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# Can Friction Cause Viscoelasticity?

## What, Can Friction Cause Viscoelasticity?

Here is a stress-strain curve from a monotonic compression test. The stress-strain curve looks reasonable, but how do we know if the results are accurate? After all, in all compression tests there will be some amount of friction at the interface between the loading platens and the top and bottom surfaces of the cylindrical specimen. Also, can the friction cause viscoelasticity in the response?

In other words, how much does interface friction influence (pollute) the results in a uniaxial compression test?

This movie shows the results from a FE simulation of a cylindrical specimen (with equal height and diameter) that is uniaxially compressed and then unloaded. In the FE simulation there is a friction coefficient of 0.1 between the specimen and the top and bottom loading platens. The movie clearly shows that the specimen undergoes barrelling during the compression. That certainly does not seem good, but how much does it influence the stress-strain results?

## Influence of Friction Coefficient

I studied the influence of the friction coefficient on the stress-strain response using FE simulations. In these simulations the cylindrical compression specimen had a height that was equal to its diameter. The results from the FE study are shown in the following 2 figures. Note that the error that is introduced by the friction can be as large as 10% (or more).

The following figure shows stress contours at an applied engineering strain of -0.3, for the case when the friction coefficient is 0.1. It is quite interesting to see that the max Mises stress is about 5.7 MPa, and the min Mises stress is 1.2 MPa. These values are very different. The stress state is clearly not homogeneous.

## Influence of Specimen Aspect Ratio

The influence of the ratio between the specimen height to its diameter is shown in the following figure. As expected, it is better to have a tall specimen in order to reduce the influence of friction. It is not good to have specimens that are too tall, however, as that can lead to buckling problems.

## A New Innovative Compression Specimen Geometry

There is no physical reason why compression specimens should be cylindrical in shape. As shown in the figure below, using a different specimen geometry can significantly reduce the influence of friction on the stress measurements. The main challenge here, of course, is that the stress and strain states are very inhomogeneous making it more time consuming to perform the material model calibration. Which in this case has to be done using an inverse method.

## Can Friction Cause Viscoelasticity?

Now, back to our starting question: “Can Friction Cause Viscoelasticity?”

If we look at the figure to the right, we see that the stress-strain curve exhibits hysteresis when the compression test contains friction at the loading platens. Also, the amount of dissipated energy can be quite large!

This type of energy dissipation is not the same as viscoelasticity, however. But, it does make it more difficult to interpret experimental compression data. One should be careful when analyzing experimental compression data in order to distinguish between frictional effects and viscoelastic effects.

## Negative Barrelling

Another curious effect that can happen during a uniaxial compression test is something called Negative Barrelling. That is, the specimen can get a hourglass shape during unloading. The following movie shows the results from a cyclic compression test with a friction coefficient 0.2. The simulation was performed using Abaqus/Standard with no stabilization. If you look carefully, you can see the negative barrelling towards the end of the simulation.

## MCalibration Features

The MCalibration software supports a “Compression with Friction” load case to help calibrate any material model to uniaxial compression data. If you select this load case type, then you also need to specify the specimen height, diameter, friction coefficient, and the number of FE elements. MCalibration will then create and run a FE model of the actual specimen deformation during the calibration. This works fine, but makes the calibration slower due to the addition computational work. Note that the Compression with Friction load case currently only works with the Abaqus and ANSYS solvers.

## Summary

• If you run a compression test, then always unload back to zero stress again. Having the unloading portion of the stress-strain curve can be very valuable. See also the following article on smart testing.
• Even if you see hysteresis in the measured stress-strain data, that does not mean that your material is viscoelastic. It can be due to frictional effects.
• Almost all polymers are viscoelastic (or viscoplastic) in their response.
• Obtaining accurate experimental data is not easy!