Volume 12, Issue 2, July 1968
Index of content:
12(1968); http://dx.doi.org/10.1122/1.549127View Description Hide Description
The direct relation between the complex longitudinal modulus and the experimentally measured quantities—the amplitude ratio A and phase angle φ—has been derived for the forced vibrating reed instrument and is given by: where terms in ρ with negative exponents are not admitted. is equal to where is the longitudinal storage modulus and is the longitudinal loss modulus.A is the ratio of the amplitude of the free end of the reed—either loaded with a pin or unloaded—to that of the clamped sinusoidally driven end and φ is the angle by which the former lags the latter. In practice, the sample dimensions and frequency range are chosen such that the sum in the above equation is rapidly convergent. The dynamic moduli then can be calculated by including only up to the first two or three terms in the sum. Where phase measurements are relatively inconvenient to make and when all but the first term under the sum can be neglected, the equation can be used to calculate dynamic moduli from two amplitude measurements at the same frequency for reeds of two different lengths; or from amplitude at resonance alone, provided Illustrative examples are given. The procedures for calculating the dynamic moduli are applicable to the data obtained in all experiments where a relation of the form given above is obtained.
12(1968); http://dx.doi.org/10.1122/1.549106View Description Hide Description
The rotation of rigid prolate spheroids, obtained by polymerization of an electrically deformed liquid drop suspended in a liquid undergoing Couette flow has been studied. The variation of azimuthal angle and the period of rotation were found to be in good agreement with the theory of Jeffery. Measurements of the equivalent ellipsoidal axis ratio of cylinders have established that the transition from disks, for which to rods occurs at a particle axis ratio and that when
12(1968); http://dx.doi.org/10.1122/1.549107View Description Hide Description
Determination of all the kernel functions for multiple integral representation of creep is very involved. In this paper the kernel functions were assumed to have a product form, such as The validity of this assumption was tested by experiments on a poly(vinyl chloride) plastic tube subjected to constant rates of stressing in combinations of tension and torsion. Some experiments also included abrupt changes in stress. Application of the theory to several complex experiments is illustrated. Agreement between theory and experiment is generally satisfactory, so the assumption seems adequate for the type stress histories investigated.
12(1968); http://dx.doi.org/10.1122/1.549120View Description Hide Description
A method is described for predicting nonlinear stress relaxation from nonlinear creep data under constant uniaxial stress. This method utilizes as a first approximation an inversion of the function obtained from the multiple integral equation describing creep at constant stress. A correction procedure accounts for the variable stress during relaxation by employing the general multiple integral function with an assumption that the kernel functions containing mixed time parameters may be taken as products. The results computed from creep data with only one stage of corrections are in good agreement with relaxation experiments on a polyurethane tube.
12(1968); http://dx.doi.org/10.1122/1.549108View Description Hide Description
A constitutive equation using a multiple integral functional relationship for stress relaxation of nonlinear viscoelasticmaterial has been investigated for uniaxial stress. The first three integrals were retained and the relaxational functions for constant strain were determined from experiments on polyurethane at constant strain. Using this information the behavior during a multistep strain history was computed using two approximate procedures (a) assuming a product form for the kernel function and (b) employing a modified superposition principle. The latter yielded the more accurate description, although both gave good results.
12(1968); http://dx.doi.org/10.1122/1.549109View Description Hide Description
A theoretical treatment of particle‐particle interaction is described from which the viscosity‐concentration behavior of multimodal suspensions of rigid particles can be related to the viscosity‐concentration behavior of the unimodal components. From this theory, the viscosity of multimodal suspensions can be calculated and shows excellent agreement with existing experimental data. Blend ratios that will produce minimum viscosities are simply derived from the theory and agree well with experimental results. Another important feature of this theory is that it predicts and defines a lower limit for the viscosity at any concentration and indicates that this lowest viscosity can be obtained with a variety of solids combinations.
12(1968); http://dx.doi.org/10.1122/1.549110View Description Hide Description
The uniaxial stress‐strain behavior of highly filled elastomers is examined in terms of a simplified thermodynamic model. Experimental data are presented showing the stress‐strain‐dilatational behavior at a series of hydrostatic pressures from which the behavior at constant volume can be obtained. Deviations from this constant volume stress‐strain state are shown to be dependent upon the rate at which pressure‐volume and surface energies are being expended by the material due to the formation and growth of vacuoles. Mathematically and experimentally the behavior is considered to be essentially reversible as experimental data indicates. Therefore, the only forms of energy considered are mechanical, and energy balances are made using only force‐deflection, pressure‐volume, and surface energies. This method of approach accounts for the energy sinks which reduce the rate at which the material accumulates mechanical energy and indicates what factors govern the stress‐strain response.
12(1968); http://dx.doi.org/10.1122/1.549111View Description Hide Description
A stochastic model has been developed that relates the stress‐strain and the dilation‐strain behavior of filled elastomers to the formation and growth of vacuoles which cause strain‐induced volume dilatation in these materials. Both the cumulative and instantaneous frequencies of vacuole formation are simply derived from this model, thereby providing a method for determining the extent of microscopic failure within the material. Comparisons of the stress‐strain and dilatation‐strain relationships of various systems shows that the nonlinear stress‐strain response is governed by these microscopic failures as are the strain capabilities. Hydrostatic pressure which normally has strong influence over the behavior of these materials is shown to be the result of suppressed vacuole formation.
Dynamic Mechanical Properties of Cross‐Linked Rubbers. IV. Dicumyl Peroxide Vulcanizates of Styrene‐Butadiene Rubber12(1968); http://dx.doi.org/10.1122/1.549112View Description Hide Description
The viscoelastic properties of three samples of a random styrene‐butadiene co‐polymer with 23.5 wt‐% styrene, cross‐linked by dicumyl peroxide to different extents, have been studied by dynamic shear and shear creep measurements, and the unvulcanized precursor has been studied in creep. The frequency and temperature ranges were 0.2 to 3600 cps and −30 to 55°C. The creep data were converted to the corresponding dynamic viscoelastic functions at very low frequencies. All data were reduced to by shift factors calculated from the equation By fitting the creep to a modification of the empirical equation of Thirion and Chasset, values of the equilibrium compliance and relaxation parameters were obtained in good agreement with results of those authors from stress relaxation in extension. All the viscoelastic functions displayed two principal regions of frequency dependence as found for other rubberlike polymers. The high‐frequency dispersion, near on the radian frequency scale, is affected very little by increasing cross‐linking and corresponds to a compliance increment of about for all samples. It is attributed to the entanglement network originally present before vulcanization. The low‐frequency dispersion, at 1 radian/sec and below, corresponds to a compliance increment which increases rapidly with decreasing chemical cross‐linking, while the dispersion broadens and shifts to lower frequencies.