Second order effects in dissipative media

Abstract

Second order or ‘cross’ effects arise as a result of quadratic terms in the constitutive equations of isotropic elastic, viscous and viscoelastic media, which are required by the condition of tensor invariance of those relations. The most pronounced second order effects arise when these are clearly separable from the first order deformation, as in the case of second order elongation and volume change of an elastic cylinder subject to a twisting moment, or of second order normal stress in the case of shear flow of polymeric liquids. The recent I. U. T. A. M. Conference on Second Order Effects (Pergamon Press, London, 1964) was mainly concerned with these two phenomena. The paper discusses second order effects in dissipative (viscoelastic, plastic and strain ­ hardening) solids and reports the results of experiments in which these effects were observed. While the experiments on elastomers confirm the Rivlin-Ericksen theory of those effects in viscoelastic media, the existence of a new accumulating second order effect has been discovered by experiments on aluminium specimens in reversed torsion (Ronay 1965). This effect, which has not been observed before, is probably responsible for the rapid acceleration of tensile creep in metals by small amplitudes of reversed torsion. While the second order effects in elastic solids vanish at zero strain since they are reversible, and vanish at zero velocity in polymeric fluids, they accumulate with the number of repeated torsion cycles in strain-hardening media. Hence their observation is very simple and does not require the elaborate procedures necessary for the observation of second order effects in elastic solids and viscous fluids. The theory of accumulating second order effects in strain-hardening media is developed; the linearity of the interaction between tensile load and torsion amplitude is demonstrated by the experiments.