CaltechDATA: Monograph
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 28 Mar 2024 11:19:05 -0700The measurement of time dependent Poisson's ratio
https://resolver.caltech.edu/CaltechETD:etd-11222004-145049
Year: 1982
DOI: 10.7907/YZTZ-MA69
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Interest in accurate measurements of the time-dependent Poisson's ratio of polymers arises because it is a component commonly needed in stress analysis and it appears in most theories predicting the behavior of filled materials and composites. Because of the paucity of data and the difficulties in determining [...](t) experimentally, it has been customary in the past to treat [...](t) as a constant. This is unsatisfactory theoretically and inadequate for accurate work.
An apparatus has been constructed that enables us to measure tensile relaxation modulus, E(t), and time-dependent Poisson's ratio, [...](t), simultaneously on the same specimen under the same experimental condition. The apparatus, which contains several novel features, is essentially in working condition. Experiments will be made on a series of selected polymers.
We hope to be able to determine the bulk relaxation modulus, K(t), and the shear relaxation modulus, G(t), from measurements of E(t) and [...](t). A method for solving the appropriate convolution integrals to determine K(t) and G(t) is already available. It would be desirable to compare the calculated G(t) and K(t) with direct measurements. The latter are very difficult. Direct measurements of G(t) will be made in a torsional relaxometer on the same specimen but not under identical conditions. Nevertheless, these data will be useful as a check on our measurements and our method of calculation.
This work will allow a comparison to be made between shear and bulk relaxation via the spectral functions. The measurements will ultimately form the basis for the development of a theory of bulk relaxation in polymeric materials.
https://resolver.caltech.edu/CaltechETD:etd-11222004-145049Studies leading to iodine-tagged crosslinked polybutadiene
https://resolver.caltech.edu/CaltechTHESIS:04222010-090826127
Year: 1971
DOI: 10.7907/7951-NC71
Work leading to the synthesis of uniformly crosslinked poly-butadiene with iodine tags at both ends of a small percentage of the crosslinking chains is described. The following reactions have been investigated: conversion of dibromopolybutadiene to diiodopolybutadiene; conversion of dihydroxypolybutadiene to polybutadiene diisocyanate; chain extension of polybutadiene diisocyanate with
3-dirnethylamino-1, 2-propane-diol to form a linear polybutadiene with pendant dimethylamino groups (PBPA); crosslinking of the PBPA by quaternization of the amine groups with diiodopolybutadiene; and formation of
the amine salt of PBPA by treatment with hydrochloric acid.
Mechanical properties of PBPA, its HC1 salt, and the cross-linked polybutadiene were determined by free torsional oscillation. Salt formation apparently leads to pseudo-crosslinking of the polymer by association of the ionic groups, so that the polymer exhibits elastomeric behavior between -30° and 40°C. Crosslinking of PBPA by
quaternization of the amine groups with diiodopolybutadiene extends the elastic region to 130°C, where creep begins due to degradation of the polymer.
https://resolver.caltech.edu/CaltechTHESIS:04222010-090826127I. A new elastic potential function for rubber. II. Thermoelastic behavior of rubbers
https://resolver.caltech.edu/CaltechETD:etd-06252004-145531
Year: 1974
DOI: 10.7907/NYF8-8467
The internal energy and the entropy components of the elastic restoring force in rubbers were determined for natural rubber up to an extension ratio of about 3.0. Four different experimental measurements were necessary to determine these components: (1) the force-temperature coefficient at constant temperature and length; (2) the force-pressure coefficient at constant temperature and length; (3) the thermal expansion coefficient at constant length; and (4) the isothermal compressibility at constant length. The force-temperature and the force-pressure coefficients were functions of strain whereas the expansion coefficients and the isothermal compressibilities were independent of strain. These measurements gave an internal energy contribution of 23% for natural rubber independent of the strain over the range of extensions studied.
To describe the thermal as well as the elastic behavior of rubbers a new phenomenological description of elastomers based on a generalized measure of strain was developed. The incompressible form of the strain energy function correctly described the elastic data on various elastomers (natural rubber, styrene-butadiene rubber, chlorinated ethylene-propylene copolymer rubber) in both homogeneous and non-homogeneous deformation fields. For a given rubber the same set of parameters fitted the data in simple tension, simple compression, equal biaxial tension and pure shear up to the point of rupture.
The compressible form of the strain energy function also described the thermoelastic data on natural rubber. The thermoelastic data on chlorinated ethylene-propylene copolymer rubber, taken out of the literature, were also predicted. From the new strain energy function it was possible to determine the interchain interactions. For natural rubber the interchain energy effects were found to be small (4%) as compared to the intrachain energy effects.
The experimental results on natural rubber established the range of validity of the statistical mechanical (molecular) and the continuum mechanical (phenomenological) theories. The temperature coefficient of the unperturbed dimensions of natural rubber determined from the internal energy component of the force yielded the conformational energies associated with the cis-polyisoprene chain.
https://resolver.caltech.edu/CaltechETD:etd-06252004-145531Superposition of the Effects of Time, Temperature, and Pressure in Polymetric Materials
https://resolver.caltech.edu/CaltechETD:etd-06152004-145433
Year: 1984
DOI: 10.7907/e970-mg79
<p>Stress relaxation was studied in torsion under superposed hydrostatic pressure using a newly constructed device. Combination of these measurements with the determination of expansivities and compressibilities and with earlier measurements of stress relaxation in tension leads to verification of the description of the combined effects of temperature and pressure on shear relaxation by an extension of the classical free volume theory. The predictions of an extension of the Adam-Gibbs theory to the pressure domain are also compared with the data. This theory is not as successful in predicting superposition. The data are also examined in light of an adaptation of the Simha-Somcynsky equation of state to the free volume theory. Prediction of the effect of pressure by the theory requires a single adjustable parameter. It was possible to calculate the free volume parameters of several polymers without use of information from high pressure experiments.</p>https://resolver.caltech.edu/CaltechETD:etd-06152004-145433Time-temperature superposition for block copolymers
https://resolver.caltech.edu/CaltechETD:etd-04122004-145357
Year: 1971
DOI: 10.7907/RQDJ-8F02
The proposition is made that simple time-temperature superposition should not be valid for block copolymers exhibiting multiple mechanical transitions; and an explanation of the time temperature behavior, which is more consistent with the behavior of the individual phases, is presented in terms of an equivalent mechanical model. Based on this model, a method for generating time-temperature shifts, which depend on the experimental time as well as temperature, is developed. This method can easily be extended to any mechanical model and should be valid for polymer composites in general.
The storage and loss compliances of three benzene cast polystyrene/l,4-polybutadiene/polystyrene triblock copolymers with different compositions were measured between -85 and 90[degrees]C over a frequency range from 0.1 to 1000 Hz. The measurements suggest the presence of four relaxation processes. Two, the polystyrene and polybutadiene glass transitions, are treated according to the method of time-temperature superposition referred to above. Anomalous behavior appearing between the two glass transitions is attributed primarily to a temperature dependent interlayer between the two phases and can be treated as a compositional change in the composite. Entanglement slippage in the rubbery matrix also contributes to the total relaxation.
The apparatus used for these experiments is an extensively modified model of the Miles shear generator. This improved version offers large experimental frequency and temperature operating ranges.
https://resolver.caltech.edu/CaltechETD:etd-04122004-145357Dynamic mechanical properties of block copolymer blends--a study of the effects of terminal chains in elastomeric materials
https://resolver.caltech.edu/CaltechETD:etd-03292004-152803
Year: 1972
DOI: 10.7907/J0FN-DS74
Blends of well characterized polystyrene-polybutadiene SB diblock and polybutadiene continuous SBS triblock copolymers provide rubbery network systems with controlled amounts of terminal chains of known molecular weight. Such systems also provide quantitative information on the concentrations of trapped and untrapped chain entanglements which is not available in conventional elastomers. Three different SB diblocks were synthesized using homogeneous anionic polymerization techniques. These diblocks were blended in various-amounts with a single research grade SBS triblock to form three series of samples for mechanical testing.
The mechanical properties of these materials were studied (1) in free oscillation at about 0.2 Hz over a temperature range from -150?C to 100?C, and (2) in dynamic uniaxial compression from 0.1 to 1000 Hz at various temperatures between -87 and 85?C.
The effect of terminal chains on the mechanical properties depends upon their length and concentration in the network. The terminal chains act as a diluent, lowering the storage modulus in the rubbery region. Above a critical molecular weight, the untrapped entanglements provided by the terminal chains can be coupled into a temporary stress-bearing portion of the network; the amount of entanglement coupling is dependent upon temperature. Several low frequency viscoelastic mechanisms appeared as a result of entanglement slippage, and their effect was enhanced as terminal chain content increased. At very high frequencies in the glassy and transition regions the presence of terminal chains had no effect on the mechanical behavior.
The various mechanisms associated with the terminal chains have been incorporated into a mathematical model whose parameters are given in terms of the structural and compositional features of an entanglement network. The model successfully predicts the level and the location of the low frequency mechanical response for the various materials studied here.https://resolver.caltech.edu/CaltechETD:etd-03292004-152803Theoretical and experimental studies of the viscoelastic behavior of soft polymers
https://resolver.caltech.edu/CaltechETD:etd-03292004-145730
Year: 1976
DOI: 10.7907/CQ68-V266
The first order approximation of the theory of the so-called simple material describes the viscoelastic behavior of soft polymers in large deformations with twelve time-dependent material functions and three material constants, all functions of the three invariants of the deformation tensor. Restricting consideration to deformations in which time shift invariance is preserved, a series of models was developed which describe the time dependence of the stress through the Boltzmann superposition integral incorporating into it a suitable nonlinear measure of strain. The theory was developed in its most general three-dimensional form. Its predictions for homogeneous deformations were tested in a series of experiments on an uncrosslinked styrene-butadiene copolymer.
For the prediction of the viscoelastic behavior of soft polymers the simplest form of the theory requires only one time function, the relaxation modulus. In addition, it requires a strain parameter which is a characteristic material constant. The dependence of this parameter on temperature and other material and experimental variables was examined on hand of estimates from published data as well as from the experimental results reported here.
Sensitive tests in which small (theoretically infinitesimal) deformations were superposed on a finite stretch, allowed a distinction to be made between the two simplest forms of the theory which, in principle, should apply to solidlike and to liquidlike behavior, respectively. Although uncrosslinked styrene-butadiene copolymer behaves in many respects like a liquid, it showed unprecedented excellent agreement with the predictions of the solid model at room temperature. It was concluded that under this condition the liquidlike character of the copolymer is not strong enough to satisfy the special requirements of the liquid model.
The new theory allows specific predictions to be made concerning the contribution of internal energy to the restoring force in rubberlike materials. It represents an advance over former theories in that it permits the contribution to be obtained on uncrosslinked as well as on crosslinked soft polymers. Literature data were reviewed and examined in the light of the theory.https://resolver.caltech.edu/CaltechETD:etd-03292004-145730Viscoelastic behavior of filled and unfilled elastomers in moderately large deformations
https://resolver.caltech.edu/CaltechETD:etd-02202004-115154
Year: 1976
DOI: 10.7907/Z2CG-8P89
A constitutive model was developed for the description of the viscoelastic (time-dependent) behavior of soft rubberlike materials in moderately large deformations. The model assumes that time shift invariance is preserved in such deformations. Hence, the Boltzmann superposition integral remains valid and time-dependent behavior can be described by incorporating a nonlinear stress-strain law into it. The elastic potential of Blatz, Sharda, and Tschoegl, which is based on a generalized measure of strain, was used for this purpose.
A slightly plasticized styrene-butadiene copolymer rubber (SBR) was subjected to various modes of deformation in simple tension. The experimental data were compared with the theoretical predictions of the model. The agreement was unprecedentedly good.
In the course of this work a curious anomaly was discovered in the behavior of emulsion polymerized compression molded dicumylperoxide cured SBR. This material showed lack of time shift invariance in the region of very small strains in which elastomers generally follow a linear stress-strain law. Normally, non-preservation of time shift invariance is linked with stress-strain nonlinearity. In the anomalous SBR the former effect can be studied free of interference from the other.
To test the applicability of the model to filled elastomers, experiments were made on both crosslinked and uncrosslinked SBR filled with a high-structure carbon black. The model, and several generalizations of it, failed to predict the behavior of the filled materials in response to small (theoretically infinitesimal) deformations superposed on a finite stretch. Such experiments may be considered looked upon as sensitive probes with which the behavior of the material may be explored in large deformations. The superposition tests confirmed that in carbon black filled rubbers there exists a network of secondary aggregates of the filler particles which is held together by Van der Waals forces. This network imparts to the filled rubber a thixotropic character with a rebuilding time of about 15 minutes at room temperature. Successful prediction of the properties of such a filled system must await the development of a new constitutive model which incorporates the thixotropic behavior.https://resolver.caltech.edu/CaltechETD:etd-02202004-115154The effect of temperature and pressure on the linear viscoelastic response of elastomers
https://resolver.caltech.edu/CaltechETD:etd-02022004-093227
Year: 1975
DOI: 10.7907/G3YM-TA68
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Stress relaxation measurements were made in uniaxial tension under superposed hydrostatic pressures up to 5 kbar at temperatures ranging from -25 to 50[degrees]C. Two lightly filled (Hypalon-40 and Viton-B) and one highly filled elastomer (Neoprene) were studied because their pressure transition lie within the range of the apparatus. The construction and operation of the apparatus are discussed. Measurements on Hypalon and Viton were made either by varying the temperature while maintaining the pressure constant at 1, 1,000, and 2,000 bars, or by holding the temperature constant while varying the pressure from atmospheric to 4,600 bars. The viscoelastic response of Neoprene was measured at 25[degrees]C and pressures up to 4,600 bars.
The measurements were converted to a time dependent shear modulus. Time-temperature and time-pressure superposition was then applied to the reduced data to obtain master curves at 1, 1,000, and 2,000 bars. By introducing either the Murnaghan or the Tait equation of state into the free volume theory, an expression was obtained which describes the shift factors, log a[subscript T,P'] resulting from the empirical shifts into the master curves at atmospheric pressure. This equation then gave an excellent prediction of the empirically found shift factors resulting from forming the master curves at 1,000 and 2,000 bars.
Because the measurements made as function of temperature and those made as a function of pressure must be consistent, certain ambiguities in the free volume theory have been removed. This leads to an essential improvement in the theory.
https://resolver.caltech.edu/CaltechETD:etd-02022004-093227Effect of pressure on mechanical behavior of filled elastomers
https://resolver.caltech.edu/CaltechTHESIS:07232014-093132642
Year: 1972
DOI: 10.7907/1vr2-7x25
<p> The Young's modulus, stress-strain curves, and failure
properties of glass bead-filled EPDM vulcanizates were studied under superposed hydrostatic pressure. The glass bead-filled EPDM was employed as a representation of composite systems, and the hydrostatic pressure controls the filler-elastomer separation under deformation. This separation shows up as a volume change of the system, and its infuence is reflected in the mechanical behavior as a reinforcing effect of variable degree.</p>
<p>The strain energy stored in the composite system in
simple tension was calculated by introducing a model which
is described as a cylindrical block of elastomer with two
half spheres of filler on each end with their centers on the axis of the cylinder. In the derivation of the strain energy, assumptions were made to obtain the strain distribution in the model, and strain energy-strain relation for the elastomer was also assumed. The derivation was carried out for the case of no filler-elastomer separation and was modified to include the case of filler-elastomer separation.</p>
<p> The resulting strain energy, as a function of stretch ratio and volume of the system, was used to obtain stress-strain curves and volume change-strain curves of composite systems under superposed hydrostatic pressure.</p>
<p> Changes in the force and the lateral dimension of a ring
specimen were measured as it was stretched axially under a
superposed hydrostatic pressure in order to calculate the mechanical properties mentioned above. A tensile tester was used which is capable of sealing the whole system to carry out a measurement under pressure. A thickness measuring device, based on the Hall effect, was built for the measurement of changes in the lateral
dimension of a specimen.</p>
<p> The theoretical and experimental results of Young's
modulus and stress-strain curves were compared and showed
fairly good agreement.</p>
<p> The failure data were discussed in terms of failure surfaces, and it was concluded that a failure surface of the glass-bead-filled EPDM consists of two cones.</p>
https://resolver.caltech.edu/CaltechTHESIS:07232014-093132642