DMTA vs. Uniaxial+Biaxial+Planar Shear. DMTA -> mat'l Mo

[cnuk]

I'm trying to analyze an NBR elastomer pump subject to cyclic loading. I am using MSC Marc 2005 because that is what our company owns and it'll be tough to justify anything different (Marc is hardly ever mentioned in these forums....don't know why).

My problem is, in everything I have read it talks about characterizing the elastomer based on uniaxial, biaxial, and planar shear testing at rates comparable to your application. This all makes sense to me, but my problem is that our company owns a DMTA and all the data I get comes in a completely different format. For example I get great looking graphs of elastic modulus vs. flexing frequency, with a data series for each temperature. I get Modulus vs. % strain at any temperature I want. Endless combinations of good data it seems like. My problem is, I don't know how to convert this into a material model in Marc. Do I just take the elastic modulus at the temperature & flexing frequency of interest and use an isotropic material in Marc? I hope not. I tried fitting some uniaxial test data with the Arruda-Boyce model in Marc. Fit looked good to me and seemed to give reasonable numbers in a test analysis. I reran the same analysis with my simple isotropic model based on DMTA data and got values that are 5x higher.

I'm confused about how to make use of DMTA data for elastomer FEA. I don't want to ask to characterize our material externally with uniaxial,biaxial,planar shear testing when we have good test equipment in house. Any pointers or advice?

Thank You

[Jorgen]

Hi cnuk,

Good questions. The main reason, I guess, that Marc is not mentioned that often here is that I currently don't have easy acess to that FE package :(

DMTA is a very useful tool to characterize polymer materials. As you mentioned, DMTA can give a lot of information about the storage and loss modulus as a function of temperature and frequency, which is very handy!

There are certain limitations to the DMTA data, however. The main problem is that it is traditionally only performed at very small strains. Hence, you can only use the DMTA data to calibrate certain rather simple models (e.g. linear viscoelasticity), and depending on the application that may or may not be sufficient. In your case what strain levels do you expect the elastomer pump will be exposed to?

In summary, the DMTA data can be used to calibrate a linear viscoelasticity model that is capable of predicting the behavior of the elastomer at different deformation rates and temperatures. But you should be aware that linear viscoelasticity will only be accurate for a limited range of frequencies, temperatures, and only for rather small strains.

- Jorgen

[cnuk]

The pumps we design typically have what I'd consider very small strains. When the elastomer thickness is approx 1/2" we will have approx .02" to .03" of interference with a metal part to generate a fluid seal. Simple math of .03/.5=6% strain. As the temperature increases the interference will increase, but no more than 10-15% strain would ever be experienced. Based on this, I think the DMTA is still a good tool. We do a lot of DMTA testing at 5% strain and can go up to 10%, however at the higher strain level the DMTA is limited in the frequency at which it can test so we don't get 100+Hz data....not a big issue.

Am I right about using the linear isotropic material model or is there someway I can go from DMTA to a simple (maybe more appropriate) Mooney model?

For a linear viscoelastic model, I am looking at Marc now and it looks like I set it up as a "standard" isotropic material but add the information for Viscoelastic properties: Marc's asking for # of deviatoric terms, # of volumetric terms and then a table of time vs. shear constant and well as a table of time vs. bulk constant. Since I read that compressibility is not that important, does that imply I only need to fill in the table of shear constant vs. time? What's the best test to collect this type of data? There's also "thermo-rheologically simple" input that lists WLF, Power Series, and Narayanaswamy options...lots to learn yet.

I wish you had Marc as well....then all my running on would be more translate-able.

Thank you once again for all your help.

[Jorgen]

I agree, DMTA should be sufficient for your application. I am somewhat confused by your terminology. Can you explain what you mean by "linear isotropic material model", is that a simple linear elastic material model? The Mooney model, which is often referred to as the Mooney-Rivlin model, is for example also isotropic. You should be able to fit many different hyperelastic models to your DMTA data.

About the linear viscoelasticity model, yes, you can assume that the bulk modulus is a constant. And then only specify the shear relaxation modulus.

- Jorgen

[cnuk]

Apologies for my slow response. It's a very busy time of year.

What I mean by linear isotropic model is basically the material model you'd use for steel...you called it linear elastic which I think is the same thing. You can specific young's modulus and a poisson's ratio...that's it. That's what I've used to date, but I'm not sure it is a valid approach, however it's all I can do with my DMTA data so far. I've just assumed v=.495 and E directly off the DMTA elastic modulus output for a high % strain test run.

A colleague tells me that if I have the E'(elastic) and E'' (viscous) modulus at a known operating point I can simply convert those to the Mooney Rivlin material constants C1(or C10) and C2(or C01). For example if I have E'=1000 psi and E''=200psi, I should be able to assign those as: C1=1000, C2=250. I'm fairly sure this doesn't work. Since initial tensile modulus, E=6*(C1 +C2), that would mean my elastomer has an initial modulus of 7500psi....no way we have ever measured numbers even close to this.

So, it there a way to take E' and E'' and directly convert those to the Mooney-Rivlin constants? That would be ideal for me, but it sounds too good to me true.

Thanks yet again!

[Jorgen]

As you know, the E' (storage modulus) and E'' (loss modulus) are typically functions of applied loading frequency. This data can be converted to Mooney-Rivlin parameters, but first there are a few things I want to highlight:
:arrow: The E' and E'' data includes both elastic and viscous effects
:arrow: The Mooney-Rivlin model is a nonlinear elastic model that does not include any consideration of viscosity. Hence, the MR model can only give a constant E' value and E''=0, for all frequencies!

You can use the E' data to determine the Mooney-Rivlin parameters. First pick E' at one representative frequency. Since E depends both on C1 and C2, there is no way to determine both C1 and C2 from the single E' value. What I would do is to assume that C2 is equal to 0, and determine C1 from E/6.

The Mooney-Rivlin model is a very simple model that is not capable of taking advantage of the DMTA data. You might want to consider using adding linear viscoelasticity to the MR model.

- Jorgen

[cnuk]

Thank you for your response once again. I talked with my colleague some more and finally here is what he said to use:

C1=E'/6 and C2=E''/6.

I did a very simple trial run and the numbers seemed fairly reasonable....it only relied on the elastic properties, not the viscous properties so I should expect so.

I will have to do some more digging into how to model viscoelasticity. I haven't done enough looking into it to know where to start even.