The indentation stress follows a relation where stress (indentation) is equal to LOAD (P) divided by pi multiplied by square of contact radius. (P/ pi a*a) where "a" is the contact radius. Similarly strain (indentation) is defined as a/Reff or a/Ri where Ri is the radius of indenter.
So does this mean that one indentation P-h curve can give me only one data point for stress strain?
You can "calculate the whole curve" using inverse modelling. The general idea is as follows:
Let's say you assume that Ramberg-Osgood relationship will describe your material well. Then you prepare a FE model of your indentation experiment, using Ramberg-Osgood as the material model. RO Model has two parameters, K and n. Then you simulate your experiment using FE-Analysis and record simulated P-h curve. Using optimization software (for example DAKOTA) you let it vary the material model parameters until the simulated P-h curve will (ideally) match the experimental curve. The corresponding parameters (K,n) will define the whole stress-strain curve. Of course, you can use any other material model with more parameters.
I've just googled and found a PhD Thesis, see p. 8 of the document for the introduction, the title is "Determination of full range stress-strain curves by
means of instrumented indentation".
I hope this helps!
"a" is contact radius which is changing and depended on normal load , so as indentation proceed, with every load there is corresponding a hence therefore u have same number of data points of a/Ri and indentation stress (P/ pi*a*a). therefore with one P-h curve you get corresponding curve of stress - strain.
A link to an article with a more in-depth example of the application of the curve-fitting approach that I described in my original answer:
Chung et al. Characterization of mechanical properties by indentation tests and FE analysis – validation by application to a weld zone of DP590 steel, International Journal of Solids and Structures, Volume 46, Issue 2, 15 January 2009, Pages 344–363.
http://www.sciencedirect.com/science/article/pii/S0020768308003582
It depends on the type of indentation you perform. In the case of indentation using a conical indenter or similar (Berkovich, Vickers), due to the geometrical similarity of the problem, you can get only one point on the stress-strain curve of the material. Therefore, to get the complete stress-strain curve you need to perform several indentation tests with several cone angles.
For indentation tests that do not respect the geometrical similarity principle, such as spherical indentation, it is possible to get the complete stress-strain curve using an inverse Finite Element analysis.
Additional information can be found in the following references :
G. Kermouche, J.L. Loubet, J.M. Bergheau, « An approximate solution to the problem of cone or wedge indentation of elastoplastic solids», Comptes rendus mécanique, Vol. 333, Issue 5, May 2005, pp.389-395.
G. Kermouche, J.L. Loubet, J.M. Bergheau, “ A new index to estimate the strain rate sensitivity of glassy polymers using conical/pyramidal indentation”, Philosophical Magazine, Vol. 86, Issue 33, Dec. 2006, pp.5667-5677.
G. Kermouche, J.L. Loubet, J.M. Bergheau, “ Cone indentation of time-dependent materials: The effects of the indentation strain rate”, Mechanics of Materials, Vol. 39, Issue 1, Jan. 2007, pp. 24-38.
G. Kermouche, J.L. Loubet, J.M. Bergheau, “Extraction of stress-strain curves of elastic-viscoplastic solids using conical/pyramidal indentation testing with application to polymers”, Mechanics of materials, Vol. 40, Issues 4-5, April-May 2008, pp. 271-283.
Hi,
Kindly let me know what is the Reff in Berkovich indenter or Ri in spherical indenter. is it constant or it changes with change in depth (h)?
Overall, what do you mean by radius of indenter?
Regards,
Mehdi
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