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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measure, study and predict their propagation, the deformation field around them and their consequences in the structure life span. A better knowledge of these fields can bring improvements in different fields of engineering, from design to inspection, monitoring, and product maintenance. Beside these, other advantages can accrue from technological evolution such as better evaluation of safety measures and less material waste, which result in economic and environmental gains. In this regard, experimental techniques play a significant role alongside analytical techniques in the field of fatigue and fracture mechanics. The development of experimental techniques to obtain the stress intensity factor (SIF) in real structures is of high interest, as it can constitute the basis for a method to evaluate the structural integrity of cracked components (Farahani, Melo, Tavares, et al. 2020; Farahani et al. 2017; Farahani, Melo, Silva Tavares, et al. 2020). Amongst all optical experimental techniques, electronic speckle pattern interferometry (ESPI) proved to be a suitable way to study the fracture mechanics problems. ESPI is a contactless optical approach utilized for displacement measurements around the crack tip, from interferometric fringe patterns (Tajik, Soltani, and Sedighiani 2011). Moreover, Hack et al. (Hack, Steiger, and Sadouki 1995) carried out a research to monitor the real time crack growth and the plastic zone on the crack tip through a 3D ESPI approach. Thus, the obtained results on crack monitoring were compared to numerical results. Chen et al. (M. Chen et al. 2019) presented a method based on noise reduction technology on ESPI fringe patterns with variable density by constructing a clustering framework. Mathematical development in addition to experimental validation have been accomplished in their work. A combined methodology including ESPI with polarizing phase-shifting techniques was proposed by Gómez-Méndez et al. (Gómez-Méndez et al. 2021) for in-plane displacement measurements. Pisarev et al. (Pisarev et al. 2017) developed a new hybrid experimental technique for determination of both singular and non-singular fracture mechanics parameters, through a modified version of the crack compliance technique, and ESPI data. Moreover, Sousa et al. (Sousa et al. 2019) developed a 3D ESPI system to study the thermal response of printed circuit boards, which measured the displacement distribution caused by said thermal effects. This study focuses on the development of an experimental optical technique based on ESPI, in order to monitor the tip of a crack caused by fatigue loadings. Therefore, the crack length is identified by the ESPI data through discontinuities occurring in the processing of the data, which will be identified as the crack. Then, it is possible to calculate the deformation field from the displacement results through a simple gradient operation, as long as the crack tip singularity is excluded from the calculation to avoid high errors. So, the mode I SIF can be calculated following the experimental data of the measured crack length and deformation field, through an overdeterministic algorithm. 2. Electronic Speckle Pattern Interferometry Methodology Electronic Speckle Pattern Interferometry, or ESPI, is an interferometric method capable of performing full-field 3D displacement measurements, with a high degree of sensitivity and accuracy, usually in the range of the dozens of nanometres (Sirohi 2002). While some ESPI systems are capable of only measuring in-plane displacement along the x - and y -coordinate directions, obtaining the displacement terms of ( , ) and ( , ) , some systems are also capable of measuring out-of-plane displacements, along the z -coordinate direction, obtaining ( , ) term. Not only do the systems differ in the capability of obtaining out-of-plane displacements or not, they can also be classified depending on the type of phase extracting technique in use. Early ESPI systems resorted to temporal phase-shift, while modern systems incorporate spatial phase shift techniques, the former being most effective for static loadings, while the later for dynamic loadings. (Yang et al. 2014). As such, there is a considerable variety of possible ESPI systems, with their physical setup and components differing from one another. While it is possible to approach all the existing variety of systems individually, demonstrating how each one operates, this paper focuses on the available one in INEGI’s (Institute of Science and Innovation in Mechanical and Industrial Engineering) installations. The employed ESPI system is capable of both in-plane and out-of-plane displacement measurements, and resorts to a temporal phase shift technique. As such, a small mention of the theory behind the phase shift technique will be done, and then the components and their disposition will be thoroughly explained. It is well known that two coherent monochromatic waves, extracted from the same original beam and respecting temporal coherence constraints, will interfere when superposed. Subtracting two of these interference patterns, obtained from different loaded states of the object, results in an interferogram with clear fringes. These patterns provide essential information about local deformation of the specimen in question – deformation that can be in-plane