PSI - Issue 66

Hendrik Baarssen et al. / Procedia Structural Integrity 66 (2024) 305–312 Author name / Structural Integrity Procedia 00 (2025) 000–000

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The position of the crack tip is required to be known to determine the FCGR. For non-standardized tests, the determination of the crack tip position is often done manually (Feld-Payet et al., 2020), by determining the J-integral of the crack (Subramanyam Reddy et al., 2018), using neural networks (Strohmann et al., 2022) and approximation methods (Feld-Payet et al., 2020). Panwitt et al. (2022) implemented a methodology to detect the crack growth, the location of the crack tip, and crack branching in steel. The FCGR is calculated based on the crack width method, based on crack kinematics, and the principal strain method, which assumes a crack when a threshold strain value is exceeded. Both methods depend on the threshold values which are unknown and require calibration using direct current potential drop. The required calibration of the threshold values using a potential drop system can be a major obstacle to using the DIC for fatigue crack growth detection. The properties of the threshold values are unknown and are material and setup-dependent since this is also dependent on the noise level. If this is the case, the threshold values are required to be determined for every experimental investigation and conditional to the use of a potential drop system. Additionally, the strain field is sensitive to noise which can lead to false positives. Melching et al. (2024) introduced the line interception method to estimate the crack tip location. However, this method is not stable without the presence of a crack. An attempt to overcome the above limitations is proposed in this study. A novel post-processing methodology for DIC measurements to determine the fatigue crack growth rate, which does not depend on material properties nor requires calibration using secondary measurement systems is presented. The methodology is verified experimentally on a steel C(T)-specimen. The results are compared to the CMOD compliance, showing good agreement between the two methods. 2. Methodology The displacement field measured by DIC at a specific number of load cycles is exported in a point cloud and transformed into an n×m matrix A ij , where n and m are respectively the number of cells in the x- and y-direction, to reduce the computational complexity. In standard specimens, which are the object of this study, the surface where the measurements are made is planar and the crack is expected to grow in one specific direction, corresponding to one of the indices of the matrix. We assume that the crack grows in the direction identified by the index i . Hence, the crack is detected by post-processing the results in A ij along j . Further, it should be noted that the results obtained on planar surfaces on which the reference camera of the DIC system is not aligned with the direction of crack growth shall be roto-translated in such a way that the planar surface under investigation is oriented correctly. The procedure is as follows. 1. At a certain number of applied cycles the results of the DIC are extracted, A ij ; 2. The displacement results along the directions perpendicular to the direction of the crack growth A j are considered; 3. For each A j , the Chow test is conducted to identify a discontinuity in the displacement field; 4. The number of A j for which a discontinuity is detected corresponds to the crack length; 5. The results are stored and the results computed on the next image are loaded. For convenience, the images are taken with a static load equal to the maximum fatigue load applied to the specimen, in order to reduce image noise and improve image quality and consistency in terms of applied load. 2.1. Crack detection using the Chow test Chow (1960) introduced a test of equality between sets of coefficients of two linear regressions, which now is known as the Chow test. This method is used to determine if there is a discontinuity in a dataset. First, the dataset is split into two subsets and the linear regressions of these subsets are determined. Hence, given a result vector A j , this is partitioned in two subsets A i=1..k,j and A i=k+1..n.j for k=3...n-3 on which the Chow test is conducted. Then the test of equality is performed between the linear regressions of the subsets using Equation 1: = − ( 1 + 2 )/ ( 1 + 2 ) 1 + 2 − 2 < (1)