Volume 9, Issue 1, March 1965
Index of content:

Steady‐State Melt Flow Behavior of Polyethylene Blends
View Description Hide DescriptionThe steady‐state melt flow behavior covering six decades of shear rate was studied for various types of polyethylene and their blends. Two instruments were used. The Kepe's cone and plate consistometer measuresviscosities at low shear rate at the range from to A gas‐driven capillary viscometer gives high shear data. The shear stress at the capillary wall was calculated by the method proposed by Bagley and the shear rate at the wall was obtained after Robinowitsch. A special effort was made to observe the change in low shear flow behavior of a resin due to an addition of gels, high ends or low ends of molecular weight distribution. Addition of low ends up to 20% does not alter the “shape” of the viscosityshear rateflow curve appreciably. But with an addition of high ends, the “shape” of the flow curve changes considerably. With an addition of gels, the flow curve at low shear rises rapidly as shear rate decreases. An inflection was observed followed by a “tail‐up” at the low shear range.

The Effect of Pressure Losses in the Barrel on Capillary Flow Measurements
View Description Hide DescriptionMelt flow data, obtained from capillaries having constant length‐to‐diameter ratios, but different diameters, do not lie on a single curve. At constant shear rate the apparent viscosity decreases with capillary diameter. This diameter effect has been interpreted by some investigators as an indication of slippage along the capillary wall. This paper presents data which demonstrate that, if corrections are made for pressure drop in the rheometer barrel, the flow curves coincide. Although it has been recognized that pressure losses in the barrel can have a significant influence on melt index values, it has usually been assumed that they are negligible in high shear measurements. However, if reliable flow curves are to be obtained, the barrel losses cannot be ignored. Furthermore, the value of losses can be used to calculate the shear stress in the barrel and thus extend the range of the measurements.

Elastic Stress‐Strain Relations in Perfect Elastic Fluids
View Description Hide DescriptionThe theory of perfect elastic fluids deals with the non‐equilibrium thermodynamics of finite viscoelasticdeformation. The thermodynamics of finite elastic strain and of perfect elastic fluids are discussed. It is shown that the stress‐strain relations for perfect elastic fluids may be written in a way which appears formally identical to those in elasticity theory, but the form of this dependence depends on past history.

Studies of a Polymer Melt in an Orthogonal Rheometer
View Description Hide DescriptionA method has been developed for measuring three orthogonal forces in a polymer melt subjected to shear. Data are presented showing the relationship of these forces to shear rate for linear polyethylene. It has been found possible to measure the elastic and viscous forces while varying the shear rate in two different independent manners: (1) by varying the time scale of applying a given magnitude of shear deformation; (2) by varying the magnitude of shear deformation for a given time scale of application. Method number one results in the usual nonlinear relationship between shear stress and shear rate for polymer melts. Method number two results in a linear relationship between shear stress and shear rate thus making it possible to determine a single value of the coefficient of viscosity for any given time scale of application of shear strain. By varying the time scale of strain application, it has been found possible to measurepolymer meltviscosities from essentially the zero shear rate viscosity to the disentangled viscosity.

Polyethylene Melt Viscosity: Shear Rate‐Temperature Superposition
View Description Hide DescriptionThe steady‐state melt viscosities of both high density and low density polyethylene have been investigated for a series of samples over four decades of shear rate and a range of temperatures from 120°C (150°C for high density samples) to 300°C. In the case of low density polyethylene a broad range of molecular weight distributions was covered. Melt viscosity measurements were made using a capillary extrusion rheometer and a capillary with for which it was demonstrated that end‐corrections were negligible. Using arbitrary reference temperatures, a superposition‐temperature method was found to be applicable over the entire region of shear rates and of temperatures. A single set of superposition shift factors (for a given reference temperature) was found to be general for all low density polyethylene samples regardless of molecular weight distribution, and a second set was applicable to all of the high density samples. The dependence of the shift factors on temperature was described by a simple exponential, or Arrhenius, equation with activation energies of 11.3 kcal/mole and 6.3 kcal/mole for low density and high density polyethylene, respectively.

Yield Stress Master Curves for Various Polymers below Their Glass Transition Temperatures
View Description Hide DescriptionYield stress master curves are presented for poly(methyl methacrylate), polystyrene, polyvinyl chloride, and polyethylene terephthalate. Tensile yield stress was measured at strain rates varying from 0.003 in./in./min to 300 in./in./min and at temperatures varying from approximately 15°C above the glass transition temperature to at least 100°C below The resultant yield, or in the brittle temperature range, failure stress, when plotted as a function of logarithm of strain rate, has been shifted laterally to construct a yield stress master curve similar in concept to the well‐known stress relaxation master curve. These master curves cover from 12 to 18 decades of shifted strain rate. The master curve for each material has a characteristic slope which leads, in each case, to a simple equation relating yield stress to strain rate and temperature and is applicable for temperatures from to approximately 100°C below The temperature‐dependent shift factors of each material were determined for both yield stress and stress relaxation over the temperature range. Comparison of these curves shows that in both the ductile and brittle temperature ranges of each material, the shape of the yield stress and stress relaxation curves are very similar. However, the absolute magnitude of the change with temperature can be substantially different. Two possible explanations for this difference are offered.

Flow of Power Law Fluids in Rectangular Ducts
View Description Hide DescriptionThe equations governing pressure flow and drag flow of the power law fluid in channels of rectangular cross‐section have been solved. Application is made to the calculation of wall effects and die characteristics for screw extrudes. It is shown that the Newtonian wall corrections usually used in extruder calculations can lead to considerable error for markedly non‐Newtonian melts in deep flighted screws.

The Stretching of a Viscous Tube over a Conical Mandrel
View Description Hide DescriptionThe theoreticalanalysis of mandrel processes has been extended to cases involving viscousmaterials. An exact solution is obtained for the Newtonian fluid. The results show that a wide range of biaxial stretching patterns can be obtained by controlling the surfacefriction, input and take‐off velocity and the temperature gradient. Conditions necessary for uniform biaxial stretching are shown.

Creep and Recovery Properties of a Zinc Phosphinate Polymer
View Description Hide DescriptionThe investigation of the torsional creep and recovery behavior of a coordination polymer at five temperatures from 100 to 200°C has revealed an unusual rheological behavior. A high temperature aging effect which appears at least partially reversible is observed. Observed creep deformation which is linear in time, followed by a delayed recovery, is explained as a consequence of a void in the retardation spectrum. Temperature reduction is achieved and the temperature shift factors are analyzed in the light of the WLF equation. The measurements were made with a recently developed creep instrument which employs a magnetically levitated rotor and a drag cup motor for precision torque production.

An In Vitro Investigation of Ciliated Activity
View Description Hide DescriptionDiseases of the respiratory tract may be related to the altered rheological properties of the respiratory tract mucus and to the altered ciliary shearing capabilities. Flow curves are presented showing that mucus has thixotropic properties and has discrete yield points. Mechanical models of cilia constructed to perform oscillatory motions comparable to those in vivo have been studied as shearing elements in a modification of the Hoppmann‐Miller Rotational Fluid Flow Generator. A description of those modifications is presented with special attention being given to the design of special cams needed to carry out the proper oscillation of the simulated cilia. Flow trends and particle path lines are described for the mechanical cilia oscillating in and out of phase. Linear velocity of small particles injected into the flow is measured as a function of frequency of oscillation. Finally, some interesting questions are raised pertaining to in vivo ciliated activity in light of experience gained with the apparatus.

Energy Dissipation of a Cohesive Soil by the Fourier Transformation of Stress Relaxation Response
View Description Hide DescriptionThe energy dissipation of a cohesive soil is obtained by the Fourier transformation of stress relaxation test data. Energy dissipation is expressed in terms of the loss tangent. The soil response is nonlinear. Because of the difficulty in obtaining a mathematical expression to fit the relaxation data adequately over the entire time scale of interest, an approximate method of evaluating the transform is used. The relaxation response functions are approximated by straight line segments to form a piecewise continuous relation. By using a large number of straight line segments, the error between the actual and approximate transformation can be made negligible. The segment slopes with corresponding values of time are used in a digital computer program to evaluate the transform. The results clearly indicate a decrease of loss tangent with increased applied strain level. For constant strain level, the variation of loss tangent as a function of moisture content is not clearly defined. The loss tangent vs. logarithm of time relation gives a characteristic single peak bell‐shaped distribution for each strain level.

A Unified Derivation of Constitutive Relations for Irrecoverable Deformation
View Description Hide DescriptionConstitutive relations are derived for isotropic materials in which local thermodynamic equilibrium obtains and for which the internal energy of each element depends only upon the volume and entropy of the element. The basis of the derivation is the principle that the material possesses a non‐negative entropy production function which depends upon the rates of deformation. Results include constitutive relations for viscous,plastic, and viscoplasticdeformation.

Polynomial Constitutive Equations for Viscoelastic Materials with Large Initial Deformation
View Description Hide DescriptionA polynomialconstitutive equation is given which governs the behavior of a viscoelastic solid experiencing small, time‐dependent strains superposed on large initial deformations. Through this equation, it is shown that the incremental state of stress is related to the history of incremental deformation through twelve relaxation functions, which may depend on the initial deformation. Finally, by means of direct comparison with a parallel relation obtained through thermodynamics of irreversible processes, further important restrictions on the number and character of the relaxation functions are established.

Statistical Variability of Ultimate Properties of SBR Gum Vulcanizates
View Description Hide DescriptionThe statistical variability of ultimate properties for 8 samples of SBR‐sulfur gum vulcanizates differing in crosslink density by a factor of about 25 was studied. It is shown that these variability data, determined at one rate and one temperature, can be correlated when plotted as a reduced failure envelope. The envelope obtained in this manner agrees reasonably well with the reduced envelope previously reported which was constructed from break data obtained by testing (a) single specimens of constant crosslink density at varying rate and temperature and (b) single specimens at constant rate and temperature but varying crosslink density. It is also shown that the statistical variability data for all samples, including a benzene‐soluble one, can be represented by a double exponential cumulative distribution function. It is also shown, in agreement with previous work, that the most probable values of when plotted as a function of exhibit a maximum in at a low value of

Experimental Study of the Flow of Two‐Phase Systems at High Temperature
View Description Hide DescriptionThis paper deals with the description of an apparatus employed for the performance of mechanical tests on specimens of 2‐phase materials. In particular, a new optical‐photoelectric method is described in some detail, which has been used for the direct measurement of deformations in the high temperature field (up to 2000°C). The strain‐time graphs obtained from isothermal short‐time creep tests of some of these materials are discussed.

The Viscoelastic Relaxation Mechanism of Inorganic Polymers. I. The Polyphosphoryldimethylamides
View Description Hide DescriptionThe viscoelastic properties of the polyphosphoryldimethylamides were investigated by the technique of stress relaxation as a function of the N to P ratio, and therewith of the chain length. From the great similarity of the shape of the curves to those of “normal” organic polymers, i.e., poly(methyl methacrylate) or polystyrene as a function of the molecular weight, from the broad distribution of relaxation times, as well as from the difficulty of preparing samples below the gel‐point, it is concluded that the relaxation mechanism in the flow region is molecular flow, with bond interchange along the backbone either completely absent or present to only a minor extent.

Stress Dependence of Poisson's Ratio and of the Softening Temperature of Plastics
View Description Hide DescriptionPoisson's ratio was measured on a variety of plastics as a function of load up to 4000 psi by two methods. Poisson's ratio generally remained constant or decreased slightly with load. However, with crazed polyblends the ratio drastically decreased from 0.33 to 0.15 at high loads applied for long times. The low value can be explained by the growth of cracks perpendicular to the direction of the applied tensile stress. It has been shown that the lowering of the heat‐distortion temperature with stress can not be explained in terms of the lowering of the glass temperature resulting from the volume increase on application of a stress. Instead, the lowering of the softening temperature can be explained in terms of the shape of the modulus vs. temperature curve. The new theory agrees quite well with the experimental values. Materials with a broad softening range have a heat‐distortion temperature which is strongly dependent upon the load.

The Effect of Branching on the Melt Rheology of Polyethylene
View Description Hide DescriptionMelt viscosity data were obtained for linear and branched ethylene polymers over temperatures of 150 to 250°C and shear rates of about one to A capillary rheometer was employed, and the appropriate corrections were made for the several sources of significant error in shear stress and shear rate. These corrected data were analyzed in terms of the Ree‐Eyring inverse hyperbolic sine relationship for viscous flow. The molecular structure was determined by infrared absorption analyses and molecular weight determinations. The rheological character of these polyethylenes was found to depend on the weight‐average length of the polymer backbone and on the branching. The major contribution to the viscosity depended on the length of the backbone and was associated with the longer relaxation times. An additional contribution to the viscosity depended on molecular segments about equal to the interbranch distance, and was associated with the shorter relaxation times. The temperature effect was found to depend on the number of the long‐chain branches, as interpreted by the reduced variable procedure applied to the shear rate.

Finite Deformations under Pressurization in an Infinitely Long, Thick‐Walled, Elastic Cylinder Ideally Bonded to a Thin Elastic Case
View Description Hide DescriptionUsing the tensor‐analytic approach of Green and Zerna, an expression relating the internal pressure in an infinitely long, hollow, elastic cylinder with a thin elastic casing to the geometry of the cylinder in the strained and unstrained states, has been derived. Assumption of incompressibility is made. The strains in the elastic case are assumed to be infinitesimal, whereas, as long as they are consistent with the above requirement, no restriction is placed on the magnitude of the strains in the cylinder. The result is specialized for the case of a Mooney material for which expressions of stresses and strains in the cylinder are also presented. In the latter case, an additional restriction is placed on the magnitude of the strains in the cylinder, namely, that of being within the limits of validity of the Mooney expression for the strain energy function. The results of the analysis are applied in the solution of a practical problem, and in this case, the discrepancies between finite and infinitesimal strain theories are discussed.

Statistics of Random Media
View Description Hide DescriptionWe define random media as certain stochastic processes and consider briefly the question of whether a consistent subfamily of distribution functions can be extended to obtain a stochastic process characterizing a random medium. We define and discuss the “statistical geometry” of “two‐phase” random media and “symmetric” random media. We also review certain aspects of random subdivisions of space into crystals, radiation scattering from particulate assemblies such as random packings of rigid spheres and percolation processes in random crystals and random networks.