During nanoindentation we use an indenter at certain loads to penetrate a surface and used the load-displacement data to calculate the hardness value and reduced modulus. But there is no mention in the literature on how to calculate the strains incurred in the bulk near the indent when the test is done. Can strain be calculated from the resulting load-displacement data?
This is a slightly difficult question to answer. For a normal sharp-pointed indenter, the strain varies strongly from place to place in the deformation zone under the indenter. For large-scale Vickers hardness tests, the usual rule-of-thumb is that hardness is related to uniaxial flow stress at about 8% strain; the hardness value being 3x the uniaxial flow stress. So the "indentation strain" (a sort of average over the whole plastic zone) is taken as 8%. Berkovitch indenters are designed to have the same area/depth ratio as Vickers indenters, so this should also apply to them. Given the shape of the sharp indents is the same at all sizes, this strain shoudl be independent of indentaion size for the same indenter angle. But on smaller scales, size effects start to occur, with rising hardness as indentation size reduces. The explanations for this are usually framed in terms of increased geometrically-necessary dislocation densities at small indentation sizes, which essentially means higher strains. But this is still a bit of a disputed area.
If you want to do measurements at different strains, a reasonably well-established method is to use spherically-tipped indenters with different radii. Andy Bushby at Queen Mary, London, has done lots of work on this at the nanoindentation scale, but the technique dates back to David Tabor's work in the 1950s.
There is one more method to use piramidal indenters with different angles at the tip (from 45 to 85), so the deformation under the indenter varies from 2 to 30%. This method is described by Milman in "Construction of stess-strain curves for brittle materials by indentation in a wide temperature range".
I think that you can complete your experimental test by numerical modeling. You can introduce the force/displacement curve obtained by instrumented indentation as loading condition in the numerical model.
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