Using Resonant Techniques to Measure Viscoelastic Material Properties

[ChrisA]

Hi,

I'm trying to measure in house the viscoelastic properties of solithane-113c in its rubbery regime (>20 deg C). It seems that the easiest method to use is a mass-spring resonance technique. The versions I'm looking at are (1) a circular cross section beam with a mass/accelerometer on it (Elastic Modulus) and (2) a cup shape of the material with a mass in the center (Shear Modulus).

The book I'm working from is published by NAFEMS and is called How to Analyze the Static and Dynamic Response of Viscoelastic Components. It says that this resonant type test is useful for about 100 Hz to 10 kHz. However, the ASTM test for this type of test says these tests are rarely useful for above 100 Hz. The ideal frequency range for my characterization is 20 Hz to at least 2000 Hz, but preferably 5000 HZ. It seems that the reason the ASTM makes the statement that the test is only useful up to 100 Hz is because the specimen must be short enough that there is no appreciable variation of stress along its length. This is accomplished by having the beam length to be much less than the wavelength of the stress wave. It is seen that very quickly the beam would shrink to a size that is impossible to mount an accelerometer on.

So I have the following questions (any help is appreciated):
(1) Is there any other reason these tests are not good above 100 Hz?
(2) Is there any way to approximate the error in calculated properties if the sample's length is not much less than the wavelength of the stress wave?
(3) Is it correct that in the rubbery region a viscoelastic solid does not show much change in elastic modulus (as well as shear modulus and loss factor) with increasing frequency?

Thanks for any information or resources you can refer me to.

Regards,
Chris Astefanous
Lead Mechanical Engineer
Frequency Electronics, Inc.

[Jorgen]

I typically do not use spring-mass resonance techniques to determine the viscoelastic properties of elastomers. So unfortunately I cannot give good advice to your first 2 questions.

I have extensive experience about the viscoelastic response of elastomers, however, and I have some feedback on your 3rd question. Typically both the (storage) modulus and the loss factor (i.e. loss modulus) depend on the frequency. If the material is non-linear viscoelastic for the test conditions the results will also depend on the strain amplitude.

I am curious, could you peform Dynamic Mechanical Analysis (DMA) instead of the resonance technique? DMA is easy and cheep to perform. You can also perform standard mechanical testing (Instron/MTS) using an oscillatory load to determine the viscoelastic properties.

-Jorgen

[ChrisA]

Thanks for the response. As I learn more about this topic I realize I am working with a thermoset, rather than an elastomer.

Unfortunately, my budget for this testing is very low and there is a time constraint. Hopefully, in the future I can have DMA performed on this material.

If I performed a test from 20 Hz to 800 Hz and the loss modulus and storage modulus varied by less than 10%, would it be reasonable to assume that they might not vary by more than another 10% up to 2000 Hz?

[Jorgen]

That may or may not be true. It will depend on your material and if that material has any transitions in that frequency range.

If you only see a < 10% change from 20 Hz to 800 Hz, then my guess is that is not going ot be any big suprises at slightly larger frequencies. That is just a guess though ...

-Jorgen