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a) With controlled shear rate (CSR): Yield point calculation via curve fitting models

Here, rotational speeds (or shear rates, resp.) are preset in the form of steps or as a ramp (see Figures 3.1 and 3.2). However, using this kind of testing, a yield point cannot be determined directly. Therefore, it is calculated by use of a fitting function which is adapted to the available measuring points of the flow curve. Curve fitting is carried out using one of the various model functions, e. g. according to the models of Bingham, Casson or Herschel/Bulkley (see Chapter 3.3.6.4). For all these approximation models, the yield point is determined by extrapolation of the flow curve towards the shear rate value γ ̇ = 0, or at the intersection point of the fitting function and the τ-axis, respectively (as described in the meanwhile withdrawn DIN 53214). The different model functions usually produce different yield point values because each model uses a different basis of calculation. Today, this method should only be used for simple QC tests but no longer for modern research and development work since a yield point value obtained in this way is not measured but merely calculated by a more or less exactly fitting approximation.

b) With controlled shear stress (CSS): Yield point as the stress value at the onset of flow

This is the “classic” method for the determination of a yield point: When increasing the shear stress with time in the form of steps or as a ramp (similar to Figures 3.1 and 3.2), the shear stress value is taken as the yield point, at which the measuring device is still detecting no sign of motion. This is the last measuring point at which the rotational speed n (or shear rate γ ̇ , resp.) is still displayed as n = 0 (or as γ ̇ = 0, respectively). The yield point τ0 occurs as an intersection on the τ-axis when plotted on a linear scale (see Figure 3.21). If presented on a logarithmic scale, the yield point τ0 is the τ-value at the lowest measured shear rate, e. g. at γ ̇ = 1 or 0.1 or 0.01 s-1 (see Figure 3.22).

Figure 3.21: Flow curve showing a yield point

(on a linear scale)

Figure 3.22: Flow curve showing a yield point

(on a logarithmic scale)

Summary: Using the flow curve analysis methods mentioned above, the resulting yield point is dependent on the speed resolution of the viscometer or rheometer used. An instrument which can detect lower rotational speeds (e. g. nmin = 10-4 min-1) will display a lower yield point value compared to a device which cannot detect such low minimum speeds (e. g. displaying nmin = 0.5 min-1 only). Of course, the latter device cannot detect any motion below its measuring limits, therefore still evaluating any speed in this range as n = 0. As a result, a lower value of the yield point will be obtained by the more sensitive instrument. This can be illustrated clearly when presenting flow curves on a logarithmic scale (see Figure 3.22): The lower the smallest shear rate which can be detected, the lower is the corresponding shear stress. Therefore counts the following: A yield point is not a material constant since this value is always dependent on the options of the measuring instrument used.

For this reason, the two methods (a and b) mentioned before should only be taken for simple quality assurance tests, thus, just for a rough estimation of a yield point.

Note: Yield point and flow point

For users in R & D, however, more modern methods are recommended compared to the simple methods as explained above, using flow curves. See Chapter 4.4 for analysis of yield points by a logarithmic shear stress/deformation diagram; or even better, see Chapter 8.3.4 to determine both yield point and flow point (oscillatory tests, amplitude sweeps). An overview on even further methods which might be used for yield point determination is given in [3.25].