## 3 Results and Discussion
### Impact Force Quantification  
The impact force with respect to the variation of compressive static force was obtained. The results show that for a static force between 0 and 10 N, the impact force is relatively constant and is on average 20 kN. After which, the force steadily increases up to 72 kN when the static force is equal to 30 N. The trend is slightly parabolic and impact forces at zero newton of static force were measured to be slightly higher than at 10 N of static force. The impact force on the fatigue samples is thus \(72\pm 11\) kN. For every second, approximately \(2.1\times 10^{4}\pm 6.0\times 10^{2}\) impacts occur at a static force of near zero, seen in Figure 13. This would mean that for an amplitude of 57% of 40 \(\upmu\)m the average absolute vertical speed of the indenter is \(0.94\times 0.03\) m/s. The high impact forces are due to metal on metal deformation between the steel pin indenter and the titanium surface. High forces are registered due to the high modulus of elasticity of the medium  
Figure 13: Force vs. time as measured by the force sensor. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Component**} & \multicolumn{2}{c}{**Treated—Plane 114**} & \multicolumn{2}{c}{**Untreated—Plane 211**} \\  & **Strain** & **Error** & **Strain** & **Error** \\ \hline \(\epsilon_{11}\) & \(-7.2\times 10^{-3}\) & \(1.8\times 10^{-4}\) & \(-1.1\times 10^{-3}\) & \(7.9\times 10^{-5}\) \\ \(\epsilon_{22}\) & \(-6.7\times 10^{-3}\) & \(1.7\times 10^{-4}\) & \(-9.7\times 10^{-4}\) & \(7.8\times 10^{-5}\) \\ \(\epsilon_{33}\) & \(2.1\times 10^{-6}\) & \(-4.5\times 10^{-8}\) & \(-1.5\times 10^{-4}\) & \(8.8\times 10^{-6}\) \\ \(\epsilon_{12}\) & \(3.2\times 10^{-4}\) & \(7.4\times 10^{-5}\) & \(-1.0\times 10^{-5}\) & \(3.4\times 10^{-5}\) \\ \(\epsilon_{13}\) & \(-1.3\times 10^{-5}\) & \(7.4\times 10^{-5}\) & \(1.2\times 10^{-5}\) & \(3.1\times 10^{-5}\) \\ \(\epsilon_{23}\) & \(4.4\times 10^{-4}\) & \(2.7\times 10^{-4}\) & \(2.2\times 10^{-4}\) & \(1.2\times 10^{-4}\) \\ \(\epsilon_{VM}\) & \(4.7\times 10^{-3}\) & \(5.6\times 10^{-4}\) & \(6.6\times 10^{-4}\) & \(2.4\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Residual strains results. and by the ultrasonic vibrations and stress waves [48]. Another factor to consider for high impact forces are due to impulses occurring over a very short time period. The force versus time plots in Figure 13 show the readings of the oscilloscope of a low static force. When minimal static forces are present, the force pattern is rather predictable and consistent. As the static force is increased, the level of stochastic behavior increases dramatically, as seen in Figure 14. The increased randomness is attributed to the increase in plastic deformation which creates widening gaps with varying depth. The subsequent plastic deformation on the surface will then begin to slightly alter the impact forces slightly due to both work-hardening and rebounding forces from the support springs. The impact force on the surface, given one UIT needle, can be replicated if an equivalent force is used to generate the plastic deformation. Hence, other work hardening processes can achieve the same effects of the UIT if similar impact forces are used combined with a transverse velocity along the surface. Possible errors in the impact force assessment can be attributed to off-axis impact forces. Loads applied to the side of the sensor may cause higher than normal readings. This is a result of coupling forces acting on the sensor. However, calibration between the distances of the applied load to sensor was made to ensure that off-axis effects are diminished. The saturation point of the sensor was reached once the static forces approached 30 N as it was close to the maximum range of the sensor. Any other force impact reading after the saturation point would not have been reliable as the sensor would have been destroyed. It is unknown what impact forces are possible after 30 N as extrapolation of the data is within an area of high uncertainty.