TY - JOUR

T1 - Finite step rate corrections in stress relaxation experiments

T2 - A comparison of two methods

AU - Flory, A.

AU - Mckenna, G. B.

N1 - Funding Information:
The authors thank the American Chemical Society, Petroleum Research Fund under grant #ACS-PRF 35695-AC7 for partial support for this project. The authors are also grateful to the J.R. Bradford Endowment at Texas Tech University for partial support of this work.

PY - 2004/3

Y1 - 2004/3

N2 - 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.

AB - 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.

KW - Finite rate step

KW - Linear viscoelasticity

KW - Nonlinear viscoelasticity

KW - Stress relaxation

UR - http://www.scopus.com/inward/record.url?scp=3543137846&partnerID=8YFLogxK

U2 - 10.1023/B:MTDM.0000027681.86865.4a

DO - 10.1023/B:MTDM.0000027681.86865.4a

M3 - Article

AN - SCOPUS:3543137846

SN - 1385-2000

VL - 8

SP - 17

EP - 37

JO - Mechanics Time-Dependent Materials

JF - Mechanics Time-Dependent Materials

IS - 1

ER -