Are compounds softer at elevated temperatures?

Finite element analysis (FEA) has been part of product development for decades in the seal industry. However, how to use FEA to predict seal performance in real-world thermal conditions remains challenging. Part of the challenge is the accurate measurement of temperature-dependent properties of rubber compounds for the analysis.

In the course of our measurement effort, one interesting question was raised: Are rubber compounds softer at elevated temperatures? The answer to this question seems trivial, and most would say that rubber compounds are, of course, softer at elevated temperatures, proven by common sense and evidence from measured and published data. Figures 1 and 2 graph data obtained from multi-temperature, isothermal tensile testing of seven different rubber compounds, based on ASTM standard D 412. The graphs illustrate that stresses at 50% and 100% strains (commonly called modulus at 50% and 100% elongations) decrease from ambient to high temperature, although the trend is inconclusive at temperatures higher than 158[degrees]F.

[FIGURES 1-2 OMITTED]

However, during the initial high temperature testing of rubber compounds for static FEA, we discovered the trend of stress change was somehow contradictory to these results. Figure 3 shows the typical tensile stress data of an FKM compound from an accredited test service, which indicates that the stress at large strain (>20%) actually increases from 73[degrees]F to 248[degrees]F and 302[degrees]F. In other words, the rubber compound is actually stiffer, rather than softer, at the elevated temperatures.

[FIGURE 3 OMITTED]

So, what's the reason for the opposite trend? Through a careful examination of the test procedures, we found that the trend change was most likely the result of different test speeds. The tests that produced the data for figures 1 and 2 were based exactly on the ASTM standard D 412, with a quite high test speed of 20 in./min. For the data gathered for figure 3, the test speed was set low for the purpose of capturing material response associated with quasi-static deformation.

Curious to clarify the issue, we selected an FKM compound and performed a controlled comparative tensile test, still based on ASTM standard D 412, but with two speeds: 20 in./min, and 0.4 in./min. To maximize test data comparability, we used test samples from the same batch of material that were post-cured and conditioned in the same way. The results of this test are presented in figure 4. The results show that under the high and low test speeds, the measured stress changes in different directions. This observation was confirmed by similar tests of other rubber compounds.

[FIGURE 4 OMITTED]

A better understanding of the test speed effect can be achieved with advanced FEA. The current North American industry practice of sealing FEA is still quite limited to what is called "hyper-elastic" analysis of rubber seals. The analysis assumes that the rubber is "perfect" elastic, and therefore, it can't simulate any speed or deformation-rate dependent rubber behaviors. To be able to predict and explain the observed test speed effect, a "thermo-viscoelastic" analysis is necessary, and must incorporate the following physics of rubber material:

* Rubber is viscoelastic, even in ambient and elevated temperature.

* Rubber elasticity (or entropy elasticity as termed in kinetic theory of rubber) is proportional to absolute temperature in a certain temperature range.

Figure 5 shows the results of such an analysis, which simulates the above-described two-speed tensile test of the FKM compound by using its viscoelastic property obtained from a DMA test. One can see that the effect of test speed on the measurement of temperature-dependent rubber properties is well predicted.

[FIGURE 5 OMITTED]

Now the answer to the question, "Are rubber compounds softer at elevated temperatures?" is not so trivial. In fact, at elevated temperatures, a rubber compound can behave either softer or stiffer, depending on how fast you deform it.

Rubber is viscoelastic, and in a fast deformation, it has less time to relax. The stress measured from a high-speed test is always larger, no matter at what the temperature. But, the amount of stress difference measured in high- and low-speed tests is smaller at elevated temperatures, since the deformed rubber relaxes much faster at high temperatures. It is these inherent viscoelastic characteristics of rubber compounds, combined with the entropy elasticity, that renders the interesting deformation-rate dependent behavior.

by Kai Zhang

Parker Hannifin, Seal Group