relation between viscosity/relaxation time on KBK-Z model and temperature.

[andradesilva]

Hi,

I am simulating the blow-moulding process based on injection using ANSYS Workbench Polyflow Module.
I am doing a viscoelastic isothermal analysis, and I am using the KBK-Z model for viscoelasticity. The inputs are Viscosity and respective relaxation time.

I know that temperature does not exist on this analysis. However, I would like to estimate the temperature at which PET has this spectrum shown next:

Mode Viscosity (Pa-s) Relaxation time (s)
1 1E+04 0.01
2 3E+04 0.1
3 1E+05 1

Or, even better, how can I calculate it? There is any way?

Best regards,
AndradeLopes

 

[rickfischer51]

Have you looked at the WLF equation?

Rick Fischer
Principal Engineer
Argonne National Laboratory

 

[andradesilva]

Hi,

Yes, I know the Williams-Landel-Ferry equation. But I don't know how to use it for this specific problem. Could you please detail a possible approach?
Is it valid for the KBK-Z model? How can I relate the two?

What are the values of u0, C1, C2 and Tr for PET in a temperature lower (but not much) that it's melting point, 70%, let's say?

Do I need to do experimental tests, in order to build a master curve? Is there any online resource with the experimental data needed to obtain the parameters and to solve the equation?

I am attaching the equation, and I ask you please to confirm if this is the correct equation.

Thank you for your replay,
Best regards,
AndradeSilva

 

[rickfischer51]

This is pretty basic stuff. Get a good text like Into to Physical Polymer Science by Sperling and study up

ln(n/nr) = -C1(T-Tg)/(C2+(T-Tg) where n=viscosity, ng = viscosity at Tg, T is temp, and Tg is the glass transition temp. For Pet, C1=39.12, C2=51.6 for many polymers, ng is approximatly 1e13 poise.

Rick Fischer
Principal Engineer
Argonne National Laboratory