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Large Amplitude Oscillatory Shear of the Prandtl Element Analysed by Fourier Transform Rheology

Abstract This work contributes to the theory of strain controlled large amplitude oscillatory shear (LAOS) as well as modelling the key properties of type III behavior of Hyun, the decreasing storage modulus and a loss modulus with considerable maximum. The latter two can be modelled with the help of the Prandtl element. Since it is a yield stress fluid, the use of LAOS is necessary to calculate the storage and loss modulus. Furthermore, a condition is presented which has to be met in order to avoid even harmonics. The storage and loss modulus as well as the higher harmonics of the Prandtl element are determined analytically in this work. They are given as mathematical functions which can be discussed conveniently. This allows the identification of characteristic points which are related to material parameters of the Prandtl element and enable a physically motivated material parameter identification. Beside this, it is observed that the yield strain do not coincide with the crossover G’(ŷ) = G’’(ŷ) but with the increasing of the loss modulus and the decreasing of the storage modulus. Thanks to the analytical calculations, it is also obvious that the stress response of yield stress fluids does not necessarily include even harmonics. In this work the steady state stress response of the Prandtl element is also presented as Lissajous plots and Pipkin diagrams to visualise the rheological fingerprint.