Abstract
For the purpose of testing recently published theoretical relationships, the dynamic viscosity and dynamic modulus of elasticity of a lightly vulcanized rubber were measured. In these experiments, a sample of rubber in sheet form was inserted axially in a torsion pendulum system, so that the sheet was subjected to a periodic torsional deformation. Because of the dynamic modulus of elasticity of rubber, the frequency, and because of the dynamic viscosity, the damping of the resulting swing, are modified. In the region examined, the viscosity, η, is independent of the amplitude of the periodic deformation. The viscosity, η, does, however, depend on the period T of the swing to which the sample is subjected, i.e., η is practically proportional to the period T. Thus, (η/T) is approximately constant. With the samples used in the experiments, the magnitude of the ratio, η/T, was found to be approximately (2.5−4)×104 poises per second. If the rubber is stretched along the torsion axis, the viscosity decreases, and for an elongation of 100 per cent, η is about one-half as great as for the unstretched rubber. The reduction of viscosity is greater immediately after stretching than at some later time after stretching. The reduction of viscosity and its time dependence can be plausibly related to a model. The dynamic modulus of elasticity is almost independent of the period that the sample is deformed torsionally, as well as of the elongation along the torsion axis. For the samples tested, Edyn=(3−5)×106 dynes per sq. cm. In order to obtain a more accurate test of the theoretical relationships, the creep curve was measured in addition to the dynamic viscosity and E modulus of one individual sample. Measurements of the linear creep curve were made, i.e., the time dependence of linear deformation at constant load, as well as of the torsional creep curve, i.e., the time dependence of the torsion angle at constant torque. The deformation, represented as a function of the logarithm of time, is a straight line in the torsion experiment and almost a straight line in the linear elongation experiment. In both these experiments, the location and slope of the flow curves defines the constants a and b, from which the absolute value of the viscosity η, e.g., for a period of 20 seconds, could be calculated. This calculated value of η agrees well with the experimental values; small deviations indicate that the density distribution of the relaxation times is increasing somewhat more than in proportion to 1/τ in the region of very small relaxation times. The constants a and b derived from the linear creep curves and from the torsion creep curves differ considerably, although the η values, computed from their combination, are almost the same. This may be due to the fact that the rubber becomes anisotropic when it is deformed and that this anisotropy affects the restoring forces and the relaxation phenomena differently in the case of linear deformation and in the case of torsional deformation.
Effect of Relative Marker Movement on the Calculation of the Foot Torsion Axis Using a Combined Cardan Angle and Helical Axis Approach
