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I am imaging and measuring mechanical properties of hardened portland cement paste. As you may (or may not) suspect these samples have fairly high surface heterogeneity arising from the intrinsic porosity even after thorough polishing. Additionally the paste is a composite of several phases from ~60GPa down to ~5GPa.
As I understand, the "tip radius" parameter in PFQNM mode is not in fact the tip radius, but rather the radius of the (assumed) circular contact area at a given indentation depth.
The problem that arises for me is that when imaging the cement paste there is a wide range of indentation depths and thus some introduced error in the measured DMT modulus. Is there any way, that you all know of, to change the tip radius parameter after the fact to perhaps correct for some of the error introduced. Or perhaps more usefully, is there some way to consider a sphere of radius R contacting the surface of the cement and then calculate the contact area "on the fly" as a function of indentation depth?
Many thanks
caj
Hi Christopher,
You are right that the tip radius used for calculation has to take into account the actual penetration depth as the contact area will obviously grow with increasing identation depth. There is right now no automated way for what you are attempting as far as I know. One way to get a feel for the error in your measurements would be to use the high speed data capture function to capture a bunch of force curves and analyse them by hand. This should give you a pretty good idea about the error in your measurments due to the varying indentation depth.
Thanks for the response. I will try what you are suggesting and see how much error I am dealing with. The changes in indentation depth are not huge and the sharper the point, the slower the change in area with depth. Unfortunately I am using one of the cube corner nanoindentation probes for the high stiffness, which does have quite a bit of area change with penetration depth. Perhaps I can get some decent results with something like an RTESPA (sharper probe) for at least a scan or two.
I will study this some more, with the suggestion that you have made, and perhaps I can work out some sort of a correction factor.
Thanks again,
Christopher
The DMT model is based on the spherical tip rather than the circular contact. Therefore as the indentation goes deeper the increased contact area is taking into consideration in the model. There is no further correction needed.
On the other hand, if the tip continue indenting beyond the spherical part, entering the linear side wall of the tip, the DMT mode is no longer valid. Much more complicated analysis, based on Sneddon model with the arbitrary section is needed. One can pursue this route with high speed captured data and applying a different analysis, as mentioned by Stefan.
In practice we recommend the user to monitor the deformation channel closely so that the deformation is from a few nm to low 10s of nm (soft materials). In this case the spherical contact may be well preserved. From 5 GPa to 60 GPa my guess is that you may not need a dynamic formula for real time correction.
To the question how tip radius changes the modulus, the calculated reduced modulus E* is inversely proportional to the square root of the tip radius.
If your sample modulus is as high as 60 GPa, you may want to consider using the diamond probe. The reason is that the Si probes has a modulus of 130-170 GPa, adding the compliance of the sharp probe, the total compliance coming out of the tip material and shape contribution may cause under-estimation of your material modulus.