle. The stress causing these holes is well defined and depends only on the elastic modulusE of the binder: The further propagation of these initial tears depends on the consistency of the boundary layer surrounding the solid inclusion. In case of no modulus gradient or a softer boundary layer, tear propagation leads to the complete separation of the elastomeric binder from the particle. High modulus layers, which are linked to the polymeric matrix by primary chemical bonds, prevent a dewetting. It is shown that the complex response of filled elastomers can be explained in terms of the above results.

The Transient Response of a Viscoelastic Torsional Pendulum
View Description Hide DescriptionThe pendulum consists of a circular viscoelastic rod fixed at one end and attached to a disk at the other end. The disk, initially at rest, is subjected to a step function of torque. The subsequent motion is analyzed in terms of normal modes and normal coordinates. The normal modes are found by separation of variables. The characteristic numbers associated with these modes depend only on the moments of inertia of the disk and rod. The normal coordinates satisfy integro‐differential equations of the Volterra type. The mechanical properties of polyisobutylene at 25°C were represented in differential operator form. The Volterra integral equations were then solved by means of the Laplace transforms. An analysis of the numerical results shows that only the oscillatory part of the fundamental mode should persist after a short time. This result is in qualitative agreement with observations. This method of analysis may be applied to other dynamic problems in linear viscoelasticity provided the characteristicequation can be reduced to a form that does not involve the mechanical properties of the material.

Thermistor Analogs for Model Viscous and Viscoelastic Systems
View Description Hide DescriptionThe physical and mathematical similarity of the resistance‐temperature relation in thermistors to the viscosity‐temperature relation in typical liquids makes it possible to simulate the essential nonlinearity of the flow of model Newtonian liquids by the use of an electric analog. Simple measurements of current and voltage take the place of detailed computation. Circuits containing a thermistor and capacitor provide a model for nonlinear viscoelastic materials. A transmission line containing thermistors would be applicable where inertial terms are important and both the time and space variation of the stress would be significant. The behavior of simple analogs described here agrees with available numerical computations. In addition, it duplicates experimentally observed temperature effects and apparent departures from Newtonian behavior in liquids as well as necking, yield, fracture, creep, strain hardening, and stick‐slip effects in solids. This electric analog literally simulates the model mechanical system. In contrast, the widely discussed simulation of linear viscoelasticity by electric networks is figurative. That is, there, the well‐developed mathematics of linear circuits was applied to the mechanical system. The new simulation is effective over wide ranges of stress, strain, and time even with a single thermistor.

Laminar Converging Flow of Dilute Polymer Solutions in Conical Sections. II
View Description Hide DescriptionThe test fluids were three aqueous solutions of Natrosol 250 H hydroxyethyl cellulose. Their nominal concentrations were 0.3, 0.5, and 0.7%. Viscosity data for each solution wee filled with a generalized Newtonian viscosity model which properly describes the zero‐shear viscosity. The test geometries were two conical sections. Their vertex angles were approximately 14 and 21°. Laminar flow rate vs. pressure drop data were taken for each Natrosol solution in each conical section. Approximate expressions relating flow rate and pressure drop were derived for the limiting cases of very low and very high flow rates. The low flow rate (non‐Newtonian flow) expression was of form: pressure of (flow rate, geometry, viscosity model parameters). The high flow rate (inviscid flow) expression was of form: pressure of (flow rate, geometry, fluid density). These two expressions were in excellent agreement with data at low and high flow rates. The sum of these two expressions was in good agreement with data over the entire range of flow rates. This superposition expression in no way accounts for normal stresses, time‐dependent elasticeffects, or the effect of the third invariant on viscosity. Its success in describing the data implies that these phenomena were not important. For engineering purposes generalized Newtonian viscosity models will probably be adequate for characterizing the flow of dilute polymer solutions in conical sections.

Non‐Newtonian Flow through Porous Media. I. Theoretical
View Description Hide DescriptionA method is suggested for characterizing viscoelastic fluids in an approximate but useful way for the description of flow in complicated geometries. This method rests on the determination of a zero‐shear limiting viscosity, a characteristic time, and a dimensionless parameter relating to the slope of a log‐log plot of viscosity vs. shear rate in the “power law” region. It is then shown how such parameters can be used in correlating experimental data on pressure drops through packed beds at constant volumetric flow rate. This is done by a combination of a porous medium model calculation and dimensional analysis. It is shown how the characteristic time of the fluid can be used to designate regions of behavior where elastic effects are important.

Non‐Newtonian Flow through Porous Media. II. Experimental
View Description Hide DescriptionIn the study of the flow of shear‐sensitive fluids through porous media, fourteen different aqueous solutions of polyethylene glycol, polyvinyl alcohol, and hydroxy‐ethylcellulose were investigated. The shear‐sensitive viscosities of these fluids were characterized by the three‐parameter Ellis model. Two different types of flow behavior were observed: (1) When the volumetric flow rates were held constant, the results were both steady and reversible. The flow data were successfully correlated by a modified Darcy's law. It is shown that the characteristic time of the fluid can be used to designate regions of behavior where elastic effects are important. (2) When the pressure drop across the porous medium was held constant, the results were both unsteady and irreversible. In this case, polymeradsorption and gel formation were believed to have occurred throughout the bed.

Experimental Determination of the Secondary Normal Stress Difference for Aqueous Polymer Solutions
View Description Hide DescriptionAn axial annular flow device has been utilised to determine the secondary normal stress difference [where the velocity field is ] for several aqueous polymer solutions. Data are presented on the radial pressure difference, at a fixed axial position, between inner and outer walls of the annulus vs. the axial pressure gradient. The data are analyzed by numerically integrating the radial component of the equation of motion using a nonlinear generalized Maxwellmodel proposed by Spriggs to obtain a trial function for Results indicate that the secondary normal stress difference, while not zero, is considerably smaller than the primary normal stress difference, for the solutions studied.

Typical Lubricating Greases as Linear Viscoelastic Materials
View Description Hide DescriptionThe results of an experimental study of rheological properties of typical lubricating greases are reported in this paper. Viscosity‐shear rate relations are compared for steady‐state shear and for transient shear conditions of stress relaxation and creep. In steady‐state shear the systems are non‐Newtonian, but under transient conditions of shear stress relaxation, they are linear viscoelastic for strains approaching their ultimate yield strain. The linear viscoelastic nature of two greases was confirmed by studies of the damping of a torsion pendulum for small strains. A sodium soap grease is shown to be linear viscoelastic by an analysis of creep data from the literature. Recognition of the wide range of strains for linear viscoelastic behavior simplifies the study of the flow and deformation of greases.

Combined Stress‐Creep Experiments on a Nonlinear Viscoelastic Material to Determine the Kernel Functions for a Multiple Integral Representation of Creep
View Description Hide DescriptionA multiple integral functional relationship has been employed as a constitutive equation for nonlinear creep of viscoelastic material under combined stress. The kernel functions of this representation for first, second and third order stress terms have been determined from tests on a single tubular specimen of polyvinyl chloride copolymer. Tests needed to determine kernel functions adequate to describe multiaxial creep under constant stress were found to be three pure tension tests at different stress levels, three pure torsion tests at different stress levels, and two combined tension‐torsion tests. Experiments include twenty tests under various combinations of tension and torsion of the same specimen. The use of only one specimen was made possible by the fact that following 2 hr of creep the recovery in 4 days was almost complete. Agreement between the multiple integral representation and experimental results was very satisfactory. Agreement with a hyperbolic sine representation of stress dependence was less satisfactory owing in part to the fact that the synergistic effect of tension plus torsion in the nonlinear range was not accounted for.

Viscoelastic Response of a Cohesive Soil in the Frequency Domain
View Description Hide DescriptionEnergy storage and energy dissipation characteristics of a cohesive soil are studied in the frequency domain using strain‐controlled vibratory uniaxial compression tests. Such characteristics are important considerations in earthquake phenomena, machine foundation design, and soil‐structure interaction under dynamic loading. The soil response is expressed in terms of the storage, loss, and complex moduli as well as the loss tangent. Dynamic stress‐strain amplitude response is nonlinear even at small values of dynamic strain. Storage, loss, and complex moduli decrease with increased dynamic strain amplitude. The energy dissipation expressed in terms of the loss tangent decreases with increases in moisture content, frequency, and dynamic strain amplitude. Loss tangent values determined by the direct method are compared with those obtained by transformation of stress relaxation test data. Effects of concentration (moisture content) are presented in terms of a non‐dimensional dynamic stress‐strength parameter using the ultimate compressive strength in uniaxial compression as a consistency index. Static stress level about which the dynamic perturbations take place has no apparent effect on the dynamic stress‐strain response for the range studied.

Viscoelastic Properties of Glucose Glass near Its Transition Temperature
View Description Hide DescriptionStorage and loss shear moduli of supercooled glucose have been measured at thirteen temperatures from 27.4 to 41.1°C in the frequency range from 0.3 to 1.8 cps. Shear creep has been measured at four temperatures from 41.1 to 47.6°C. The temperature dependence of the storage moduli and the creep compliance was described by reducing the time and frequency scales with shift factors calculated from the WLF equation, the constants corresponding to a fractional free volume of 0.026 at 41.1°C and a free volume expansion coefficient of The loss moduli plotted against reduced frequency did not give a single composite curve, however. Conversion of the dynamic measurements to creep compliance by approximation methods provided the latter function over ten decades of logarithmic time except for a gap of three decades in the middle of the range. At long times, the creep was indistinguishable from viscousflow; the viscosity at 41.1°C was At short times, the limiting creep compliance appeared to be and there was an additional time‐dependent compliance of at least this magnitude with a broad distribution of retardation times. The relaxation and retardation spectra were calculated for this region.