Determining elastic limit for a nonlinearly elastic material, to be used for calculating chord modulus (i.e. Young's modulus) in tensile testing

Question

I have a protein material that is nonlinearly elastic; from the get-go, the stress-strain curve shows quite an immediate curvature.

I have to use chord modulus (reference to ASTM E11-04).

The problem! How should I choose the 2nd point to get the chord modulus, by plotting from origin to this 2nd point? The 2nd point should be the point of elastic limit; how do I find it?

My solution:

1. I calculate the chord modulus at increment of 1% strain;
2. I compare the mod calculated using 1% strain as elastic limit, and the mod calculated using 2% strain as elastic limit;
3. if the difference is <5%, then I continue my increament to 3%, get the mod, and compare this new mod to the mod calculated using 1% strain;
4. I keep doing this until the difference is >5%; then that strain will be my elastic limit.

I ran this for quite a few samples and most of them have elastic limit (determined by my method) to be either 4 - 6 %.

Is this the right way to go about it? Does anyone has reference, papers, standards etc that show how to determine the elastic limit of nonlinearly elastic materials? Or how should I explain it?

Appreciate your help!

Answer 1

This is not an answer to your question, but to show the content of the linked article, which may provide the help you need.

http://qpeng.org/publication/pdf/Peng_2014_nanoscale_silicane.pdf

Answer 2

The 2nd point should be the point of elastic limit; how do I find it?

By running load-unload tests.

i.e. load to 0.1% strain then unload. load to 0.2% strain then unload. load to 0.3% strain then unload. If you come back to 0% strain (or very nearly 0%) after the unloading, then you are still in the elastic region. If you come back to a high positive value, then you are in the plastic region.

For a linear elastic material with a clear proportional limit (i.e. starts with a straight line and then starts to yield), you can determine the yield strength purely from the loading curve (e.g. using the 0.2% offset method). But if your material is non-linear elastic, there is no way to tell the elastic region other than by load-unload and looking for plastic deformation.