# Adaptive Subset-Based Digital Image Correlation for Fatigue Crack Evaluation
## 4 Fatigue Crack-Opening Evaluation Tests  
The fatigue crack-opening phenomenon, which is a typical local deformation, is experimentally traced on a speckle-patterned fatigue crack specimen, as shown in Figure 8. In this experiment, four steps of the fatigue crack-opening images are acquired under the uniaxial tensile conditions of 0.2, 1.0, 1.4 and 1.7 mm using UTM. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**The Number of Spatial Error Points**} \\ \hline
**Case** & **200 \(\upmu\)m** & **500 \(\upmu\)m** & 1 mm \\ \hline Adaptive subset & 0 & 0 & 0 \\ \hline SSSIG 7 × 7 pixels & 829 & 134 & 0 \\ \hline SSSIG 9 × 9 pixels & 67 & 8 & 71 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the number of spatial error points between the adaptive subset and the SSSIG. Figure 8: Experimental setup: (**a**) data acquisition system and (**b**) the ROI on the fatigue crack specimen. Figure 7: Validation test results of SSSIG: the subset size of 7 × 7 pixels with a horizontal displacement of (**a**) 200 \(\upmu\)m, (**b**) 500 \(\upmu\)m and (**c**) 1 mm. The subset size of 9 × 9 pixels with a horizontal displacement of (**d**) 200 \(\upmu\)m, (**e**) 500 \(\upmu\)m and (**f**) 1 mm. Figure 8a shows the fatigue crack-opening test setup, consisting of the digital camera, speckle-patterned dog-bone test specimen and UTM. Figure 8b displays the zoom-in speckle-patterned image of the specimen with a real fatigue crack and the random speckle pattern similarly made by the stone spray. First, the reference images are captured from the target specimen surface, which is installed at the UTM without loading. Here, the ROI is \(1000\times 400\) pixels, which is equivalent to \(20\times 8\) mm\({}^{2}\) on the target specimen, as shown in Figure 8b. Then, the uniaxial tensile loads of 0.2, 1.0, 1.4 and 1.7 mm are applied using UTM, and the corresponding test images are sequentially acquired according to the loading steps. Note that the single pixel resolution of the captured image is 20 \(\upmu\)m when the working distance between the lens and specimen surface is 487 mm. The speckle-patterned images are obtained under normal indoor lighting conditions and the camera settings are similarly fixed at ISO 1600, F 22, with an exposure time of 0.5 s. INSTRON 5982 UTM has a 100 kN axial force capacity with a 0.01 mm displacement resolution control. Similar to the feasibility test, 15 reference images are acquired from the ROI without any deformation with five second time intervals; the corresponding 105 pairs of reference images are obtained according to Step (1). Then, 6250 \(O_{i}\) are assigned to the ROI with respect to the spatial interval of seven pixels. For all \(O_{i}\), the \(V_{i}\) values are determined while increasing \(M_{j}\) from 3 to 27 with intervals of 1 through Step (2) and Step (3). Finally, in Step (4), 105 convergence maps are established. Subsequently, the \(A_{i}\) values are determined with respect to 105 \(V_{i}\); they are then assigned at each \(O_{i}\). Figure 9 shows the determination results of \(A_{i}\). \(A_{i}\) varies from the minimum \(15\times 15\) pixels to the maximum \(43\times 43\) pixels depending on \(O_{i}\). Here, 78.4% of \(A_{i}\) has a subset size of between \(21\times 21\) and \(29\times 29\) pixels, as shown in Figure 9a,b, which shows the spatially different and randomly distributed subset sizes within the entire ROI of the test specimen. Figure 10 shows the DIC analysis results with the automatically optimized adaptive subset sizes corresponding to the test images acquired under the uniaxial tensile loading conditions of 0.2 mm, 1.0 mm, 1.4 mm and 1.7 mm. The color bar of Figure 10 shows the minute displacement of the target specimen according to the loading step. Figure 10a shows that only a random displacement distribution can be observed, because a 0.2 mm displacement is too small to be observed by the determined physical subset sizes.