## 3 Experiment and Discussion
### Effect of Elastic Recovery
It was approximately the same as the indentation depth of 25 nm, which was evaluated based on the outputs of the inside and the outside sensors of the nanoindentation system. The control accuracy of the indentation depth in the designed nanoindentation system was, therefore, verified from the result. The points in the apex of the measured revered cutting edge were fitted using the least square method, as shown in Figure 7b. The radius of the reverse fitted arc, referred to as \(R_{\text{mark\_m}}\), was evaluated to be 21.04 nm. Similarly, the reverse fitted arc was a geometric convolution of the AFM tip and the reverse cutting edge. The value of 21.04 nm was not the reverse diamond tool cutting edge radius. Assuming \(\xi\) is equal to zero, the actual cutting edge radius, \(R_{\text{tool}}\), was calculated by substituting the evaluated \(R_{\text{tool\_m}}\) and \(R_{\text{mark\_m}}\) into Equation (4) to obtain 30.68 nm. The difference between \(R_{\text{tool}}\) and \(R_{\text{tool\_m}}\) was evaluated to be 9.64 nm, which was close to the nominal AFM tip radius of 7 nm. On the basis of the experimental results, the effectiveness of the proposed measurement method for cutting edge radius using an AFM and a reverse cutting edge artifact was verified. \(R_{\text{mark\_m}}\) of other reverse cutting edges with various indentation depths were also evaluated using the proposed measurement method for cutting edge radius. The evaluated \(R_{\text{mark\_m}}\) and \(R_{\text{tool}}\) are  
Figure 6: Measured diamond tool cutting edge. (**a**) AFM topography; (**b**) Profile of Section B–B’. Figure 7: Measured reverse diamond tool cutting edge. (**a**) AFM topography; (**b**) Profile of Section C–C’. plotted in Figure 8. As can be seen in the figure, the average diamond tool cutting edge radius was estimated to be 30.38 nm with a standard deviation of 0.31 nm. Therefore, it was verified that the elastic recovery of the reverse cutting edge artifact did not affect the measurement accuracy of cutting edge radius when the indentation depth was within 20 to 200 nm. In addition, the effect of elastic recovery on measurement uncertainty of cutting edge radius was investigated. The indentation area between the diamond tool cutting edge and the workpiece, shown in Figure 9, can be recognized as a cylinder and a plane surface. According to the Hertz theory [26], for a plane surface and a cylinder with a radius of \(R_{\text{tool}}\), the elastic recovery \(d_{\text{er}}\) of the reverse cutting edge along the \(X\)-direction can be expressed by the following equation:  
\[d_{er}=\frac{4}{\pi}\cdot\frac{1}{L}F.\frac{1-v^{2}}{E} \tag{6}\]  
where \(F\) is the applied indentation force between the diamond tool and the workpiece, which can be obtained from the deflection of the cantilever at the indentation position and the spring constants of the cantilever in the designed nanoindentation system. \(L\) is the length of cylinder, which can be obtained based on the indentation depth and the nose radius of the diamond tool. \(E\) and \(v\) represent the Young's modulus and the Poisson's ratio of the diamond tool, respectively. Figure 10 shows the elastic recovery of the reverse cutting edge under various indentation depths. The values were employed to evaluate the measurement uncertainty induced by the elastic recovery. The measurement uncertainty of cutting edge radius of a diamond tool with 1 mm nose radius was evaluated based on the Guide to the Uncertainty in Measurement (GUM) [27]. Figure 8: Experimental results under various indentation depths. Figure 9: Schematic of the indentation area between the diamond tool and the copper workpiece. Table 1 shows the calculated uncertainties when the indentation depth was equal to 25 nm. The uncertainty in \(R_{\text{tool\_m}}\) and \(R_{\text{mark\_m}}\) was evaluated to be 1.36 and 1.42 nm, respectively.