Continued from page 12
which shows that critical stress is not an appropriate indicator of pumpability. The existence of such variations can be associated with a high degree of samples heterogeneity, large dimensions of ordered domains, and long internal structure relaxation times. Further complications may arise from the slip of grease at the wall of the measuring plates, leading to wrong (strongly overestimated) strain readings for a given stress.
(ii) Grease rheology intersection stress Grease rheology intersection stress σGRIS
refers to the stress when
the storage modulus and the loss modulus are equal to each other. σGRIS
is determined from frequency sweep experiments by
plotting G’ and G’’ vs. frequency (at a constant strain amplitude), see Figure 3. This point marks the change from solid-like (G’ > G’’) to fluid-like (G’ < G’’) rheological behaviour. In general, σGRIS has the same order of magnitude as the yield stress [5].
Figure 1. A diagram showing how the LVE region is located in the amplitude sweep experiment. In the LVE regime, both G’ and G’’ should not depend on the strain amplitude.
When the storage modulus, G’, has decreased to 90% of its initial (zero-stress) value, the corresponding stress value is called the critical stress, σc
. It should be noted that some authors [4] prefer to define σcrit based on the 10% drop in the complex
modulus, G* = G’ + iG’’, rather than that in the storage modulus, G’. Either definition lacks scientific rigor, but the first one seems to be more logical, given the fact that it is G’ that is associated with ordered cross-linked domains contributing to the sample elasticity.
Figure 3. A schematic diagram showing how the rheology intersection point is located.
The results of σGRIS determinations are summarized in Figure Naphthenic greases have much lower σGRIS
4. As expected, σGRIS decreases with increasing temperature. values at low
temperatures than paraffinic greases. This observation agrees with the results of flow pressure determinations, also demonstrating higher fluidity (also pumpability) of naphthenic greases at low temperatures [3].
Figure 2. Temperature-dependence of storage modulus for paraffinic and naphthenic greases.
Table 1. Properties of the lithium greases in study.
The experimental data on temperature-dependence of the storage modulus for a few common NLGI 2 greases (see Table 1) used in this study conform to this general tendency (see Figure 2). However, for the critical stress, there have been significant variations between consecutive determinations, with results scattered anywhere from a few tens up to a few hundreds of Pa,
Figure 4. Grease rheology intersection stress as a function of temperature. Continued on page 16
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LUBE MAGAZINE NO.126 APRIL 2015
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