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# Calibration prodcedure to determine Prony Parameters from tensile creep data

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(@fepgyou)
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Joined: 8 years ago

Hello everyone,

from tensile creep experiments I have test data for different nominal stresses. I want to use this data to calibrate a generalized Maxwell model of the form

E(t) = E_inf + sum_i (E_i * exp(-t / tau_i)

I came across a procedure with the following steps:

1. Calculate creep modulus E(t) = sig_nom / eps (t), with sig_nom as the nominal stress and eps (t) as the time-dependent creep strain

2. Find E_inf, hence E(t=t_inf) with t_inf as the last point in time

3. Calculate the first Prony parameter N=1 (E_1, tau_1) --> E(t) = R_1(t) + E_1*exp(-t/tau_1), using logarithmic transformation LN ( E(t) ) ~ LN (E_1) - (1/tau_1)*t with linear regression

4. Follow same steps as in 3. using R_1(t) = E(t) - E1*exp(-t/tau_1) --> R_1(t) ~ E_2*exp(-t/tau_2)

Now my question is how should I preferably determine E_inf (long-time creep modulus)? If it is exactly E(t=t_inf) the slope of LN ( E(t) ) does not remain constant for t--> inf. However this is needed to perform the linear regression.

Does anyone have some hints or different approaches to determine E(t)?

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3 Replies Posts: 3990
(@jorgen)
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Joined: 4 years ago

I typically dont use linear viscoelasticity (I use non-linear viscoelasticity), but if I do then I would use direct calibration of the Prony series using the [URL= https://polymerfem.com/content.php?9-Material-Model-Calibration-MCalibration ]MCalibration[/URL] apporoach.

-Jorgen

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3 Replies Posts: 7
Topic starter
(@fepgyou)
Active Member
Joined: 8 years ago

Thanks!

Would you recommend in general to always go back to non-linear viscoelastic models as the stress-strain relation of most materials (in my case polypropylene) is non-linear and linear-elastic models only can be used for a specific load level? Posts: 3990
(@jorgen)
Member
Joined: 4 years ago

Yes. That sounds right. I would not say that it is always true, though ...

-Jorgen

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