Читать книгу The Rheology Handbook - Thomas Mezger - Страница 257

Evaluating creep curves, many users prefer the J(t)-function to the γ(t)-function.

Since J(t) = γ(t) / τ0, all J(t)-curves essentially overlap with one another, independent of the preset stress τ0 as long as the limit of the LVE range is not exceeded. Since the elasticity law (τ / γ = const) applies to each measuring point, the preset stress results in the corresponding proportional deformation value. Therefore, the corresponding ratio value of J(t) is independent of the preset stress value when still measuring in the LVE range.

It is easy to check whether the limit of the LVE range has been exceeded by presenting in the same diagram all of the individual J(t)-curves resulting from several creep tests which are performed by presetting a different constant τ0-value for each individual test. Those J(t)-curves, which are not overlapping with one another but deviate significantly upwards, have obviously been measured under conditions outside the LVE range (see curve b in Figure 6.9). In this case, the internal structure has been deformed already too much by the preset stress, which was too high in this case. As a consequence, the partially destroyed structure of the material is yielding more, i. e. it will be deformed to a greater extent as corresponding to the elasticity law. In other words: The compliance of the structure increases, and then, higher J-values are obtained.

Therefore, tests which are nevertheless carried out under these conditions reveal information on non-linear behavior outside the LVE range. For the above reasons, J(t)-diagrams are well suited to check whether the LVE range has been exceeded or not. For detailed information on the LVE range, see Chapters 8.3.2 and 8.3.3 (oscillatory tests), and about non-linear behavior, see Chapter 8.3.6 (LAOS tests).

Note: Master curve of J(t)-functions via time/temperature shift (WLF method)

For all thermo-rheologically simple materials tested in the LVE deformation range, a temperature-invariant master curve of the J(t)-function can be determined from several individual J(t)-functions of which each one was measured at a different temperature. By the way, this is also possible for all other parameters of rheology, if data are measured within the LVE range. The corresponding master curve is generated using the WLF relation and the time/temperature shift (TTS) method (see Chapter 8.7.1). This method is useful to produce J(t)-values also in a time-frame for which no measuring data are available, e. g. in the short-term range.