An Analysis of the Corrections to the Normal Force Response for the Cone and Plate Geometry in Single-Step Stress Relaxation Experiments

An analysis and experimental results are presented for the transient response in single-step stress relaxation experiments in a cone and plate geometry. Results from experiments on a polyisobutylene solution show deviations from unity of the ratio of the first normal stress difference to the product of the shear strain times the shear stress. These are accounted for by including three important corrections in the analysis. First, it is shown that the finite time required to apply the step introduces errors in the normal stresses which are greater than those for the shear stress. Second, the machine compliance introduces errors in the normal force by causing an increased gap separation which subsequently relaxes as the normal force relaxes. Third, the constrained geometry of the cone and plate results in the compliance errors being “magnified” by some 1600 times, leading to the need for large corrections and apparent violations of the universal relation at long times. Experimental results for extension and compression in a parallel plate geometry are presented for different gap settings and used to demonstrate that the constrained cylinder problem in viscoelastic fluids is similar to that observed in elastic bodies.