Niget: NanoIndentation General Evaluation Tool

12 F-h{}^{2} analysis

The analysis of F vs h^{2} follows [10, 9, 8].

Figure 12: F vs h^{2} analysis

12.1 Window

The window consists of several blocks:

  • •

    Parameters allows the user to set the width of the moving average window. The value 1 corresponds to no smoothing. This value is saved in settings.

  • •

    Run perform calculation and display curve, see section 12.2.

  • •

    Save save parameters and results to given file.

  • •

    Graph

    • Top: display the loading curve and the smoothed curve.

    • Bottom: display the F/h^{2} and the \mathrm{d}F/\mathrm{d}h^{2} curves.

    Stepwise zooming/unzooming can be performed by selecting a range with the mouse and pressing the Zoom/ Unzoom buttons. The graph is restored to its original size by the Restore button. Zooming in the two graphs is independent.

12.2 Procedure

  1. 1.

    We use a moving average with a fixed width and constant weight. This means we substitute a value with its average with s values to the left and to the right, w=2s+1

    \hat{x}_{i}=\frac{1}{w}\sum_{j=-s}^{s}x_{i+j}.

    The value w=1 corresponds to the original data. There is only one moving average type defined for both depth and load. Increasing the value of w noise becomes less influential but important small effects can get lost as well. Therefore, the value should not be too large, below 11 is recommended.

  2. 2.

    The ratio F/h^{2} is calculated for for each data pair (\hat{h},\hat{F}) of the (smoothed) loading curve and plotted as a function of the (smoothed) depth \hat{h}.

  3. 3.

    The derivative \mathrm{d}F/\mathrm{d}h^{2} is calculated for for each data pair (\hat{h},\hat{F}) of the (smoothed) loading curve and plotted as a function of the (smoothed) depth \hat{h}. The derivative is done numerically as the ratio of the derivatives of F and h with respect to the (time)step or index i

    \frac{\mathrm{d}F}{\mathrm{d}h^{2}}=\frac{\mathrm{d}F}{\mathrm{d}i}\left(\frac% {\mathrm{d}h^{2}}{\mathrm{d}i}\right)^{-1}.

    The numerical derivatives are calculated using the three-point formula for equally spaced data.

References