Finite elastic wave propagation in rubber

Abstract

A detailed experimental study has been made of the free retraction which occurs when one end of a stretched rubber filament is released. The essential feature of the retraction process is the passage of an unloading wave of finite amplitude from the point of release to the fixed end of the filament. Cine films taken at 2500 frames per second showed that for natural rubber the unloading wave proceeded without dispersion at a velocity increasing from about 40 m/s for low extensions to 85 m/s at an extension of 300 %; at higher extensions the unloading wave showed dispersion, the initial stages of unloading proceeding several times more rapidly than the later stages. A hysteretic synthetic rubber (butyl rubber) showed considerable dispersion even for low extensions. An explanation of the observed phenomena is given from which it follows that finite wave-propagation without dispersion is a consequence of the linearity of the force-extension relation in the relevant range of strain. As a test of the theory the technique is modified to demonstrate that (i) unloading waves of different wave forms show no dispersion in natural rubber at extensions up to 250 %. (ii) the predicted dispersion of both stress and strain waves is in agreement with observation, and (iii) the predicted behaviour of a rubber strip on loading by displacing one end at constant velocity is in agreement with observation. A method is proposed for obtaining load-extension relations at high rates of strain using microflash photography.