Modulus Of Rubber Research Articles

Kinetic and rheological studies of an unsaturated polyester cured with different catalyst amounts

An unsaturated polyester resin was cured with different catalyst contents. The crosslinking process was followed by static and dynamic viscosimetry and by differential scanning calorimetry (d.s.c.). Activation energies were determined from the gel times obtained by viscosimetry and from the variation in the maximum exotherm temperature obtained by d.s.c. at different heating rates. The existence of a threshold in the amount of catalyst to use is shown by analysis of the gel times. The effect of catalyst content on the glass transition temperatures of the different mixtures has been analysed taking into account the crosslink density, measured by means of the rubber modulus obtained by dynamic mechanical tests.

Volume fraction and temperature dependence of mechanical properties of silicone rubber particulate/epoxy blends

At all temperatures, both the Young's modulus and tensile strength of silicone rubber particle/epoxy resin blends decreased as the volume fraction of the silicone rubber particles was increased, and this decrease became greater with falling temperature. A volume fraction-temperature superposition held for both the Young's modulus and tensile strength of the blends. The shifted volume fraction of silicone rubber particles needed to obtain master curves increased with increasing temperature and the shift was almost the same for both properties. An optimum suitable volume fraction of rubber particles existed in terms of improving impact fracture energy. A volume fraction of silicone rubber particles of 5–10% appears to be the most suitable for obtaining a blend in which the decrease in Young's modulus and the tensile strength is relatively low and the increase in impact fracture energy is relatively high.

Effects of chemical structure of hardener on curing evolution and on the dynamic mechanical behavior of epoxy resins

AbstractA diglycidyl ether of bisphenol‐A‐type difunctional epoxy resin was cured with different amine‐type curing agents at stoichiometric ratios. The crosslink process was followed by viscosimetry and differential scanning calorimetry. The gelation time and the apparent activation energy were found to be strongly dependent on the structure of the hardener. The heat of reaction did not vary significantly when the hardener was changed. An interpretation based on structural aspects such as amine reactivity, steric hindrance, and chain rigidity is proposed for the variations corresponding to the curing process. Master viscosity curves have been built up for all mixtures. The effect of the hardener on the glass transition temperatures of the different mixtures has been analyzed taking into account the crosslink density, measured by the rubber modulus obtained by dynamic mechanical studies, and the chemical structure of the hardener chains. © 1995 John Wiley & Sons, Inc.

Liquid Crystalline Epoxide Thermosets. Dynamic Mechanical and Thermal Properties

Dynamic mechanical and thermal properties of a certain liquid crystalline (LC) diepoxide cross-linked with three different aromatic diamines were studied. For one epoxy-amine mixture, the position of the gel point was determined with the aid of frequency-dependent rheological measurements. The value of the critical relaxation exponent was 0.5. The gel point was also determined by solubility experiments. There was a clear agreement between the two methods. The degree of conversion of the epoxy groups at the gel point (55 ± 3%) corresponded well with the value predicted by the statistical theory for network formation in isotropic stoichiometric epoxy-amine mixtures. Mechanical measurements were carried out on macroscopically ordered networks in the direction of orientation. In highly ordered networks prepared from the LC diepoxide and a rigid aromatic diamine, the value of the rubber modulus deviated from the predictions of rubber elasticity theory by a factor of 30 times higher. In networks with the same high level of macroscopic orientation prepared from the LC diepoxide and a relatively more flexible diamine, the deviation from the classical theory was much less (factor of 1.7). In the rubbery region, the value of the Young's elastic modulus decreased as a function of temperature, which seems to be connected to the decrease of the order. This is confirmed by a theory, presented by T. Odijk, concerning the polymer nematic gels under tension (see Appendix). The thermal expansion coefficient of the macroscopically ordered networks was highly anisotropic. It was indeed possible to combine the good mechanical and thermal properties of conventional epoxy polymer networks with the special features that LC polymers offer.

Volume fraction and temperature dependence of mechanical properties of silicone rubber particulate/epoxy blends

At all temperatures, both the Young's modulus and tensile strength of silicone rubber particle/epoxy resin blends decreased as the volume fraction of the silicone rubber particles was increased, and this decrease became greater with falling temperature. A volume fraction-temperature superposition held for both the Young's modulus and tensile strength of the blends. The shifted volume fraction of silicone rubber particles needed to obtain master curves increased with increasing temperature and the shift was almost the same for both properties. An optimum suitable volume fraction of rubber particles existed in terms of improving impact fracture energy. A volume fraction of silicone rubber particles of 5–10% appears to be the most suitable for obtaining a blend in which the decrease in Young's modulus and the tensile strength is relatively low and the increase in impact fracture energy is relatively high.

Influence of mineral fillers on stabilizer consumption in rubbers

There has been ever raising concern in last few decades about the utilization of biomass for different commercial applications such as filler materials in rubber composites. In this context, an interesting pathway has been proposed to develop such composites by introducing waste lignin as a reinforcing constituent in high cis-polybutadiene rubber (BR). With a judicious selection of rubber curing ingredients and, simultaneously, adopting suitable solid-state mixing protocols, particularly, a relatively high-temperature multi-steps melt-mixing process (above the glass transition temperature of lignin), rubber composites with an outstanding mechanical performance were prepared. The reinforced rubber composites with 50 (weight) parts lignin loading per hundred parts of rubber (phr) offer ∼10 MPa tensile strength (TS), ∼276% elongation at break (EB), and ∼3.51 MPa tensile stress at 100% elongation (so-called rubber modulus M100). These values are superior when compared with the composites comprised with standard reinforcing carbon black (∼8.5 TS, ∼224% EB, ∼2.79 M100) and even with a silica-silane system (∼7.34 TS, ∼229% EB, ∼2.44 M100) with same filler loading. The unique combination of the curing packages and four-stage mixing process allowed us to establish a homogeneous and fine dispersion of lignin. Furthermore, this is the first time that available models of rubber reinforcement are applied to the description of the reinforcement mechanisms of lignin in a soft elastomer involving various aspects like filler-filler interaction, rubber-filler interactions, critical strains for destroying the filler-filler network, effective filler volume fractions, shape factor, etc. The developed compounding methods for BR and their characterization and modeling can be easily applied to other commercial rubbers facilitating a real breakthrough in developing cheap and bio-based high-performance rubber composites.

Nylon-6-rubber blends

The macroscopic cavitation and yield behaviour of nylon-6/rubber blends was studied. The type of rubber (poly(butadiene), ethylene propylene copolymer (EPDM) or polyethylene (LDPE), the rubber concentration and the rubber particle size was varied. The onset of cavitation was determined by measuring the intensity of the transmitted light from an incident laser beam. Both the yield stress and the cavitation stress appeared to increase with increasing strain rate and rubber modulus. No linear relation between the shear modulus and the cavitation stress was found. The data indicate that blends with a very small particle size have a relatively high cavitation stress. In all cases, a high cavitation stress of the elastomer resulted in a high yield stress of the blend.

Toughness of model polymeric networks in the glassy state: effect of crosslink density

Relationships between the microscopic structure (chemical composition and topology) and the macroscopic properties, especially the toughness, of well defined polymeric networks below T g, were investigated. Model networks were prepared from a triisocyanate, i.e. tris(4-isocyanatophenyl)-thiophosphate (Desmodur RFE) and well defined polymeric diols, namely poly(propylene glycol)s (PPGs) of various molecular weights (425, 725, 1000, 2000, and 4000). The experimental equilibrium rubber moduli of the various Desmodur-PPG networks are in good agreement with those calculated by means of the theory of branching processes. These networks are therefore considered to behave as model polymeric networks. Toughness was measured as a function of the crosslink density at temperatures well below the T g. The model networks are surprisingly tough. A linear dependence of the critical stress intensity factor, K Ic, on the strand density is observed. The size of the plastic zone is related to the maximum extensibility of the network chain. Other properties of the glassy state (e.g. glass modulus and yield stress) have only a very slight dependence on the crosslink density.

Dilatational bands in rubber-toughened polymers

A theory is advanced to explain the effects of rubber particle cavitation upon the deformation and fracture of rubber-modified plastics. The criteria for cavitation in triaxially-stressed particles are first analysed using an energy-balance approach. It is shown that the volume strain in a rubber particle, its diameter and the shear modulus of the rubber are all important in determining whether void formation occurs. The effects of rubber particle cavitation on shear yielding are then discussed in the light of earlier theories of dilatational band formation in metals. A model proposed by Berg, and later developed by Gurson, is adapted to include the effects of mean stress on yielding and applied to toughened plastics. The model predicts the formation of cavitated shear bands (dilatational bands) at angles to the tensile axis that are determined by the current effective void content of the material. Band angles are calculated on the assumption that all of the rubber particles in a band undergo cavitation and the effective void content is equal to the particle volume fraction. The results are in satisfactory agreement with observations recorded in the literature on toughened plastics. The theory accounts for observed changes in the kinetics of tensile deformation in toughened nylon following cavitation and explains the effects of particle size and rubber modulus on the brittle-tough transition temperature.

Similarity of the relaxation modulus of polydisperse polymers

AbstractA similarity rule due to Markovitz is used for the correlation of the relaxation modulus for different polymeric materials. This rule has long been employed implicitly in the empirical shifting rules for the reduction to common curves of viscoelastic data measured on the same polymer over a range of temperatures and concentrations. It is shown here for the rubbery regime of polydisperse polymers that when relaxation moduli are scaled with the steady‐state compliance and the time with the mean relaxation time, data for a variety of amorphous polymeric materials tend to plot on a common curve. This suggests that the dimensionless rubber modulus is, to first order, a common function of dimensionless time for materials which include whole polymers and polymer solutions, the effects of temperature and concentration being automatically incorporated into the two scaling parameters. For materials with sufficient polydispersity the correlation appears to be valid over a wide range of the available experimental data. These amorphous materials appear to share only one feature, flexible molecules with broadly distributed molecular weights. For narrowly dispersed polymers the modulus in the terminal zone is also correlated according to the above rule, but the influence of other parameters appears as the transition to the glassy regime is approached. An additional application of the similarity rule allows the relaxation modulus computed from molecular dynamics simulations of idealized polymers to be compared with experimental moduli for real materials even though the characteristic times for these systems differ by more than ten orders of magnitude.

Stiffness characteristics of twisted cords for cord-rubber composites

A finite element model is presented to predict the stiffness characteristics of twisted cords by treating them as structures and considering the stiffness couplings due to extension-bending-torsional deformations. The axial, bending, and torsional stiffnesses are calculated for both the aramid-cord and steel-cord, and compared to an approximate expression with good agreement where applicable. To illustrate the stiffness behavior, all the three stiffnesses are presented with variations in the number of twists per unit length, the surrounding rubber modulus and the thickness. The stiffness couplings among the extension, bending, and twisting deformations are presented for aramid-cords with varying number of twists per unit length and rubber thickness. The results illustrate that stiffness characteristics are strongly dependent upon the number of twists per unit length, type of cord, surrounding rubber layer thickness and modulus. The stiffness coupling presented illustrate the mechanisms of load transfer, which are important for understanding failure mechanisms of cords, and cord-rubber composites.

Analysis of the master curve for the viscoelastic behaviour of polymers

A detailed analysis of typical master curves reported in the literature for the dynamic modulus and compliance of unfilled polyuretane rubber and poly(n- octyl methacrylate ), respectively, and for the transient modulus of styrene-butadiene rubber is performed. It is shown that the time-temperature superposition is not strictly obeyed, that is, the individual curves do not satisfy the scaling conditions with a translation path parallel to the horizontal axis. In fact, only a partial matching of the individual curves is obtained, on constructing the master curve, which can be described by a Maxwell Finally, the meaning of the parameters obtained for the Maxwell element and for the constants of the Williams-Landel-Ferry equation is discussed.

A non-rotational universal rheometer. Part II. Experimental procedures and results

Stress-strain, stress relaxation, creep, dynamic mechanical and squeezing flow measurements are performed on different solids and liquids to demonstrate the capabilities of the new instrument. The modulus of steel determined by stress-strain and dynamic mechanical measurements is 2·007 × 10 11 Pa with a precision of about 0·1%. The limiting factors in the determination of modulus are therefore sample preparation and determination of sample dimensions. Compression of a vertical cylinder is used for the determination of the modulus of rubber but simple compression is obtained only when the end surfaces of the cylinder are lubricated. Steady-state and dynamic viscosity on low to medium viscosity liquids are measured with the annular pumping geometry. The instrument is very good for stress relaxation measurements and less good for creep measurements. For dynamic mechanical measurements, the accuracy of the phase angle is approximately 0·2 degrees for frequencies below 0·1 rad/s, decreasing to about 1 degree at the highest possible frequency of 1 rad/s. Squeezing flow is used for the determination of polymer melt viscosity.

Finite-Element Calculations on the Stress of an Aramid Cord in a Clamped and Elongated Goodrich Block Fatigue Specimen

Abstract In the Goodrich Block Fatigue Test, a rubber block containing a tire cord is cyclically compressed and extended. The retained strength of the cord, obtained after a certain running time, is a measure of the fatigue resistance of the cord. In this test, the compression and extension is applied to the clamps of the block. This induces an indirect loading of the cord through shear forces in the rubber. This cord load varies along its length and depends on variables such as cord modulus and diameter and rubber modulus and cannot be obtained experimentally. A three-dimensional finite-element model together with a calculation procedure is presented. With these, not only the overall force-displacement behavior of the GBF specimen can be predicted, but also the detailed cord stress distribution, both for clamping and elongating the specimen. Only three different linear finite-element computations have to be performed. Results at any arbitrary elongation of the specimen are obtained by superposition of these calculation results. The accuracy can be enhanced by combining them with the measured value for the elongation at which the cord is just fully tensioned. Experimental verification was carried out for an aramid cord with a diameter of 0.6 mm. The presented model produces results that agree well with the measured values for the force on the specimen (both for clamping and elongating) and for the breaking force of the cord. Clamping of the specimen causes compression of the cord in the center area of the block. For the aramid cord used in this study, this compression area has a length of about 10 mm. At an elongation of approximately 0.4 mm (the corresponding extension setting of the machine is 3%), the cord is just fully tensioned. When elongating the block a certain amount above this setting, the stress in the center of the aramid cord is only 6.3% of the stress of a cord which would be strained the same amount as the block. In this study, no account has been taken of temperature and viscoelastic effects, which may play an important role in the actual fatigue test!

Effect of type and concentration of carbon black on the elastic modulus of butyl rubber

Measurements of the modulus of butyl rubber (IIR) containing a range of concentrations of three types of carbon black were carried out at room temperature. For SRF and FEF black, the modulus increases exponentially with concentration over a concentration range from 40 to 100 phr. For HAF composites the modulus increases up to 60 phr. At 70 phr of HAF there is a sudden drop in the modulus followed by an exponential increase. The change in modulus with carbon black concentration can be described by an empirical relation which has the form E = exp ( c a )b where a and b are constants which depend upon the type of carbon black (surface area and structure). The increase in E with concentration can be attributed to the interaction between rubber and carbon, and the occluded rubber. The drop in E at 70 phr for HAF composites is attributed to a reduction in the interaction between HAF black and butyl rubber at concentrations higher than 60 phr. The increase in E again above 70 phr is attributed to secondary agglomeration of HAF black.

Semiempirical Relationships between Properties and Loading in Filled Elastomers

Abstract The dynamic storage modulus of uncured silica-filled silicone rubber increases sharply when a critical filler loading is reached. A similar behavior has been observed for the conductivity in the same compounds. The experimental data fit a percolation law fairly well, and microscopy confirms the formation of a filler network according to the percolation model. This behavior depends on a polymer-filler interaction level, suggesting a filler network consisting of filler particles bridged together by adsorbed polymer. It has been found that the percolation threshold coincides with the optimum value of elongation at break of the corresponding vulcanizates. The percolation behavior and the relations between properties of filled rubbers described here were observed in various filled rubbers of quite different compositions. This seems to suggest the general validity of the presented relationships in all elastomers reinforced by particulate fillers.

Flexible Rubber-Steel Sandwich Springs

Abstract This novel form of spring has been developed to the point where the force-deflection behavior can be predicted with confidence from the known modulus of the rubber and the bending stiffness of the metal layers. Different geometries have been studied including three-point bend and cantilever configurations, with satisfactory agreement between theoretically predicted and experimentally measured stiffnesses. Dynamic behavior can be controlled by selection of the rubber compound. Depending on the geometry, the proportion of the deformation energy stored in the rubber itself, compared with the metal, can be varied, and this also influences, in a predictable manner, the overall damping characteristics of the spring. Epoxidized natural rubber, for instance, may be a candidate for the applications requiring higher damping. As the deflection of the spring is increased, a point is reached at which waves form in the metal layer that is under compression. This leads to a buckling of this layer and clearly limits the deformation which the spring can undergo. This important failure process has been studied experimentally and theoretically, and it is possible now to predict with some confidence the conditions under which it will occur. Fatigue failure under repeated stress has also been studied for a cantilever configuration. Lifetimes of over a million cycles were obtained with a range of samples, even when the deflection was close to that required to produce catastrophic buckling. However, for certain metal thicknesses, there is some indication that fatigue failure of the metal itself due to bending may become the dominant failure process. No failures either in the rubber or at the bond were observed.

Measurement of Young's modulus of rubber in the high‐frequency range

There is a close relation between Young's modulus of a medium and the oscillation behavior of a cavity in the medium. Young's modulus of polyurethane rubber was measured in the high‐frequency range by a new technique. A measurement of the transmission loss of a rectangular rubber plate (1×20×20 cm) with spherical cavities in a water tank was made. It was shown that when the center‐to‐center spacing between the cavities was much larger than the diameter of the cavity, there exists a frequency at which the plot of the transmission loss versus frequency attains a maximum. This maximum loss frequency occurs when the circumference of the spherical cavity is equal to two shear wavelengths in rubber. Thus Young's modulus for rubber from the maximum loss frequency was obtained. It was shown that Young's modulus for rubber in the high‐frequency range increased with frequency in the same manner as in the low‐frequency range.

Influence of structure on the impact behaviour of nylon‐rubber blends

AbstractBlends of nylon‐6 and EPDM rubber were prepared by reaction blending to study the influence of rubber concentration, rubber particle size and interfacial adhesion on the impact strength. Rubber particles induce a sharp brittle‐tough transition which is independent of the glass transition of the nylon matrix. Increasing the rubber concentration or decreasing the particle diameter shifts the brittle‐tough transition temperature for notched Izod impact tests to lower values.A toughening mechanism is proposed in which the interparticle distance, the rubber modulus and the temperature play crucial roles.

Development and Validation of a Method for Approximating Road Surface Texture-Induced Contact Pressure in Tire-Pavement Interaction

Abstract In tire-pavement interaction, road surface texture is an important variable that influences many properties such as tire noise, skid resistance, vehicle performance, and rolling resistance. Efforts to understand and quantify these texture effects have been limited by difficulties in experimentally and theoretically determining the many individual contact areas and contact pressures produced by irregularly-shaped asperities indenting the tire tread. The numerical method developed here to approximate the contact information is based on classical two-dimensional (2D) contact theory. The purpose of this paper is to describe this development. The method computes information on texture-induced contact pressure and length. The required inputs are 2D road surface texture data, tread rubber modulus, and tire inflation pressure. The approximated contact information is used to characterize road surfaces and advance understanding of how their textures affect tire-pavement interaction.