تعیین توابع خزش و آرامش از یک آزمایش واحد The determination of creep and relaxation functions from a single experiment

We have presented the theoretical framework for the simultaneous measurements of creep compliance and relaxation functions with a single spring-loading experiment. It has been shown that the proposed iterative numerical algorithm for determining both Et
and Dt
is stable, and yields results that satisfy the interconversion constraint to within an acceptable tolerance. It has been shown also that care is needed in calculating long-time discrete convolutions. Numerical errors can be significantly reduced by calculating the two estimates obtained from reversing the order of convolution, and taking an appropriate linear combination of the two estimates. This approach may be used as an alternative to increasing the number of measured data points per unit of time, when this is experimentally costly or infeasible. All the data encountered in this work have been simulated. More sophisticated numerical methods based on spline interpolation or smoothing may be required when dealing with experimental data. The developed mathematical framework presented here may serve as the underlying theory for new generation apparatus for the characterization of time-dependent behavior of solid polymers in the linear viscoelastic regime. However, by determining the two material functions of creep and relaxation simultaneously we can examine whether the determined functions satisfy the linear constraint ۸d
. If this is found not to be the case, then the material behavior is outside the linear viscoelastic regime. The experimentalcomputational hybrid
approach embodied here, therefore, can be used for determining the linear-viscoelastic limit of polymeric materials.