Hi, you can find in some work  that young modulus decrease with plastic déformation but after 3 ou 4 days,  it comes back to the initial valor. Some researchs explained that phenomeno exemple Yoshida et al., Morinstin et al.

I know this effect when the sample bar is not ideally machined. If the sample is slightly twisted it needs some value of pre-stress to get the sample in full contact with the 3pb holder. Higher pre-stress -> better contact -> higher measured modulus 

I agree with Olaf. 

However, did you check how far are the test from the instrument sensitivity?

Dear Olaf

there are some points that I have to mention.

1: as you must know, the values reported as bending modulus of PMMA are not exceeded from 4. so, even If some pre-stress is required for complete contact, the value shouldn't be as high as I mentioned above.

2: I did a transient test with same strain rate on my sample to check the stress-strain curve by which the value I found for modulus were 2.5GPa.

3: I tried this experiment for a 3D-printed sample which had a very precise rectangular geometry and I observed this oddity on this sample, too.

So, I think there should be another reason behind this phenomena.

at last, what I realized is that with increasing the pre stress value the amplitude of sinusoidal force increases to have the same strain amplitude. I can not justify this.

Mr Alberto,

If you mean the how much is standard deviation by instrument sensitivity, I'd say it was less than 5%. and I have done the experiments many times.

Please, look at the strain in play  (too much deflection may give rise to non linearity from geometric point of view- in this case the simple deflection/force relationships for 3pb, as derived by classical linear elasticity theory,  are no longer valid), and check the status of  the instrument ,the quality of fixtures and their alignement and the geometry of your sample. The sample's surfaces should be very flat in respect to the radius of curvature of the indenter and supports.

Having checked all above, please keep in mind that the dynamic mechanical analysis is a spectroscopy  of the mechanical relaxation  of polymers. For example PMMA shows a marked beta relaxation just around the room temperature (i.e. 20°C).

If you are looking at the modulus of  your sample please use a dynamometer.

Please,  check the status of  the instrument ,the quality of fixtures and their alignement and the geometry of your sample. The sample's surfaces should be very flat in respect to the radius of curvature of the indenter and beam supports.

Having checked all above, please keep in mind that the dynamic mechanical analysis is a spectroscopy  of the mechanical relaxation  of polymers. For example PMMA shows a marked beta relaxation just around the room temperature (i.e. 20°C).

Anyway, your experiment is wrong , in principle. The reason is that you impose a constant stress and apply an alternatig strain.

The pre-stress gives rise to creep (namely, the sample undergoes continuous deflection). This may induce a loss of contact between the indenter and the sample during the cyclic loading when loading in under "displacement control".

Please , try to work in "load control mode".  For example apply a pre-stress of 350 g and an alternating stress of 35 g. 

Please,  check the status of  the instrument ,the quality of fixtures and their alignement and the geometry of your sample. The sample's surfaces should be very flat in respect to the radius of curvature of the indenter and beam supports.

Having checked all above, please keep in mind that the dynamic mechanical analysis is a spectroscopy  of the mechanical relaxation  of polymers. For example PMMA shows a marked beta relaxation just around the room temperature (i.e. 20°C).

Anyway, your experiment is wrong , in principle. The reason is that you impose a constant stress and apply an alternatig strain.

The pre-stress gives rise to creep (namely, the sample undergoes continuous deflection). This may induce a loss of contact between the indenter and the sample during the cyclic loading when loading in under "displacement control".

Please , try to work in "load control mode".  For example apply a pre-stress of 350 g and an alternating stress of 35 g. 

I would tend to believe it might be geometric non-linearity. Are you working on clamped beams, simply supported beams or beams with simple supports on both sides for load reversal? On clamped beams, the supports may contribute too much to the overall stiffness. I've heard some say that clamped tests are really to be used as a last resort.

Also, I can't recall precisely the guidelines I used to follow, but I remember following ratios of recommended thickness to width and length to width for the specimen dimensions and if memory serves me well, a ratio of 2.5 for width to thickness would require some corrections due to edge effects/transverse shear or something like that.

I have almost no experience with PMMA so there might be some materials propertiy to be aware of. The low temperature relaxation discussed by Pr. D'Amore certainly is worth attention. Be aware that the manufacturing process (and its related material characteristics) may greatly affect the DMA tests. For example, if your 3D printing induced a preferential orientation of the molecules and/or made for a relatively porous material, this will reflect in tour test results. Porosity in particular may change the stress field in the part quite significantly.

Finally, obtaining values that are too high compared to the literature might come from a calibration error. Some DMA machines, if not all, come with a metalic sample that is meant to be tested and the values obtained allow for the quick verification of the calibration.