The energetic contribution to rubber elasticity in the range of small uniaxial compression and moderate elongation

Abstract

The relative energetic contribution to the retractive force of a deformed rubber sample, fef, has been evaluated from thermoelastic measurements at constant pressure. Extension ratios λ have been studied in the range 0.88 ⩽ λ ⩽ 1.70 at 20° and 40°C. The results are given for a reference temperature, 30°C. Since data in the transition region from uniaxial elongation to compression were to be evaluated, a new set of equations was derived on the basis of the Gaussian force law, because the usual equation for measurements at constant pressure tends towards infinity when approaching the undeformed state λ = 1.Considerable difference between the results obtained by different, though apparently equivalent, equations have their origins in the deviation of the experimental data from ideal Gaussian behaviour. The influence of this inaccuracy on the terms of the equations is discussed and the most reliable functions for small deformations 0.88 ⩽ λ ⩽ 1.15 and for moderate elongation λ > 1.10 have been identified. With these precautions the Gaussian force law is a satisfactory approximation for the determination of reliable values of fef.The evaluation of data at small deformations is extremely sensitive to experimental error. Even smoothed polynomials L (f) were not sufficient to eliminate an apparent maximum in the fef vs. λ curve. Therefore the linear thermal expansion coefficient βlin(λ), which is a major term in all the fef equations at small deformations, had to be scrutinized critically. Although experimental data in this range showed that βlin(λ) is a slightly S-shaped function, a linear approximation is adequate at moderate elongations.Using one of the new equations together with the linear approximation for βlin(λ) in the region of small deformations, and two equivalent equations at moderate elongation, the energetic contribution to the total stress was found to be fef = 0.18 ± 0.02 for lightly crosslinked natural rubber. Little variation in fef was observed over the full range of measurements: 0.88 ⩽ λ ⩽ 1.70.