# Adaptive Subset-Based Digital Image Correlation for Fatigue Crack Evaluation
###### Abstract  
This paper proposes a fatigue crack evaluation technique based on digital image correlation (DIC) with statistically optimized adaptive subsets. In conventional DIC analysis, a uniform subset size is typically utilized throughout the entire region of interest (ROI), which is determined by experts' subjective judgement. The basic assumption of the conventional DIC analysis is that speckle patterns are uniformly distributed within the ROI of a target image. However, the speckle patterns on the ROI are often spatially biased, augmenting spatially different DIC errors. Thus, a subset size optimization with spatially different sizes, called adaptive subset sizes, is needed to improve the DIC accuracy. In this paper, the adaptive subset size optimization algorithm is newly proposed and experimentally validated using an aluminum plate with sprayed speckle patterns which are not spatially uniform. The validation test results show that the proposed algorithm accurately estimates the horizontal displacements of 200 \(\upmu\)m, 500 \(\upmu\)m and 1 mm without any DIC error within the ROI. On the other hand, the conventional subset size determination algorithm, which employs a uniform subset size, produces the maximum error of 33% in the designed specimen. In addition, a real fatigue crack-opening phenomenon, which is a local deformation within the ROI, is evaluated using the proposed algorithm. The fatigue crack-opening phenomenon as well as the corresponding displacement distribution nearby the fatigue crack tip are effectively visualized under the uniaxial tensile conditions of 0.2, 1.0, 1.4 and 1.7 mm, while the conventional algorithm shows local DIC errors, especially at crack opening areas. f 22 April 202018 May 202021 May 2020222 April 2020218 May 2020222 April 2020218 May 202022022 April 2020218 May 2020222 April 2020218 May 20  
typically able to achieve the higher DIC accuracy by increasing the spatial resolution. On the other hand, an excessively small subset size often inversely increases the DIC errors, because they may not contain enough distinctive speckle pattern features within each subset for a proper DIC analysis. Although commercial DIC software--such as StrainMaster from LaVision [35], GOM Correlate from GOM [36] and VIC-2D from Correlated Solution [37]--have been used, they commonly select the subset size depending on users' subjective judgement without a speckle pattern analysis. To determine the optimal subset size, a number of subset size determination algorithms have been proposed. [PERSON] and [PERSON] suggested a subset entropy, calculating the sum of the absolute difference of eight neighboring points for the selection of a single subset size [30]. [PERSON] et al. proposed a sum of the square of the subset intensity gradient (SSSIG), which evaluates the local speckle pattern intensity using a threshold value of standard deviation (SD) error within the subset for selecting a single subset size throughout the entire region of interest (ROI) [31]. Additionally, [PERSON] et al. proposed a grey-level co-occurrence matrix (GLCM) to determine a single subset size using a critical GLCM offset concept [32]. Although the aforementioned algorithms can properly determine a single optimal subset size within the entire ROI, the following technical hurdles still remain to be overcome. First, the conventional algorithms evaluate the speckle patterns at a certain local area in the target image and determine a single subset size under the assumption of uniformly distributed speckle patterns within the entire ROI. If the speckle patterns are spatially biased, it may augment spatially different DIC errors. Furthermore, the conventional algorithms highly depend on the experts' subjective judgement or experience to determine an optimal threshold value for the subset size determination. Although dynamic subset selection algorithms to adopt various subset sizes in the ROI were recently proposed [33; 34], they are not fully validated in spatially biased speckle patterns yet.