Evaluation of discrete relaxation-time spectrum in the torsion of a round polymer rod

Abstract

The torsion of a round polymer rod is examined on the basis of the generalized Maxwell equation, taking into account two terms of the relaxation-time spectrum. In finding the relaxation constants corresponding to the younger term, we used experimental torsion diagrams obtained with thick cylindrical specimens having a significantly inhomogeneous stress pattern. It was shown that use of the generalized nonlinear Maxwell equation with two terms makes it possible to obtain satisfactory agreement between the theoretical and experimental torsion diagrams and between the theoretical and experimental creep curves over a considerable time interval. It was established that calculation of the maximum tangential stresses by use of experimental torsion diagrams yields values virtually identical to those calculated by the refined method. The polymer constants given, determined on the basis of experimental torsion diagrams, can be used to find a first approximation of the two polymer relaxation constants constituting the youngest component of the spectrum. The theoretical and experimental curves were compared.