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

878

6

is improved by using an SVD (single value decomposition) approach, resulting in a much faster computational process, and a stable orthogonal basis. For the plane problem of a homogeneous isotropic solid for plane stress, Williams’ series expansion in y-direction was considered, since the opening stress in loading direction is dominant (Williams and Pasadena 1957). = ∑ ( 2 ) 2 −1 {[2 − (−1) − 2 ] ( 2 − 1) + ( 2 − 1) ( 2 − 3) } ∞ =1 (3) = √2 × 1 (4) Table 1 reports the obtained SIF results from ESPI measurements compared to the reference solution proposed by ASTM (ASTM International 2015).

Table 1. Results obtained from ESPI analysis compared to the reference solution.

Deviation |100 × ( − ) ⁄ | 4.73

Result Crack length, ( ) SIF, ( . √ )

Reference

ESPI 28.40 482.6

27.48 495.5

2.60

5. Conclusions In this study, a middle tension (MT) specimen was fatigued and the crack length was measured by a travelling microscope at the end of fatigue cyclic test, being considered the reference value. The mode I stress intensity factor, SIF, was calculated through an equation proposed by the Standard Test Method for Measurement of Fatigue Crack Growth Rates, standing as a reference solution. Furthermore, an experimental methodology was developed based on an optical technique, Electronic Speckle Pattern Interferometry, ESPI, in order to monitor the crack tip. The experimental data was captured while the specimen with the fatigue crack was subjected to a uniaxial tensile load, and then the displacement field was obtained. The deformation field in y -direction, perpendicular to the crack surface, was thereby computed through the differentiation of the displacement field. The mode I SIF was calculated using the ESPI results, with an overdeterministic algorithm. Furthermore, the crack was experimentally identified through the discontinuities detected on the cracked region, and therefore it was feasible to estimate the crack path, while also measuring its length. A comparison was then drawn on the experimental results and the reference solutions. A reasonable agreement was verified, leading to the conclusion that ESPI is an efficient and reliable optical technique in crack tip monitoring. Acknowledgements The authors sincerely acknowledge the funding received from Ministério da Educação e Ciência, Fundação para a Ciência e a Tecnologia (Portugal), under grant PTDC/EME-EME/29339/2017. References ASTM International. 2015. ASTM E647 - 15 Standard Test Method for Measurement of Fatigue Crack Growth Rates . United States: ASTM International. http://www.astm.org/Standards/E647. Bertram, Albrecht, and Rainer Glüge. 2015. Solid Mechanics Theory, Modeling, and Problems . 1st ed. Springer International Publishing. https://doi.org/10.1007/978-3-319-19566-7. Carré, P. 1966. “Installation et Utilisation Du Comparateur Photoélectrique et Interférentiel Du Bureau International Des Poids et Mesures.” Metrologia 2 (1): 13. https://doi.org/10.1088/0026-1394/2/1/005. Chen, Lujie J., Chenggen Quan, and Cho Jui Tay. 20 05. “Simplified Carre Method for Phase Extraction.” In Third International Conference on Experimental Mechanics and Third Conference of the Asian Committee on Experimental Mechanics , 5852:198 – 202. Singapore: International Society for Optics and Photonics. https://doi.org/10.1117/12.621505. Chen, Mingming, Chen Tang, Min Xu, and Zhenkun Lei. 2019. “A Clustering Framework Based on FCM and Texture Features for Denoising ESPI Fringe Patterns with Variable Density.” Optics and Lasers in Engineering 119: 77 – 86. https://doi.org/https://doi.org/10.1016/j.optlaseng.2019.03.015. Farahani, Behzad V., Francisco José Malheiro Queirós Melo, Paulo José Silva Tavares, and Pedro Miguel Guimarães Pires Moreira. 2020. “Stress Intensity Factor Evaluation for Central Oriented Cr acks by Stress Dead‐zone Concept.” Material Design & Processing Communications , January, mdp2.139. https://doi.org/10.1002/mdp2.139.