Hye-Jin Ahn  Gap-Shik Chang  Ki-Won Song

Vol. 54,  No. 4, pp. 230-245, Aug.  2017
10.12772/TSE.2017.54.230

viscoelastic polymer liquid large amplitude oscillatory shear (LAOS) time-strain separable K-BKZ constitutive equation Wagner model discrete relaxation spectrum memory function damping function nonlinear viscoelastic function

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The present study has been designed to describe the nonlinear viscoelastic behavior of concentrated polymer systems in large amplitude oscillatory shear (LAOS) flow fields using a time-strain separable K-BKZ constitutive equation (i.e., Wagner model). Using an Advanced Rheometric Expansion System (ARES), the dynamic viscoelastic behavior of aqueous poly(ethylene oxide) (PEO) solutions with various molecular weights and different concentrations has been investigated with a various combination of several fixed strain amplitudes and constant angular frequencies. The linear dynamic data (storage modulus and loss modulus) over a wide range of angular frequencies were obtained to determine the relaxation spectrum parameters and the stress relaxation moduli at various deformation magnitudes were measured to determine the damping function. The effects of the number of relaxation spectrum parameters and damping functions on the prediction results of the Wagner model were examined in depth. The nonlinear viscoelastic functions were analyzed by the aid of 3D plots and predicted over a wide range of strain amplitudes to evaluate the overall predictability of the Wagner model. The main findings obtained from this study are summarized as follows : (1) The Lissajous patterns predicted by the Wagner model are in good coincidence with the experimentally obtained stress-strain rate hysteresis loops both in linear and nonlinear viscoelastic regions and are independent of the number of relaxation spectrum parameters used in the calculation of memory function. (2) The effect of damping function on the predictive ability of the Wagner model is more sensitive than that of memory function. When the damping function is smaller than that of the experimental data, the stress amplitude predicted by the Wagner model also becomes smaller. (3) The Wagner model predictions are closely coincident with the experimental results in the linear viscoelastic region. As the strain amplitude is increased, the predicted nonlinear viscoelastic functions are somewhat larger than that of the experimental data. Nevertheless, all trends of the nonlinear viscoelastic behavior are in good agreement with the experimental results in a qualitative sense. (4) The Wagner model predicts the first harmonic loss modulus more exactly than the first harmonic storage modulus. As the strain amplitude is increased, the first harmonic storage modulus is somewhat overpredicted. The third and fifth harmonic storage and loss moduli exhibit an overshoot or an undershoot at large strain amplitudes. This constitutive equation has an ability to qualitatively describe well such dramatic behavioral changes.