An Analytical and Computational Investigation of High-Rate Rheometry

Abstract

This paper examines a class of experimental techniques used to develop constitutive models for lubricants, by simulating the shearing of a thin lubricant layer while accounting for transient phenomena. The complete transient thermal problem with fully nonlinear constitutive relations is solved, and heat conduction is accounted for both in the lubricant layer and into the walls. Numerical simulations are used to examine the shear stress history, the velocity profile, and the temperature profile as functions of time. As a particular example, the high-rate torsional Kolsky bar rheometer (Feng and Ramesh, 1993) is simulated. The computations indicate that the Kolsky bar experiments, which are able to examine the time-histories of the stresses and of the motion, can he used to obtain material properties for lubricants at high shear rates. A full numerical analysis may be required to properly interpret some of the data available from the Kolsky bar experiments, since at longer times (greater than that associated with the peak shear stress) the thermal softening may dominate the response and the velocity field may become strongly inhomogeneous. The numerical simulations are performed using both rate-dependent and limiting stress constitutive laws, and the effects of the layer thickness and the rise time of the relative velocities are examined. The simulations show that the film thickness and the rise time of the relative velocities can have strong effects on the character of the solution when the transient phenomena are included in the analysis. The computations also demonstrate that highly inhomogeneous and even localized flows may occur within rheometers as a result of transient effects. The development of these flows depends on the layer thickness, the rise-time of the boundary velocity, the thermal boundary conditions, and the constitutive behavior of the lubricant.