Volume 12, Issue 3, September 1968
Index of content:
12(1968); http://dx.doi.org/10.1122/1.549121View Description Hide Description
Upon addition of sufficient electrolyte to two poly(n‐butyl methacrylate) latices, differing in particle size by a factor of 11, their viscosities were identical, within experimental error, over the range of volume fraction, , from 0.05 to 0.33. The viscosities agreed with those predicted by Mooney’s formula: provided was the random close‐packing value found for monodisperse spheres, 0.637. Upon combining the two latices on an equal weight basis, the viscosities at equal volume fractions were lower than those found for the individual latices. The data, however, fit Mooney's formula provided a larger value of was used.
Viscoelastic Properties of a Styrene‐Butadiene Vulcanizate in Large Biaxial and Simple Tensile Deformations12(1968); http://dx.doi.org/10.1122/1.549122View Description Hide Description
Biaxial tensile tests were made by stretching thin‐wall cylindrical specimens in the axial direction and controlling the internal pressure to maintain constant the initial outside diameter; this procedure gives essentially pure shear. From −40 to 20°C, stress‐relaxation data were obtained at axial extension ratios, up to about 2.5; relaxation data in simple uniaxial tension at −20°C were also obtained. From 25 to 90°C tests were made at constant extension rates between 0.0031 and in both biaxial and simple tension. The data is biaxial tension conform to equations of the form: and where and are the axial and circumferential stresses and is the time‐ and temperature‐dependent stress‐relaxation modulus in shear; and are functions only of that approach the Cauchy strain at sufficiently small deformations. From this behavior, observed over a time‐temperature range within which the modulus varies about 1.5‐fold, it follows that and are time and temperature independent, where W is the “strain energy” and and are strain invariants. (For pure shear, ) The data show that is a decreasing function of the deformation and that is sensibly constant for i.e., at larger deformations appears to decrease somewhat. Subject to the assumption that is independent of or equivalently that is independent of a calculation of simple tensile behavior gave results in reasonable agreement with experimental data. Under the conditions that remains constant, the strain energy is represented closely by: A representation of data by the product of a time‐ and temperature‐dependent modulus and a deformation function is strictly valid only when is independent of time and temperature; the limitations of this method are briefly considered.
12(1968); http://dx.doi.org/10.1122/1.549113View Description Hide Description
The constitutive equation for nearly viscometric flow is put into a form that allows easier comparison with experiments involving small oscillations superposed on steady shearing. Part of the stress perturbation is evaluated directly in terms of the stress for the undisturbed motion. Two different dynamic viscosities, referring to oscillations parallel and perpendicular to the main flow, are discussed. The low‐frequency limits of these viscosities are evaluated in terms of the steady‐shearing viscosity, and it is pointed out why these two limits must usually be unequal.
12(1968); http://dx.doi.org/10.1122/1.549123View Description Hide Description
Examination of the flow of branched polyethylene melts leads to molecular weight‐viscosity, activation energy‐molecular weight, and activation energy‐shear stress relationships which are anomalous when compared to the behavior of most polymers. In addition, the activation energy for viscousflow is much higher than would be expected by a comparison with linear polyethylene. Published data on branched polyethylene are examined, and various explanations for the anomalous behavior are considered. Order in the melt and abnormal melt volumes are rejected as possible explanations for the anomalous effects. It is shown that short branches contribute at most ca. 2 kcal to the activation energy at zero shear and cannot, therefore, be completely responsible for the observed values. Long chain branches are postulated for several reasons to be responsible for the anomalous flow behavior and activation energy. The mechanism by which long chain branches cause the anomalous behavior of branched polyethylene is not established, but several possible explanation are discussed.
12(1968); http://dx.doi.org/10.1122/1.549114View Description Hide Description
Viscosities of suspensions of dispersed spheres and permanent aggregates ranging from doublets and triplets to clusters composed of a very large average number of spheres are reported. In all cases, glass spheres of a very narrow distribution of particle diameter were used and the suspending fluid was a chlorinated biphenyl (Aroclor). Results were obtained using a Couette type viscometer as a function of volume fraction of the dispersed phase. In addition, measurements on the aggregated systems were made as a function of the number of spheres per aggregate with the average aggregate size controlled over a relatively narrow range. Aggregates were obtained by a sintering and sieving technique. For the larger aggregates the shape was generally elliptical. This is the first time rheological data has been reported for suspensions with a dispersed phase composed entirely of permanent aggregates of controlled size, size distribution, and shape. The results for the dispersed and aggregated systems, with concentrations as high as volume fraction solids, are shown to fit the Mooney equation over the entire concentration range, if the Einstein coefficient is increased for the aggregated systems to a limiting maximum values as suggested by Gillespie and if experimental values of the maximum volumetric packing fraction of solids are used. The value of the Einstein coefficient is shown to be a function of the hydrodynamic volume of the aggregates and reach a maximum value for the larger aggregates.
12(1968); http://dx.doi.org/10.1122/1.549115View Description Hide Description
A stress relaxation ball indentation penetrometer was designed and constructed with the intent of measuring the time‐dependent stress relaxation modulus of materials incapable of supporting their own weight. An equation is derived to relate the modulus to the geometry of a deformation by a sphere into a plane. The relevance of this equation to creep experiments is discussed.
12(1968); http://dx.doi.org/10.1122/1.549116View Description Hide Description
Expressions for the relative viscosity of fluid suspensions are obtained using a continuum model. A substructure spin boundary condition intermediate between zero spin and zero antisymmetric stress is formulated by introducing a wall condition parameter. Simple shearing motion is examined and a simple relation between the boundary condition parameter and the suspension concentration is postulated. The resulting expression for relative viscosity is found to agree closely with the experimental results of V and for concentrations below 0.3.
12(1968); http://dx.doi.org/10.1122/1.549126View Description Hide Description
The dynamic behavior of a homogeneous slab subjected to a short pressure pulse on one face is explored from a simple rheological point of view. The analysis is one dimensional, but involves two strain modes in the material. The early response is shown to be controlled by the bulk viscosity which influences the distortion and attenuation of propagating disturbances. In particular, the peak stress at interior points is shown to be very sensitive to the duration of the pressure. This result is quite different from that usually applied in the analysis of impact data in which it is assumed that the controlling differential equations are hyperbolic and that the density pressure relation is not time dependent. It is also more compatible with some of the experimental results. Criteria for mechanical similarity are described which may be useful in the design and development of systems subjected to impacts. The uniaxial deformation generated in this type of experiment is contrasted with the uniaxial load condition generated in the usual tensile test. In the present case, not only the wave propagation is distinctive, but the tendency toward strain homogeneity and strain stability can also be greatly enhanced. This is likely to be relevant to the understanding of material‐forming processes.