Читать книгу The Rheology Handbook - Thomas Mezger - Страница 194

Preset is a controlled shear stress function (similar to Figure 3.1 or 3.2). The steps or the ramp, respectively, should begin at shear stress values at least one decade below the assumed yield point and end up at least one decade above that point [4.16]. The yield point τ1 is the shear stress value at which the linear-elastic deformation range is exceeded (Figure 4.3). The measuring points are usually presented on a logarithmic scale, with the shear stress τ [Pa] on the x-axis and the shear deformation γ [%] on the y-axis, as a logarithmic stress/deformation or τ/γ diagram.

The measuring curve shows a constantly rising slope in the range of low values of τ and γ. For analysis, a straight line is fitted on this curve interval, based on the following consideration: In this first interval, the sample shows linear-elastic deformation behavior. Sometimes, this line is also called a “tangent”, and correspondingly, the procedure is termed the “tangent method”. When properly speaking however, tangents are usually adapted to curves and not to points of straight lines. The elasticity law applies here since the increasing values of τ and γ are still proportional in this deformation range. These kinds of samples behave like homogeneously deformable, gel-like or soft solids.

Figure 4.3: Determination of the yield point τ1

at the limit of the linear-elastic deformation range, using a single straight fitting line in the logarithmic tau-gamma diagram

Figure 4.4: Determination of the yield point τ2 using the “tangent crossover point method” in the logarithmic tau-gamma diagram

Summary

The yield point is the one shear stress value at which the range of the reversible elastic deformation behavior ends and the range of the irreversible deformation behavior begins. Then, visco­elastic or viscous flow is occurring.

A sample’s structure is already deformed below the yield point, however, this deformation is only very small. The structure would completely reform after removing the load as long as the yield point has not been exceeded. In analysis, usually by use of a software program, the τ-value is specified as the one point just before the measuring curve deviates significantly from the straight fitting line. Before starting the analysis, the user has to define the bandwidth of the tolerated deviation (e. g. as 5 or 10 %).

When using this method, the very small deflection of the measuring system in the range below the yield point can only be detected by very sensitive instruments showing a high resolution for the values of torque and deflection angle (or rotational speed, respectively). Therefore it is senseful to use here an air-bearing rheometer (see also Chapter 11.7.5b). This method should be selected for scientific experiments to be on the safe side to get the yield value still in the reversible elastic deformation range . Some examples of tests results obtained with ketchups and coatings are shown in [4.17].