Dynamic mechanical analysis with torsional rectangular geometry: A critical assessment of constrained warping models

Abstract

Dynamic mechanical oscillatory shear measurements with torsional rectangular geometry are widely carried out in order to determine the mechanical properties of soft solid materials in a quick and practical way. This technique has the advantage of avoiding slip effects, thus being particularly attractive for testing stiff elastomers such as vulcanized rubber compounds. However, one of its drawbacks is the clamping system required to keep the specimen edges in place. Since it imposes a constraint to warping deformations (i.e., out-of-plane cross-section distortions about the torsional axis), a certain increase of dynamic moduli with respect to their values in simple shear is observed and considered as an experimental artifact (i.e., de Saint-Venant's assumption of primary torsion of the specimen is no longer valid). The increase of dynamic moduli in torsion depends on the specimen's cross-section geometry and relative dimensions. We test here the capability of different torsion models to describe the constrained warping effect for an industrial rubber with rectangular specimen cross section using a wide range of different geometric parameters (length-to-width p ratio and width-to-thickness u ratio). We compare two theoretical models (Vlasov's model and Timoshenko's approach) and a phenomenological model (based on finite element simulations by Diani and Gilormini) with our experimental data set. We propose a slight modification of Vlasov's model to obtain realistic predictions of torsion over a wider parameter range. It is shown to be particularly useful in soft rubber testing, and the limitations in the choice of specimen geometry to obtain sufficient torque signal are overcome.