# Microcrack Detection Using Spectral Response Data Alone
## 3 Crack Inspection with Simple Specim
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Specimen** & \begin{tabular}{c} **Resonance** \\ **Frequency (Hz)** \\ \end{tabular} & \
\begin{tabular}{c} **Modal Damping (\%)** \\ **(In-Plane)** \\ \end{tabular} &
\begin{tabular}{c} **Mode Shape** \\ **(In-Plane)** \\ \end{tabular} \\ \hline No crack & 1145 & 0.38 & Bending (X-Y plane) \\ \hline Crack & 1090 & 0.51 & Bending (X-Y plane) \\ \(1150\) & 1.15 & Bending (X-Z plane) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of experimental modal analysis for two specimens. Figure 5: Measured maximum crack depth in simple specimen. The first bending mode can be found at 1090 Hz (with 0.39% modal damping coefficient) and only effective on X-Y planes. In case of cracked specimen, another impact hammer test was also conducted by assigning the impact force at #5 to figure out the behavior at X-Z plane more visibly. However, the modal test result was similar to the impact hammer case at #1. Accordingly, both X-Y planes and X-Z plane are denoted as the in-plane and the out-of-plane for the first bending mode. Second mode could not be found under the maximum frequency band, 3200 Hz. That means the response at #6, #7 was small at the resonance frequency so that the microcrack detection at the two locations will be less reliable as compared to other measurement locations, #1-#4. The crack detection was mainly conducted for the four measured data, from #1 to #4, and the results from the out-of-plane locations, #6 and #7, are discussed later. The microcrack depth was measured using X-ray equipment (Dual Tube 3D CT, TECHVALLEY, South Korea), and the maximum depth was 200 \(\upmu\)m, as shown in Figure 5. Therefore, the crack depth in the specimen was acceptable for inspection. Under these conditions, another test set-up with an impact hammer was designated to measure the response data by imposing an impact force at locations #1-#6 in both specimens. Figure 6 shows the measured impact forces in the specimen with a crack. To impose the same impact force on the target specimen, the impact hammer was moved with a circular trajectory by clamping one end of the impact hammer as in the Charpy impact test, as shown in Figure 7. The experimental results indicated that the impact hammer was setup suitably, and the similar impulse spectrum pattern obtained indicated that the approximation in Equation (2) was acceptable. When an impulse force was imposed using the impact hammer at node #i, the response accelerations were measured at all sensor-attached locations in Figure 3. In practice, it was difficult to localize the microcrack from the target structure of inspection so that the microcrack inspection method would consider the distance between the impact position and the microcrack position, in the determination of microcrack existence. So, the response data were only considered for the same location of impact position, and the relationship between the crack indicator (see the Equations (3) and (4)) and the measurement position was analyzed in this study. In each case of impulse force input at node #i, the response acceleration at the same node #i was selected and shown in Figure 8 for two rectangular simple specimens with and without microcrack. Sideband frequencies between 1000 and 1200 Hz that were derived from the crack position were seen at nodes #1 and #3 near the crack; these frequencies seemed very sensitive to the distance from the crack. In case of uncracked specimen, single frequency peak could be found at X-Y plane, #1-#4, and small peak were also shown in X-Z plane, #5 and #6, near 1145 Hz frequency. In case of cracked specimen, the frequency peak was observed near 1090 Hz at X-Y plane, #1-#4, and small two sideband frequencies were found at #1 and #2 (front face of X-Y plane). On the other hand, the sideband frequencies were highlighted at X-Z plane, #5 and #6, but the bending mode near 1090 Hz was relatively small.