Volume 15, Issue 1, March 1971
Index of content:

A Comparison of Creep Theories for Multiaxial Loading of Polyethylene
View Description Hide DescriptionSeveral creep theories are investigated for multiaxial loading of high‐density polyethylene, a slightly cross‐linked polymer demonstrating a nonlinear stress‐strain‐time relationship. Among the theories considered are nonlinear viscoelastic models, isochronous stress‐strain diagrams employing a hyperbolic sine relationship, and multiple integral representations. The material parameters for these theories were determined from simple tension, compression, torsion and biaxial creep tests using single step loading. These theories were then analyzed for multiple step pressure‐tension loading of a thin walled cylinder, in which the internal pressure and the axial load were varied independently of each other to check the effect of stress history on theory accuracy.

Determination of the Shear Rates of Non‐Newtonian Fluids from Rotational Viscometric Data. I. Concentric Cylinder Viscometer
View Description Hide DescriptionA method is proposed for determination of the shear rate of non‐Newtonian fluids sheared in a concentric cylinder viscometer. The mathematical expression of the shear rate is an exact solution. The method has been shown to be convenient. Furthermore, only one set of experimental data, torque versus angular velocity, is needed in the calculation. Three examples are given to illustrate the application of the proposed method.

Determination of the Shear Rates of Non‐Newtonian Fluids from Rotational Viscometric Data. II. Cone‐and‐Plate Viscometer
View Description Hide DescriptionA method for determination of the shear rate in a cone‐and‐plate viscometer is developed. The method to obtain the shear rate is shown to overcome the limitation of the existing method which requires a small angle between the cone and the plate as well as a linear velocity field with respect to the angle. Examples for non‐Newtonian fluids with and without prior knowledge of the rheological equation of state are presented to demonstrate the proposed method.

Theoretical and Experimental Treatment of Fracture in an Adhesive Interlayer
View Description Hide DescriptionFrom the viewpoint of continuum mechanics, cohesive and adhesivefracture have been shown to be similar. The energy approach to adhesivefracture has provided a method of interpreting the results from a convenient “blister” test that may be used quantitatively to evaluate bond strengths for particular bi‐material bond systems. Inquiring further into adhesivefracture, the effect of including an elasticadhesive interlayer between the two other materials is investigated analytically and experimentally. The experimental system is typical of the propellant‐liner‐steel combination frequently encountered in a solid rocket motor.

Characteristics of Thixotropic Behavior
View Description Hide DescriptionThe shear stress‐shear rate behavior of a thixotropic hectorite clay‐water suspension was studied in a Couette viscometer under a wide variety of rest and shear rate histories. Shear stress decay and build‐up transients resulting from step changes in shear rate were measured. The transient stress data were used to construct equilibrium and constant structure flow curves. The constant structure curves could be described by the Power Law model with a constant exponent but varying coefficient. Normalized stress transients could be described by an exponential time series similar to those used in stress relaxation studies on viscoelasticpolymers. This method was applicable to literature data and to data obtained for other fluids in our laboratory. The transient behavior of thixotropic fluids is heavily influenced by past history of deformation. Structural rebuilding during rest seemed to begin with the formation of a weak gel structure. Structural rebuilding was also observed under shear rate. In experiments with a short rest period, stresses measured after reapplication of shear rate returned quickly to the values measured before the rest period.

An Integral Constitutive Equation Based on Molecular Network Theory
View Description Hide DescriptionA new constitutive equation for concentrated polymer solutions and melts is presented that is based on the entanglement theory of Lodge. The strain rate dependence of the memory function is determined using a physical hypothesis of interacting spheres where the spheres represent spheres of influence of the network junctions. The resulting equation has one constant that can be estimated theoretically in addition to the natural relaxation spectrum. At high strain rates, a second empirical constant is introduced to account for the orientation of the spheres of influence. Predictions of the equation and the equations of Bogue, Bird‐Carreau, and Tanner were compared to steady and transient shear stress and normal stress data obtained on a Weissenberg rheogoniometer. The new equation fits nonlinear transient data more satisfactorily than other equations of similar complexity.

Viscoelastic Properties of a Rubber Vulcanizate Under Large Deformations in Equal Biaxial Tension, Pure Shear, and Simple Tension
View Description Hide DescriptionStress‐strain data were determined on an unfilled styrene‐butadiene rubber vulcanizate in equal biaxial tension (EBT) at deformations up to rupture. Tests were made at temperatures from −43° to 90°C and at extension rates from 0.15 to 4 min. The data are represented in terms of a time‐ and temperature‐independent function, the reduced modulus, and the maximum extensibility, the latter two quantities being functions of the temperature‐reduced time, The function gives the stress‐strain relationship for the material in a reference state for which the modulus is unity and the equilibrium value. The maximum extensibility equals the extension ratio at which the slope of a stress‐strain curve from isochronal data becomes infinite; it cannot be measured directly because rupture always occurs at an extension less than Data from extensive tests in simple tension (ST) have been reported previously, as well as data in pure shear (constrained biaxial tension, CBT) at where λ is the extension ratio. The three functions, which represent stress‐strain behavior in ST, CBT, and EBT, were considered in terms of the Valanis‐Landel theory of finite elasticity, which is based on the assumed validity of the strain‐energy function In this way, the characteristic function was evaluated over the range From this function along with the modulus, the stress‐strain behavior in any pure homogeneous deformations can be calculated readily over extended ranges of temperature and extension rate. Because depends somewhat on the type of deformation ( in ST is at least 30% greater than in EBT), data at very large deformations under an arbitrary pure homogeneous deformation can be derived only if is known as a function of both and the type of deformation.

Multiple Step, Nonlinear Creep of Polyurethane Predicted from Constant Stress Creep by Three Integral Representations
View Description Hide DescriptionThe following three integral representations for nonlinear creep were considered: a product form of the multiple integral representation, a second‐order memory representation, and an integral form of the modified superposition principle which is equivalent to a first‐order memory representation. The latter two representations were derived by limiting the memory capability of the multiple integral representation. These three representations required information from constant stress creep tests only to predict the creep resulting from multiple‐step loading programs. The three representations were applied to the creep of polyurethane resulting from multiple‐step loadings of combined tension and torsion. The second‐order memory representation and the modified superposition principle predicted the multiple‐step creep behavior more satisfactorily than the product form of the multiple integral representation.

Elongational Viscosity of Nonlinear Elastic Dumbbell Suspensions
View Description Hide DescriptionThe Kramers method for analyzing bead‐rod suspensions in potential flow has been extended to a suspension of inverse‐Langevin‐spring dumbbells in elongational flow. The elongational viscosity and root‐mean‐square bead separation for two different inverse‐Langevin‐spring models are calculated numerically and presented in graphical form. The numerical calculations for one model are in excellent agreement with similar, approximate calculations made by Peterlin. For linear (Hookean and Fraenkel) spring models with finite spring constants, the elongational viscosity and mean‐square bead separation are unbounded, but for both inverse‐Langevin‐spring models these quantities approach an upper bound with increasing elongation rate.

Measurement of the Axial Pressure Distribution of Molten Polymers in Flow through a Rectangular Duct
View Description Hide DescriptionThe authors have experimentally determined the axial pressure distributions for the flow of polyethylene and polypropylene melts through a rectangular duct having an aspect ratio of 2. “Exit pressures,” which were found by extrapolating the pressure profiles to the duct exit, were found to correlate well with the volumetric flow rate. This result is quite understandable in light of previous results regarding the flow of melts through circular capillaries, because the nature of fluid flow through a capillary is the same as that of the flow through a rectangular duct having a very large aspect ratio (i.e., simple shearing flow). Thus, the rheological implication of the “exit pressure” is the same for both of these geometries. The analysis of flow through a rectangular duct having a very large aspect ratio shows that the normal stress difference is approximately equal to the “exit pressure” for polymer melts. A preliminary analysis of flow through a rectangular duct having a small aspect ratio is presented, and it gives a clear direction to future experiment.

Dynamic Mechanical Properties of Polyethylene Melts: Calculation of Relaxation Spectrum from Loss Modulus
View Description Hide DescriptionDynamic mechanical properties of several polyethylene melts were investigated using the Weissenberg rheogoniometer. The use of the rheogoniometer for oscillatory shear testing has been discussed. The methods of determining relaxation spectrum from loss modulus based on second‐order approximation of Schwarzl and Staverman, and first‐ and second‐order approximations of Ninomiya and Ferry were found relatively inaccurate in reproducing the original loss modulus and storage modulus data. As a result, the iterative procedure based on Roesler and Twyman's derivation and that based on Tanner's algorithm were employed and found to regenerate accurately the original experimental data. Of all the approximation methods, the one based on the second‐order approximation method of Williams and Ferry was subject to least error in its ability to regenerate the original melt data.

Kinematics of Deformable Suspensions
View Description Hide DescriptionIn this paper we investigate the ability of recent microstructure theories of fluid mechanics to explain the behavior of polyisobutylene. In particular it is shown that a director microstructure theory yields a natural explanation of the observed “tank‐tread” motion of the macromolecules as well as shear rate dependence of apparent viscosity and normal stress differences. This is accomplished by means of linear constitutive equations involving only four new material coefficients.

Note: Measurement of Normal Stresses
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