Techniques in oscillatory shear rheology - Indian Institute of ...

Techniques in oscillatory shear rheology 13The stress–strain curves, in case of LAOS are departure from ellipses. This can beunderstood based on the qualitative features shown in Fig. 2.1. The departure fromlinear response (or the response at the input frequency) is exhibited as stretched anddeformed ellipses. The response being considered is tress–strain, and therefore thisdeparture is described again in terms of softening and/or hardening of the materialduring a cycle.LAOS response can therefore be examined through stress–strain or stress–strainrate plots. Examples of these are shown in Fig. 2.1. The plot shown in Fig. 2.1(a),is for a vanishing cream. As can be seen, there is significant departure from linearviscoelastic response (or elliptical plot). At larger strains in a cycle, proportionallylarger stress is required for higher strain and therefore this behaviour is referred toas strain hardening during the cycle.Stress–strain curves for mucus gel [7] at different strain amplitudes are shown inFig. 2.1(b). Variation of G ′ and G ′′ , for the various strain amplitudes was observed tobe minimal. Therefore, little departure from linear response as described in the firstfeature, was observed. However, when Lissajous plots are observed (Fig. 2.1(b)),one can notice a striking departure from linear viscoelastic behaviour. Only at lowamplitudes (shown in inset), one can observe the elliptical plots.Another example of cyclic response during LAOS is shown for a concentratedparticulate suspensions [20]. The data, which corresponds to Fig. 2.1(c), have beenshown with stress–strain rate plot. A linear plot would indicate viscous response,with stress and strain rate in phase. As mentioned earlier, departure from this behaviouris observed during certain duration of the cycle.Frequency spectrum: Fourier transform of the time domain signal is used to evaluatethe frequency spectrum. The magnitudes of the peaks at higher harmonics canbe used to quantify the nonlinear response of materials.The deviations from a sinusoidal response with a single frequency (input frequency)can be captured by analyzing the signal as a combination of several frequencies[25]. This is shown in Fig. 8 with the Fourier Transform of the time domainsignal. As will be discussed later, higher harmonics (multiples of input frequency)10 5 % strainFig. 6 G ′ and G ′′ as functionsof strain amplitude forgels [10]G ′ (Pa)10 410 30% CMF0.2% CMF0.5% CMF1% CMF10 210 −2 10 −1 10 0 10 1 10 2