Finite step rate corrections in stress relaxation experiments: A comparison of two methods

The material response after the application of a constant strain rate ramp, followed, at time t₁, by a constant strain differs from the response to an ideal (instantaneous) step of strain at short test times. Due to experimental limitations, the ideal step-strain cannot be achieved. As a result, short time stress relaxation data have to be corrected in order to obtain reliable estimates of, for example, the modulus G(t) at times shorter than approximately ten times the ramp time. Here we compare two methods of correction to the stress relaxation data obtained after a linear ramp, assuming a relaxation modulus of the form G(t) = G₀ e ^-(t/τ)β. The Lee and Knauss correction uses an iterative scheme based on Boltzmann superposition. We compare this method with the Zapas-Craft approach in which the 'true' relaxation time becomes t-t ₁/2 (t is the experimental time and t₁ is the finite time to apply the step in strain). Our numerical computations show that when the relaxation time is short, there is a substantial error in the Lee-Knauss correction. Although the Zapas-Craft approach provides a better correction for times just slightly greater than t₁/2, it is limited in that it cannot be used for times shorter than t₁/2. We also investigate the case for which the ramp-step is replaced with a more realistic nonlinear function of time. Finally, it is often desirable to have a similar correction for large deformation responses. The Lee-Knauss method is valid only for linear viscoelastic systems whereas the Zapas-Craft approach has not been rigorously evaluated for large deformations. We evaluate the use of the latter for large deformations within the context of the Bernstein, Kearsley and Zapas single integral model.