The Rheology Handbook. Thomas Mezger

S. E. (Editor), Complex fluids in bio­logical systems, Springer, New York, 2015

[5.26]Kumar, A., Graham, M. D., Cell distribution and segregation phenomena during blood flow, in: S. E. Spagnolie (Editor), Complex fluids in biological systems, Springer, New York, 2015

[5.27]Vasquez, P. A., Forest, M. G., Complex fluids and soft structures in the human body, in: S. E. Spagnolie (Editor), Complex fluids in biological systems, Springer, New York, 2015

6Creep tests

      In this chapter are explained the following terms given in bold:

Liquids		Solids
(ideal-) viscousflow behaviorviscosity law(according to Newton)	viscoelastic flow behavior Maxwell model	viscoelastic deformation behavior Kelvin/Voigt model	(ideal-) elasticdeformation behaviorelasticity law(according to Hooke)
flow/viscosity curves	creep tests, relaxation tests, oscillatory tests

6.1Introduction

      Creep and creep recovery tests are used to analyze the viscoelastic (VE) behavior performing two shear stress steps. This method is mostly used to examine chemically uncrosslinked and unfilled polymers (melts and solutions), but it is also suitable to evaluate the behavior of chemically crosslinked polymers, gels and dispersions showing a physical-chemical network of forces.

      In industrial practice, however, creep tests have lost of importance since rheometers with air bearings are meanwhile available enabling the user to directly preset very low rotational speeds. Previously, creep tests have been the only way to produce very low shear rates, even if indirectly and therefore to obtain information about the behavior of uncrosslinked polymers in the

      zero-shear viscosity range, for example, to determine the average molar mass. Today however, with modern rheometers measurements with direct shear rate control are possible as well in the low-shear range. For these reasons since around 1995, creep tests are mostly carried out by scientists only, especially to achieve results under the extreme low-shear conditions of γ ̇ < 10-3 s-1.

6.2Basic principles

      6.2.1.1.1Experiment 6.1: Creep and reverse creep of a hot-melt adhesive

      At room temperature, the hot-melt adhesive at hand behaves like a flexible but tacky, soft solid. Placed in a flat cylindrical container, the adhesive is sticking to both its base and its top cover. Turning the cover manually with a constant force against the base causes the adhesive to resist at first, but then yielding slowly, showing creeping motion with increasing deformation until the cover reaches a twist angle of approximately 90° against the base of the container. When releasing the force on the cover, external forces are no longer acting on the adhesive and together with the cover it is turning back. This motion is faster at first, becoming slower and slower then, reaching finally the initial position again.

6.2.1Description of the test

      6.1.2.1.1Preset: Shear stress step function τ(t), see Figure 6.1

      1 Immediate step in stress from τ = 0 to τ0, then keeping constantly τ0 = const; this stress interval lasts from the time point t0 to t2 (τ0 = const, stress phase)

      2 Immediate step in stress from τ0 back to τ = 0, then remaining constantly at τ = 0; this interval at rest lasts from t2 to t4 (stress removal phase, or rest phase)

      Both steps should be performed as fast as possible. This requires the use of a highly dynamic rheometer drive.

       Figure 6.1: Preset of two intervals when performing creep tests:

      1) stress phase: After an immediate step onto a constant stress value follows the creep phase

      2) rest phase: After the immediate removal step to zero-stress follows the creep

      recovery phase

       Figure 6.2: Creep and creep recovery curve, showing also the final values of the re-formation γe and the permanently remaining deformation γv

      1 For polymers (uncrosslinked and unfilled, solutions and melts):γmax ≤ 50 %, however, sometimes even up to γmax = 100 %

      2 For most dispersions (i. e. emulsions, suspensions, foams), crosslinked polymers (such as elastomers, rubbers, thermosets), and gels:γmax ≤ 1 %, however, sometimes counts γmax < 0.1 % only

      When applying higher deformation values, there is the risk of exceeding the limiting value of the linear viscoelastic (LVE) range. In this case, the basic laws of rheology are no longer valid, i. e. viscosity law (according to Newton) and elasticity law (acc. to Hooke) and also the relations of Maxwell, Kelvin/Voigt and Burgers. More information about the LVE-range and further γmax values, see Chapter 8.3.3.1: oscillatory tests, amplitude sweeps.

      6.1.2.1.2Example: Test preset for a polymer sample

      1 Stress phase: step in stress to τ0 = 500 Pa, this stress value is kept constantly for t = 5 min

      2 Rest phase: step to τ = 0 Pa, the sample remains unstressed for t = 10 min

      Measuring result: Creep curve and creep

       recovery curve γ(t), see Figure 6.2

      As a test result, the time-dependent deformation function γ(t) is measured. In a diagram, the creep curve and creep recovery curve are displayed showing γ on the y-axis, and time t on the x-axis. Usually, both parameters are presented on a linear scale.

      The first part of the curve in the time interval between t0 and t2 is termed creep curve (or deformation curve). The second part between t2 and t4 is referred to as creep recovery curve (or re-formation curve). The re-formation value γe indicates the elastic proportion of the VE behavior of the sample, and the value of the finally remaining deformation γv represents the viscous proportion.

6.2.2Ideal-elastic

      behavior

      When presetting a step in stress, ideal-elastic solids show an immediate, step-like deformation. After removing the load, the re-formation takes place immediately and completely (see Figure 6.3). In the creep recovery phase, the complete deformation energy which was previously stored by the deformed material during the creep phase immediately can be used up for the re-formation process.

      Here, the following applies for the ratio of the finally occurring deformation values:

      γe = γmax and γv = 0,

      with γmax = γv + γe (see Figure 6.2).

6.2.3Ideal-viscous

      behavior

      As long as under a constantly acting constant stress, ideal-viscous fluids are showing continuously increasing deformation. After removing the load, there is no re-formation at all since this kind of material does not have any elastic proportion (see Figure 6.4). Ideal-viscous fluids are not able to store any deformation energy during the stress interval, and therefore after releasing the load, they finally remain deformed to the same extent as they showed in the end of the stress phase.

      Here, the following applies for the ratio of the finally occurring deformation values:

      γv = γmax and γe = 0 (see Figure 6.2).