Читать книгу The Rheology Handbook - Thomas Mezger - Страница 186

Definition of the shear deformation, also termed shear strain:

Equation 4.1

γ = s/h

γ (pronounced: gamma), with the deflection path s [m] and the distance h [m] between the plates, see Figure 4.1. The following holds: s/h = tanφ, with the deflection angle φ [°], (phi, pronounced: fee or fi).

The unit of the shear deformation γ is [1], it is therefore dimensionless.

Most samples have to be measured at very low γ-values in order to remain in that limited part of the deformation range which can be analyzed scientifically. Therefore, in most cases, it is useful to specify the γ-values in % (= 0.01 = 10-2).

Example: A deformation of γ = s/h = 0.1 = 10 % occurs in a shear gap of h = 1 mm if one of the plates is deflected by s = 0.1 mm.

Note: Use of the terms deformation and strain

Sometimes, the terms “deformation” and “strain” are used as synonyms. In order to use a clear language, strain should be chosen if a controlled shear strain test is performed. And “deformation” should be selected to outline the consequences for the passively reacting sample if a controlled shear stress test is carried out. However, in many industrial laboratories people use both terms without making a difference. In most other languages besides English there are existing no different terms for γ when performing these two different test modes, and therefore then, in both cases the term deformation is used.

For “Mr. and Ms. Cleverly”

The relation between deformation γ and shear rate γ ̇

The symbol γ ̇ for the shear rate is derived from γ. The following holds:

Equation 4.2

Δγ / Δt = (γ1 – γ0) / (t1 – t0)

with the deformation γ0 [%] at the beginning, and γ1 [%] at the end of the test, with the time points t0 [s] at the beginning and t1 [s] at its end, with the change in deformation Δγ [%] and the test period as time interval Δt [s]. Using the scientific notation for infinitesimal parameters:

Equation 4.3

dγ / dt = γ ̇

Therefore, a shear rate γ ̇ is an infinitely small change in deformation (dγ) which takes place in an infinitely short time period (dt). In other words (according to ASTM D4092): The shear rate γ ̇ is “the time rate of change of shear strain”. Expressed mathematically: γ ̇ with the unit [s-1] is the time derivative of γ. In other words: The shear rate is the time-dependent rate of deformation, or briefly, strain rate.

End of the Cleverly section