Creep and relaxation contraction ratio of linear viscoelastic materials

Abstract

The theory of linear viscoelastic behaviour under any kind of loading is extended to include not only the mechanical properties of the materials but also their optical properties. Relations expressing the lateral contraction ratio function with time are also established.It is shown that data derived from a simple tension test in creep and relaxation suffice for the complete description of the viscoelastic behaviour of the materials. Indeed, while the mechanical quantities measured define the extension creep compliance and relaxation modulus, the measurement of birefringence yields the stress-optical and strain-optical coefficients if another pair of characteristic functions are known. Lateral contraction ratio functions are particularly easy to derive because they are related to the extension and bulk creep compliances and relaxation moduli functions by rather simple functions. By taking advantage of the fact that the bulk creep compliance and relaxation modulus of viscoelastic materials are rather insensitive functions with time, an approximate method is introduced yielding the values of the lateral contraction ratio functions with time. The variation of the lateral contraction ratio in creep and relaxation was determined for a cold-setting pure epoxy polymer by applying this approximation process. It is shown that the lateral contraction ratio functions are monotonically increasing functions which present a moderate transition from the glassy to the rubbery region and take values equal to 0.5 in the rubbery region. There is a difference between the creep and relaxation functions at the transition region, the relaxation function being slightly retarded with respect to the corresponding creep function. This phenomenon is in agreement with the behaviour of the other characteristic functions of viscoelastic substances. Moreover, the ratio of the two functions, which is equal to unity at the glassy and rubbery consistencies of the material, diminishes in the transition region and presents a minimum located at the vicinity of the so-called characteristic time k in creep.The lateral contraction ratio functions being determined, the bulk and shear compliance and relaxation functions may be readily evaluated as well as the exact values of the optical coefficients. Moreover, the values of the contraction ratio yield the exact values of the cross section of the specimen tested along the whole response spectrum and allow a final slight correction of all values of the characteristic functions.