I am trying to compare the relaxation times of various polymer melts in order to analyze their melt fracture behavior.
I have conducted stress relaxation (5% strain) tests as well as frequency sweep (0.01 - 150 Hz @ 3% strain) tests with a DMA, but I am having trouble extracting the relaxation time from these data. I tried fitting the Maxwell model (exponential decay) to the stress relaxation curve, but the fit is very poor.
I thought perhaps that I might have multiple relaxation times, but I was not sure how to calculate these from my data. Furthermore, if I do have multiple relaxation times, how can I use these values in other contexts, i.e. to calculate Weissenberg and Deborah number?
Dear Steven,
The relaxation time is not properly defined for a material, metal or polymer, but for a particular mechanism taking place in such material. Indeed, the relaxation time is well defined for relaxation processes, which are thermally activated, in solid materials, and then the dependence with frequency is well established. This is the case of the alfa and beta relaxations in polymers. However, you are looking for "polymer melts" and then I imagine that you are first undergoing a glass transition and then a fully melting of your polymer.
In such case, you are analyzing "Phase Transitions", which are not strictely relaxation processes, and then their dependence on frequency has not to follow the typical expressions used for analysing such processes.
I recommend you a book devoted to relaxations in polymers: Physics and Mechanics of amophous polymers, Jo Perez, Tec-Doc, Lavoisier, 1992. This is a classic textbook addressing well this kind of problems.
Another interesting book, addressing both relaxation and creep is: Viscoelastic Solids, Roderic S. Lakes, CRC Press 1999.
I think that your problem is more related to "creep behaviour" at high temperature than to a "relaxation process", and then your Relaxation Time will be linked to the strain rate of the material at a particular stress and temperature (and less dependent with frequency). I suggest you to look for clasical books on "Creep in Polymers".
I am aware that my comment does not answer your quetion, but I hope that could be useful for approaching it.
Best regards,
Prof. J. San Juan
Can you explain why you used DMA to determine relaxation of a polymer melt? Why not small amplitude oscillatory shear (SAOS) test?
The concept of DMA and SAOS are similar but we use DMA to examine dynamic mechanical properties of solid polymers and SAOS for polymer melts, sometimes we use DMA for high viscosity polymer melts to compare with their non-linear rheological analysis.
Because when you go close to melting point of polymer, the linear viscoelastic (LVE) region in DMA becomes such narrow that may not be experimentally accessible, so you are basically doing your tests in non-linear region which means you may change your micro-structure in a non-reversible way.
Simplest way to check for melt relaxation is to do SAOS test, then plot imaginary part of complex viscosity against its real part, this graph is known as cole-cole plot. If you see a peak in the cole-cole plot, it means that the relaxation of your polymer melt was in the studied range of frequency, if not, then you can use test methods to get broad frequency range data [1] and then analyze the data accordingly.
When you see that you have the relaxation in your experimental window, then you can begin fitting generalized Maxwell model.
Hope this could help you in your experiments,
Good luck
[1] Article Broad frequency range characterization of molten polymers
Thank you for the answers. Could you elaborate a little bit on why SAOS tests avoid the problems of DMA tests for polymer melts?
Additionally, how does the value from the Cole-Cole plot relate to the cross-over point of the loss and storage moduli?
- Badges
- Science topic
- Similar topics
- Biological Science
- Physiology
- Physiological Processes
- Stress