PSI - Issue 37

Behzad V. Farahani et al. / Procedia Structural Integrity 37 (2022) 873–879 Behzad V. Farahani et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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Shifting technique (see Figure 2-a). The specimen is then loaded, and the second set of images is captured. The number of captured images per set has been defined as four, so, in total, eight images are obtained. During the acquisition, the software calculates a live difference image, subtracting the current loaded state image to a reference state one, obtaining interferometric fringes (see Figure 2-b). Afterwards, the first step is transforming the set of images into a phase map, which is realized resorting to the Carré method (Carré 1966), selected due to the fact that it does not require a particular value of the phase jump between images to calculate the phase map, as long as the value is constant. With the phase map calculated, as shown in Figure 2-c), a filtering operation is the crucial second step. There is a wide variety of filtering algorithms available; in this case, a Windowed Fourier Transform was selected, proposed by Kemao (Kemao 2007). After this set of operations, a filtered phase map is obtained, Figure 2-d), and an unwrapping operation has to be done. Unwrapping is required because phase is a quantity that spans 2p whereas the measured phase difference is much larger. For the unwrapping, a quality-guided unwrapping algorithm was selected, which was also proposed by Kemao (Wang, Kemao, and Gao 2008). It is well known that the unwrapping process is extremely sensitive to discontinuities, which must be excluded. In the present specimen, there exist two potential discontinuities, the initial notch, characteristic of the Middle Tension specimens, and the generated fatigue crack. As such, it is necessary to remove these discontinuities before the unwrapping process is realized, and a mask was drawn for this purpose. The unwrapping process also enabled the possibility of measuring the crack length, by manipulating the sensitivity to discontinuities. Exclusively removing the initial notch, allowing the process to malfunction when it met the fatigue crack, while manipulating the path in which the unwrapping process was realized, allowed to quantify the crack length, which was used in the SIF calculation.

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Figure 2. ESPI processing stages: a) reference image, b) live interferometric fringes, c) phase map and d) filtered phase map.

The outcome of the unwrapping process is the displacement field, expressed in radians. As the information is more useful in length units, a simple equation allowed the transformation (L. J. Chen, Quan, and Tay 2005): = 4 Δ s in ∙ ( ) (1) In which ∆ is the unwrapped phase map, in ( ), is the laser’s wavelength, measured as = 532 ( ) , and is the incident angle of the laser, calculated as = 25 (°). At this point, the displacement field has been calculated; see Figure 3-a). The last step is converting the displacement field into a deformation field. This transformation is feasible by a simple gradient operation according to the solid mechanics formulations (Bertram and Glüge 2015). The strain field in y -direction has been obtained as shown in Figure 3-b). Regarding the crack length measurement by ESPI, the mask drawing process is quite sensitive, as enlarging the area that must be deleted would lead to losing some important information around the crack. Therefore, it is possible to obtain an estimation of the crack’s position on the specimen by manipulating the unwrapping process, as Figure 4 clarifies. This methodology contributes to the reduction of the eliminated area, allowing the conservation of data around the crack and enabling the crack length measurement, essential for the SIF calculations. Therefore, the