Dear Colleagues, Most articles recommend using E' or G' for estimating the crosslink density in rubbers. In an actual set of measurements I tried to compare 10% secant moduli with E' values above Tg and I observed signficant (but systematic) difference between the two (the secant modulus is about 3 times higher). Both are tensile young moduli, so it cannot be a G vs E discrepance. Of course, I am also aware of the fact that DMA is a dynamic modulus (1-10 Hz) while the tensile curve is more like a quasitatic test with lower effective frequency. Nevertheless, as we are definitely above the Tg, I did not expect such high difference. Any idea about the pyhsical resons? If others have similar experience please indicate.
I would agree that a factor of three is quite high and i would have expected that the DMA value should be higher as it typically correlates to smaller strain values in comparison to the secant modulus.
Before thinking about an explanation i would first like to ask for some more information:
What was the strain amplitude during DMA? Which strain rate was used for the secant modulus?
Was the system highly filled or pure rubber? Which hardness?
You can read this book
https://books.google.dz/books?id=xl8hBQAAQBAJ&pg=PA136&lpg=PA136&dq=tensile+young+moduli,+so+it+cannot+be+a+G+vs+E+discrepance&source=bl&ots=xu4N5v51RV&sig=ACfU3U2uT7oQxsNZq-HOuuhIqB2SXxH67A&hl=fr&sa=X&ved=2ahUKEwi72dm3pY3qAhWHnxQKHdRWCEsQ6AEwAHoECAUQAQ#v=onepage&q=tensile%20young%20moduli%2C%20so%20it%20cannot%20be%20a%20G%20vs%20E%20discrepance&f=false
I would agree with Matthias Jaunich, and also assume a possible effect from an amplitude dependency, taking into consideration probably different testing modes and deformations.
DMA tests are usually carried out (often by default...) at very small deformations, while quasi-static tests, for technical reasons, are often carried out at significantly larger deformations. (example from my experience: DMA-test-results at 0.05% shear strain, in comparison with results of a quasistatic test according to ISO 1827 (example): you get deformations maybe at 1% ... 10% or even more, which look quite linear.... But the nonlinearity towards higher stiffnes is somehow hidden "at the beginning". In my case the material was getting signicantly softer at shear-deformations > 0,08%, but the DMA test was conducted at 0,05% (in the "stiff" region...)
If you have a highly filled rubber, i can report you from my personal experience, that we identifed a factor 5 higher stiffness at a DMA test at 0.05% shear strain, compared to amplitudes of 1% (which is still "small" in an engineering sense). This behavior can be related to the Payne-Effect (which is also known as Fletcher-Ghent-Effect). For such kind of rubbers i'd recommend some additional series of DMA-tests under isothermal conditions, fixed frequency, with a variable deformation sweep, beginning at small strains.
Thank you for all for the answers. The rubbers were not filled, ShA between 40 and 70, tensile rate was 10 mm/min, the deformation in DMA was very minor.
At which temperature you determined the dynamic E‘? The tensile tests were done at standard laboratory temperature? Were both the same or could there be an effect from entropy elasticity as your system is unfilled?
For the strain amplitude you are sure that it was sufficient for getting reliable test results, so you measured a sufficient force? We had the problem sometimes with soft systems that we went below the detection limit of our DMA when using amplitude controll and not force controll.
Dear Matthias,
Regarding temperature the Tg was below room temeprature. I checked the E' value at 50, 100, 150 oC. As expected, the E' valueincreased with temperature (slowly). I used the 50 oC values for comparison as at that temperature the tan delta curve showed that we are safely above Tg. Regarding the amplitude, I will check. the curve seemed to be smooth and reliable.
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