In microindentation and nanoindentation tests you have to take into account the surface roughness of the samples along with the penetration depth of the diamond indenter into the samples.

Thanks for your comment, but how surface roughness and depth of indentation can help in this case? Can you explain a bit more please. Consider that the gradient of grain size is along the length not along the depth of the sample...

Dear Mehdi,

To get a collective response of the grains you can make us of a mixture rule. The upper and the lower bounds are given by the Taylor and Reuss (iso-strain and iso-stress) assumptions. Other homogenization schemes base on the mean-field theories also exist. But the main question here is whether you can obtain a reliable stress-strain curve for each grain by doing a nano-indentation test. Because when you are indenting an individual grain, your results are not only dependent on the size of the grain but also on the crystallographic orientation of the grain and the residual stresses.

Regards,

Ali

Thanks Ali for your comment. I believe I can run the test and have the nano-indentation test and see how the results reacts. But I am no so sure how precise the homogenization results will be and that was my initial motivation to stay away from the mixture rule. By any chance have you seen these homogenous techniques used for gradient materials?

For example:

"Impact of the grain size distribution on the yield stress of heterogeneous materials"

I think microhardness and nanoindentation are more like surface characteristics. even if you take a distribution it does not tell you accurately what is going on in the bulk. just try.

In fact, we are discussing the problem of adequate averaging. This procedure may be performed in two ways, namely, 1) by mathematical (statistical) averaging, 2) by physical averaging. For second way you may use macroindentation without nanoindentation. Then you will realize physical averaging because of contact area (and deforming volume of material) become essentialy larger than grain size.

Sure I totally agree

Thanks Gabi and Serge. I have thought of microhardness test but I was not sure how to average the area and combine all the results as one single stress_strain curve that represent the sample.

It is like we average asperities roughness

There is a good article by Vander Voort on low load hardness testing. It gives details on how to get accuracy tests

https://pdfs.semanticscholar.org/3097/a88af6994c9e7193a8309965ba7a32bb7457.pdf

Hi.

Using nanoindentation, one can try to evaluate the hardness and the associated yield stress.

It is more difficult to estimate the elastic modulus.

Get a stress-strain curve is unlikely to succeed.

Even without any averaging.

Best regards.

V.N.

Thanks Valery. You are right about nanoindentation. My main focus is on microhardness now.

Macroscopic properties depend not only on the properties of grains, but also on the properties of grain boundaries

Exactly...I already considered the effect of grain boundaries and orientation of grains in the code I wrote for this work...