I studied some papers on the nanoindentation, various models are used for data analysis, oliver pharr, nix-gao, and Al-rub etc.
I have a problem in the AL-rub model, how can we will calculate the unknown parameters in the Al-rub model. i.e Hy, Ho, Beta, and h*?
We get only theses two known values from the loading and unloading curve, but how can we use this data to find the other four parameters?
yes, i have the AL-rub model, used for the analysis of nano indentation data,
for your convenience, i am attaching the original paper. thanks
Sorry for the late answer...
I never used this model but I understand as follow.
The fit parameters are determined in two different ways for fig. 3 and fig 4.
In fig. 3 H0 was taken as the limit of hardness at high indentation depths. Hy is obtained by using Tabor's law, Hy = k*sy where sy was obtained by uniaxial traction experiments and k by taking a literature value for this kind of materials. \beta is chosen such as (H-Hy/H0-Hy)^\beta give the best alignments of points on a straight line. This means, in my opinion, that it has been changed "manually" until you obtain the best alignment of points. h* was obtained as the slope of the straight line by effectuating a linear regression (the slope is h*^(\beta/2)).
In fig. 4, in my opinion, the author simply effectuated a non linear least square optimization of experimental points on equation (19) to obtain \beta, Hy, H0 and h* as the parameters of the fit (non linear fitting using any software like Origin, Matlab or Python)
http://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.optimize.curve_fit.html#scipy.optimize.curve_fit
THANKSA. Benedetto,
i was waiting for your reply very anaxiously, Thanks for you kind information.
Please go through below links. These articles might be helpful.
http://onlinelibrary.wiley.com/doi/10.1002/app.43532/full
http://www.sciencedirect.com/science/article/pii/S0032386116301227
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