Lawrence A. Wood

Some Relations Between Stress, Strain, and Temperature in a Pure‐Gum Vulcanizate of GR‐S Synthetic Rubber

Stress‐temperature relations at constant elongation and at constant length have been studied in a pure‐gum vulcanizate of GR‐S. Such studies yield information useful for calculations involved in the theory of its elastic behavior, and furnish practical data regarding its tensile properties at different temperatures. The compounding recipe was: 100 parts by weight of GR‐S, 2 parts of sulfur, 1 part of zinc oxide, and 0.5 part of zinc dibutyl dithiocarbamate. The specimens were first held at constant length and constant temperature for a period of ½ hour to 2 hours, after which time the effects of relaxation of stress during the observation of stress‐temperature relations were negligible. The value of the stress after relaxation at each elongation was used to plot a stress‐strain curve. The stress‐temperature relations observed for temperatures below the relaxation temperature were linear and reproducible on successive runs of increasing and decreasing temperature. When the temperature was raised above the relaxation temperature straight lines were not obtained, since further relaxation occurred at the higher temperatures. The intercepts at 0°K for the lines obtained below the temperature of relaxation are useful in evaluating the internal energy changes. The intercepts of the lines representing the experiments at constant elongation were found to be negative. The absolute values were of the order of 10 percent of the stress after relaxation for the lowest elongations, and increased to almost 30 percent of the stress at the highest elongation.

Influence of the Temperature of Crystallization on the Melting of Crystalline Rubber

Abstract Data presented in this communication show an instance in which melting of a crystalline material is very much dependent on the temperature at which the crystals have been formed. It is well known that many substances in which crystallization is relatively slow can be crystallized at different temperatures in a range below the melting point, but no effect of the crystallization temperature on the temperature of melting seems to have been previously reported. The quantitative results for crystalline rubber, the material under investigation, are shown in Figure 1. The crystallization of unvulcanized rubber in the unstretched state has been found to occur at temperatures between about −40° C and 13° C. The time required for crystallization is about one year at 13° C, about ten days at 0° C, and a few hours at −20° C. Below −40° C the mobility is presumably insufficient for the formation of crystals. Crystallization and fusion are accompanied by changes in volume, heat capacity, light absorption, bire...

Synthetic Rubbers: A Review of Their Compositions, Properties, and Uses

Abstract Synthetic rubber has been the dream of many during the century which has passed since Faraday first determined the carbon-hydrogen ratio in natural rubber, but it has completed only about a decade of commercial success. Every year of the past ten has seen an increase in the quantity produced, the number of varieties available, and the number of applications. The aims in various countries have been different, and the development has proceeded in different directions. The most active research has been carried on in Germany, Russia, and the United States. There has been relatively little collection and intercomparison of the rather limited data on the physical properties of the different varieties of synthetic rubber. Scientific articles have been largely devoted to descriptions of single varieties or to discussions of limited phases of the work with respect to one variety. The present paper represents an attempt to make a summary of the facts regarding the different varieties, an intercomparison of...

Tables of Physical Constants of Rubbers

Abstract Where a range is given, available observations differ. In most cases the differences are thought to be real, arising from differences in the rubber specimens, rather than from errors of observation. Where a single value is given, it is either because no other observations are available or because there seems to be no significant disagreement among values within the errors of observation. Where no value is given, no data have been found. Where dashes are shown, either the physical measurement is impossible or the constant in question is not adequately defined under the given conditions. Values are given, in most instances, in terms of the units used by the respective authors. Where the calorie has been used, it may be defined, with sufficient accuracy for the purposes of these tables, as the thermochemical calorie, which is equal to 4.1840 joules. The kilogram weight is taken as 980.665 dynes (0.00980665 newton). Values are given for 25° C and 1 bar (=106dyne cm2=106newton m−2), equivalent to 0.98...

Density Measurements on Synthetic Rubbers

Abstract For many purposes the density of a material need be known with an accuracy of only a few per cent. For many materials the density of one sample may differ from that of another by this amount, and no useful purpose may be served by making more precise measurements on individual samples. In natural rubber, the densities of different samples have been shown, in a compilation of twenty-one values, to lie with two exceptions between 0.905 and 0.919 gram per cc. at 25° C. The variations probably represent real differences in the samples and not accidental errors of observation. Since one can seldom know exactly the origin and subsequent treatment of a sample of natural rubber, there is little value in increasing the precision of measurement. Synthetic rubbers, on the other hand, can be regarded as usually produced under conditions which are much better controlled and known. It is logical, then, to measure the density with greater precision and to hope to be able to ascribe significance to its variation...

Uniaxial Extension and Compression in Stress-Strain Relations of Rubber

Abstract A comprehensive literature survey shows the general applicability of the generalized normalized Martin, Roth and Stiehler equation to uniaxial stress-strain data in extension and compression on rubber vulcanizates. The equation can be expressed as F/M=(L−1−L−2) expA (L−L−1) where F is the stress on the undeformed section and L the ratio of stressed to unstressed length. The equation contains two constants—M, Youngs Modulus, the slope of the stress-strain curve at L=1, and A an empirical constant. The conformity of stress-strain data to the equation can readily be determined by a plot of logF/(L−1−L−2) against (L−L−1). In almost every case a straight line is obtained, from the slope and intercept of which both the constants can be determined. The range of validity of the equation usually begins near L=0.5 (in the compression region) and continuing through the region of low deformations often extends to the region of rupture in extension. If uniaxial compression data are available the modulus can ...

Modulus of Natural Rubber Crosslinked by Dicumyl Peroxide. I. Experimental Observations

Abstract Natural rubber mixed with varying amounts of dicumyl peroxide are crosslinked by heating 120 min at 149° C. The quantitative measure of cross- linking was taken as the amount fp of decomposed dicumyl peroxide, the product of p, the number of parts added per hundred of rubber and f the fraction decomposed during the time of cure. The shear creep modulus G was calculated from measurements of the indentation of a flat rubber sheet by a rigid sphere. The glass transition temperature Tg, was raised about 1.2° C for each part of decomposed dicumyl peroxide. Above (Tg+12) the modulustemperature relations were linear with a slope that increased with increasing crosslinking. The creep rate was negligible except near the glass transition and at low values of fp. Values of G, read from these plots at seven temperatures, were plotted as a function of fp. The linearity of the two plots permits the derivation of the general relation: G=S(fp+B)T+H(fp+B)+A where A, B, H, and S are constants. The lines representi...

Stress-Strain Relation of Pure-Gum Rubber Vulcanizates in Compression and Tension

Abstract The empirical function of Martin, Roth, and Stiehler represented by Eq. (1) where A has the value of 0.38 may be regarded as an adequate representation of the available experimental data covering both the compression and tension of pure-gum vulcanizates. The stress and strain are to be measured after a constant time of creep. The approximate validity extends over the range 0.5<L<3.5. The success of the single empirical function in representing data obtained in both compression and tension over a range as great as this is regarded as very significant. In the range of values of L from 0.5 to 1.0 (compression) the empirical function gives results in agreement with the predictions of the statistical theory of rubber elasticity. After representing the stress and strain in a transition region extending from L=1.0 to 1.5, the empirical function gives approximately constant coefficients C1and C2 in the Mooney equation over the range from 1.5 to about 3.5. The behavior of the empirical function in the tra...

Molecular Interpretations of Modulus and Swelling Relations in Natural Rubber Cross-Linked by Dicumyl Peroxide

Abstract A survey of published experimental work on the modulus of natural rubber crosslinked by dicumyl peroxide permits a comparison with the results and molecular interpretations obtained in recent NBS work. Excellent agreement was found among values of the shear modulus G at the same crosslinking when the crosslinking is calculated from the amount of decomposed dicumyl peroxide. The types of deformation included torsion as well as uniaxial extension and compression. G increases linearly with crosslinking (except at the lowest degrees) with a slope from 5 to 15 percent greater than that predicted by the simple statistical theory. Data of Mullins demonstrated that at each degree of crosslinking the value of G is intermediate between 2C1 and 2(C1+C2) where C1 and C2 are the Mooney-Rivlin constants. Measurements of equilibrium swelling at a given degree of crosslinking are in reasonable agreement with each other. However, the entropy components of the modulus and the sub-chain density calculated from swel...

Modulus of natural rubber cross-linked by dicumyl peroxide. II. Comparison with theory

Thermodynamics and molecular considerations are applied to an examination of the equation G = S(fp + B)T + H(fp + B) + A = 5.925 × 10-3(fp - 0.45)T + 0.0684(fp - 0.45) + 2.70, found experimentally in Part I. G is the shear modulus in Mdyn cm-2 at a temperature T for natural rubber cross-linked by adding p parts of dicumyl peroxide per hundred of rubber (phr) and heating until a fraction f of the peroxide is decomposed. G*, the energy component of the modulus, is H(fp + B) + A. The ratio G*/G decreases from 1.00 at the gel point (fp = 0.45 phr) to 0.5 near 2 phr and to 0.09 at 23.8 phr. The modulus G is related to ν e , the number of moles of effective sub-chains per cm3, by the equation G - G* = v e RT where R is the gas constant. If each molecule of decomposed dicumyl peroxide of molecular weight M d produces one cross-link in the rubber of specific volume υ ¯ r , then it is predicted that S = 2 R ( 100 M d υ ¯ r ) - 1 = 5.5535 × 10 - 3 Mdyn cm-2 phr-1 K-1, as compared with the experimental value 5.925 × 10-3. Theory gives no prediction of the values of A, or of H. The gel point may be located experimentally as the point where the slope of the modulus-temperature relation is zero. The value of G at the gel point is the energy component G*. The experimental value of fp at the gel point permits a calculation of the molecular weight of the rubber before cross-linking as 193,000. The results afford a very satisfactory confirmation of the essential validity of the statistical theory of rubber elasticity in its simplest form, if due regard is paid to G*, the energy component of the modulus.