WLF shift function

[benutella]

Hello, my friend

i just have a question about time-temperature supositon. i am modelling material property with Marc mentat, but after i input the reference temperature, and constants. The relaxation curve is a simple line,how can this happen?

Many thanks!
^Q^
benutella

[Jorgen]

Hello Benutella,

What stress relaxation function did you specify? Did you use a Prony series? The WLF shift function specifies how the relaxation behavior depends on temperature and a broader time scale, but you still need to specify a stress relaxation function.

Cheers,
Jorgen

[benutella]

hello,Jorgen

thanks for your reply!
but i am still lost. what i want to do is to get the master curve for long-term bebaviour. i use WLF function to specify the shift factor.
but the result was quite strange
no idea how to define boundary condition and material property in Marc mentat
how to get master curve with it?

Thanks~~~~~~~~~~~~~~!

[Jorgen]

Hello Benutella,
I am not sure how much I can help you to input the master curve since I currently do not have access to Marc :(
Best of luck.
Jorgen

[benutella]

hello,Jorgen

Thanks for your reply!

just another question about the shift factor. i was using WLF function to calculatethe shift factor, suppose the refference temperature is 30C, the constant is 17.44 and 51.6, the glass transition temperature is 90C

from all the given, i got the shift factor is -124.6, so i just shift the curve at 30C to left with a value of 124.6, but it seems i shift too much to get a master curve.

what is wrong? any problem with calculation or something else?
Thanks in advance!

[Jorgen]

The WLF equation is often written as follows:

log aT = C1 * (T-T0) / (C2 + T - T0)

Where C1=17.5 and C2=51.6 K. If I understand you correctly, you have T=30 deg C, and T0 = 90 deg C. Hence, the difference T-T0 is so large that the denominator has switched sign :!:

You are attempting to apply WLF 60 deg away from the T0, this is more than I would recommend. At 60 deg below Tg you will have very little viscoelastic flow.

[benutella]

Hello,Jorgen

It is said that if T<Tg or T<Tg+100C,the WLF function can be used to get the long-term behaviour, i just learned that by reference

so you mean the temperature difference should be far smaller than that range?
any suggestion about the application of WLF?

Thanks a lot!

[Jorgen]

Here's a simple test: if T0=90 deg C, C2=51.6 K, and T=38.4 deg C, then the denominator C2+T-T0=0, and log aT goes to minus infinity and aT=0. Hence, no stress relaxation will occur.

[benutella]

Hello,Jorgen,

what does it imply when shift factor has a value with minus infinity? from my understanding, it only suggests that the temperature is lower than reference temperature, so the relaxation curve should be shifted to the left with an infinit value, am i in the right way?

and also, i made some relaxation tests at 30C, there seems to be relaxation from my experiment result. Theory does not agree with experiment? :roll:

the shift factor must always be positive? :?:

Thanks again!
benutella

[Jorgen]

The factor aT is always a positive number, the term log aT can be either positive or negative. For temperatures above T0, the shift is to the right (log aT > 0); and for temperatures below T0, the shift is to the left (log aT < 0).

The WLF equation with the constants that you quoted predicts no relaxation at 30 deg C. In your stress relaxation experiments, what strain did you go to? The WLF equation combined with linear viscoelasticity is typically only valid at very small strains. What strains are you trying to simulate?

[becc]

Hi,

I read with interset this old messages on WLF shift function.
I also have a problem with the use of WLF type shift function in ANSYS.
The fact is that about 50 degrees below Tg the "universal" WLF function diverges and indeed there is no more viscoelastic flow: the material has become an elastic solid. For even lower temperatures than there is no need of a viscoelastic material model but rather a simple elastic one. My problem is: how can I switch from a viscoelastic to an elastic model in the FEA code. ANSYS does not permit a simple change of material for such cases.

Please help me.

Cheers,
Giuseppe

[Jorgen]

Hi Giuseppe,

I suspect that there is no simple way to switch material model depending on the temperature :(

If you really need to be able to capture the behavior at such a wide variety of temperatures in one simulation, then I can only think of one solution: write a user material model that automatically switches between different model representations depending on temperature. I realize, however, that writing a user material subroutine can be quite time consuming and perhaps not feasible.

Best of luck,
Jorgen

[pateno]

Hey all,

The origin of the WLF equation is devoted to a temperature range above Tg and about 20 to 40deg.
Below Tg, the evolution of the shift factor as a function of temperature is assumed constant (dAt/dT = Cte) (we are in the glassy regime) and the Arrhenius assumption is relevant. If you still use the WLF equation to determine the long term response of your system far below Tg, the equation will give you no evolution, which is not completely correct.

Also, as Jorgen is saying, this theory applies for the small strain regime and should be used carefully.

pateno