## 6 A Damage Quantification Based on SAW  
The changes in time of flight of the SAW due to perturbation in surface material properties were determined using cross-correlation technique. [PERSON] et al. have shown that such small differences in TOF (>10 ns) can be obtained using cross-correlation where the sampling rate of the signal is significantly high [50]. Referring to the experimental results (Section 4), the TOF of the first arrival  
Figure 11: The Dispersion relationship of quasi-slow transversal wave mode resulting from intrinsic length scale effects (\(\varepsilon_{ls}\) = 0 to 1) (**a**) with piezo stiffening and (**b**) without piezo stiffening at frequency 1 MHz–10 MHz. Figure 12: Dispersion relationship of quasi-longitudinal wave mode resulting from intrinsic length scale effects (\(\varepsilon_{ls}\) = 0 to 1) (**a**) with piezo stiffening and (**b**) without piezo stiffening at frequency 60 MHz–120 MHz. is determined using the cross-correlation technique applied to the time history obtained from the undamaged and damaged sample. The cross-correlation technique was employed to determine the first arrival of the time of flight. The excitation signal was selected as the reference signal. The reference signal was cross-correlated with the first arrival time of the flight signal. We correlated the leading edge of the reference signal with the leading wave packet of the received signal. The maximum cross-correlation of the reference signal with the received signal demands first arrival TOF. Therefore, the dispersive nature of the guided wave is not considered during the determination of the first arrival. The active time duration of excitation was 1.12 \(\upmu\)s and the total duration of the received signal is 30 \(\upmu\)s. Therefore, sufficient time difference was presence for avoiding the interaction of input chirp wave with the total duration of flight of the guided wave. Our intention was to determine the first arrival of time of flight of guided waves and thus the time of the flight of the multimodal signal are not considered in the analysis. Based on the cross-correlation technique, the difference in the SAWs first arrival in TOF of the damaged and undamaged sample was determined to be 47 ns (refer Figure 5a,b). Such small differences in TOF can only be obtained if the sampling rate of the signal is significantly high. The group velocity of the SAW wave mode in the undamaged specimen is 3571 m/s and in the damaged specimen is 3455 m/s. We assume that the path length between the transmitting and receiving IDT was not changed in the presence of microcrack of depth 0.2 micron. The microscale damage in the path of SAW causes scattering and attenuation of waves. The surface micro defect influences the time of flight of SAW and caused internal multiple reflections. It is usually difficult to quantify the multiple paths of scattering and reflection of SAW in presence of defects. [PERSON] et al. have demonstrated that the changes in time of flight (TOF) are attributed to the scattering, reflection, and attenuation of guided waves in the presence of surface and subsurface defects [PERSON] et al. (2010). Based on the changes in TOF, we concluded that the surface damage exists on the sample. It can be seen in Figure 7 that the central frequency for undamaged and damage state is 5.8 MHz and 5.1 MHz respectively. Due to changes in TOF, the speed of transversal wave velocity in reference state and damage state is 3571 m/s and 3455 m/s, respectively. In Figure 11, a point \"A\" is marked having abscissa and ordinate as 5.8 MHz and 3571 m/s respectively. The point \"A\" overlay on the nonlocal line has the nonlocal damage parameter as 0.1. Similarly, in the Figure 11, a point \"B\" is marked having an abscissa and ordinate as 5.1 MHz and 3455 m/s. Point \"B\" lies on the nonlocal damage parameter line of 0.7. Therefore, the difference of the two nonlocal intrinsic length scale parameters is \(\Delta\varepsilon=0.6\).