The Rheology Handbook. Thomas Mezger

at a different shear stress value.

      6.2.1.1.1Example: Determination of the yield point of a bentone suspension

      Preset for four tests at

      τc1 = 0.5 Pa, τc2 = 1.0 Pa, τc3 = 1.5 Pa, τc4 = 2.0 Pa, each for t = 20 min = 1200 s long.

      Result (Figure 6.11): Finally, for the two presets of τc1 and τc2 each of the creep curves in the form of γ(t)-curves is approaching a constant and relatively low γ-value. Each of the preset shear stress values is proportional to the correspondingly obtained deformation values. Therefore here, shearing still takes place within the linear-elastic range, according to the elasticity law: τ / γ = const.

      For the two presets of τc3 and τc4 however, each of the creep curves finally shows a slope upwards, i. e., increasing, and therefore different deformation values. Each of the preset shear stress values is proportional to the correspondingly resulting change in deformation (shear rate). Thus here, shearing takes place in the flow range now, according to the viscosity law:

      τ / (Δγ / Δt) = τ / γ ̇ 0 = const

      Summary: In this example, the yield point can be found between τc2 and τc3. In other words: Only for the presets of τc3 and τc4 constant viscosity values are resulting finally. Here, for the shear rate counts: Δγ / Δt = γ ̇ 0 > 0 (see Chapter 6.3.4.1a). For the presets of τc1 and τc2 however, with

      Δγ / Δt = γ ̇ 0 = 0, a shear rate value of zero would be obtained. Therefore, there is no motion, no flow, no creep process, and consequently, an infinitely high viscosity value would be obtained by calculation. See also [6.11] [6.12].

       Figure 6.11: Determination of the yield point via four creep tests. For each, a constant shear stress is preset, with τc1 < τc2 < τc3 < τc4. The yield point is exceeded if the resulting time-dependent deformation function (creep curve) is sloping up continuously. Here, it can be found between τc2 and τc3

      Note: Yield point and flow point

      Beside the methods described above, there are existing further methods for yield point determination: in Chapter 3.3.4 using flow curves obtained by rotational tests, in Chapter 4.4 via fitting straight lines using a logarithmic shear stress/deformation diagram, and in Chapter 8.3.4. The latter method is more meaningful in a scientific sense, since here are determined both the yield point and the flow point (oscillatory tests, amplitude sweeps). An overview on diverse methods for yield point determination is also given in Chapter 12.4.1a (guideline) and in the Index, as well as in [6.10].

      End of the Cleverly section

6.5References

[6.1]Barnes, H. A., Hutton, J. F., Walters, K., An introduction to rheology, Elsevier, Amsterdam, 1989

[6.2]Burgers, J. M., Mechanical considerations, model systems, phenomenological theories of relaxation and of viscosity, 1st report on viscosity and plasticity, Nordemann, Amsterdam, 1935

[6.3]Giesekus, H., Die Elastizität von Flüssigkei­ten, Rheol. Acta, 1966; Phänomenologische Rheologie, Springer, Berlin, 1994

[6.4]Malkin, A., Isayev, A. I., Rheology – concepts, methods, and applications, Chem Tec, Toronto, 2006

[6.5]Tscheuschner, H. D., Rheologische Eigen­schaften von Lebensmittelsystemen, in: D. Weipert et al., Rheologie der Lebens­mittel, Behr’s, Hamburg, 1993

[6.6]Läuger, J., Bernzen, M., Getting the zero-shear viscosity of polymer melts with different rheological tests, Ann. Trans. Nordic Rheol. Soc. 8/9, 2000/2001

[6.7]Boltzmann, L., Zur Theorie der elastischen Nachwirkung, Sitzungsber. Kgl. Akad. Wissensch., Math.-Naturwiss. Classe, Wien, 1874

[6.8]Ehrenstein, G. W., Polymer-Werkstoffe, Hanser, München, 2011 (3rd ed.)

[6.9]Menges, G., Haberstroh, E., Michaeli, W., Schmachtenberg, E., Werkstoffkunde der Kunststoffe, Hanser, München, 2011 (6th ed.)

[6.10]DIN SPEC 143-1 (pre-norm): Modern rheological test methods, part 1: Determination of the yield point (fundamentals and comparative test methods) , Beuth, Berlin, 2005/2019 (in German: Moderne rheologische Prüfverfahren, Teil 1: Bestimmung der Fließgrenze, Grundlagen und Ringversuch)

[6.11]Coussot, P., Rheophysics – matter in all its states, Springer, Cham, 2014 (original in French: Rhéophysique – la matière dans tous ses états, EDP Sciences, Les Ulis, 2012)

[6.12]Meichsner, G., Mezger, T., Schröder, J., Lackeigenschaften messen und steuern, Vincentz, Hannover, 2016 (2nd ed.)