PSI - Issue 37

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Author name / Structural Integrity Procedia 00 (2021) 000 – 000

O.N. Belova et al. / Procedia Structural Integrity 37 (2022) 888–899 © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of committee of Pedro Miguel Guimaraes Pires Moreira Keywords: Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm; optomechanics, digital phototelasticity; digital image processing; isochromatic fringe pattern, isoclinic phase map, fringe analysis; multi-parameter stress field approximation; higher-order terms; finite element analysis; numerical simulation. 1. Introduction Stress intensity factors and coefficients of higher-order terms of the Williams series expansion are the characteristic parameters of linear elastic fracture mechanics. In spite of comprehensive theoretical analysis, numerical simulations and laboratory experiments accurate measurement and characterisation of deformations even in elastic regime are still complicated problems. Experimental and numerical determinations of the stress-strain field in the immediate vicinity of the crack tip in isotropic linear elastic materials have been an area of wide study for many decades and the problem continues to actual and vital nowadays (Hou et al. (2021), Qiu et al. (2021), Stepanova and Dolgikh (2021), Mirzaei et al. (2020), Ramesh and Sasikumar (2020), Jobin et al. (2020), Vivekanandan and Ramesh (2019), Dolgikh and Stepanova (2020), Patil et al. (2017), Tabanyukhova (2020), Stepanova (2020), Ayatollahi et al (2011), Stepanova and Dolgikh (2018)). The near crack-tip field distributions in the immediate neighbourhood of a crack tip can be obtained experimentally by means of optical measurements using interference-optical methods such as caustic, digital holography, moire, digital photoelasticity, speckle interferometry or digital image correlation method. The main objective of this study is to determine the stress field in the vicinity of the crack tip in the plate with two interacting cracks in an isotropic linear elastic material experimentally by the digital photoelasticity method and computationally by finite element analysis based on the multi-parameter Williams series expansion keeping the higher-order terms. The use of the multi-parametric representation of the stress, strain and displacement field is not just for academic curiosity but an urgent need in many cases of engineering interest ((Jobin et al. (2020), Yang et al. (2021), Vivekanandan and Ramesh (2019), Dolgikh and Stepanova (2020), Patil et al. (2017), Tabanyukhova (2020), Stepanova (2020), Ayatollahi et al. (2011), Stepanova et al. (2017)). The effects and importance of higher-order terms in the Williams series expansion of the crack-tip fields were thoroughly analysed for different cracked specimens by different authors (Jobin et al (2020), Patil et al (2017), Malikova and Vesely (2014)). Nowadays the multi-point over deterministic technique for evaluating the multi-parameter stress field is used (Yang et al (2021)). The over deterministic approach can be based on the experimental evaluation of the stress or displacement fields, for instance, on the interference-optical methods of measurements (Dolgikh and Stepanova (2020)), or on the finite element analysis (Li and Zheng (2021)). However, many questions both in digital image processing procedures and in the technique of the multi-point over-deterministic method are still unanswered. Thus, the aim of the contribution is to obtain the stress fields near the crack tip based on the stress data obtained experimentally via optical measurements and to compare the stress field approximations with the stress field derived from finite element analysis. Experimental data such as isochromatic phase maps and isoclinic phase maps obtained from the photoelasticity observation are taken as inputs. It should be noted that digital photoelasticity is an experimental technique used by many engineering applications to evaluate the stress fields in bodies under mechanical loads (Ramesh (2000), Ramesh et al. (1997)). The photoelasticity method is currently undergoing a Renaissance (Ramesh (2021), Su et al. (2021), Liu et al. (2020)). After being developed and then largely abandoned in 2000-2010, the photoelasticity method is now in active use and can be considered as a viable technique for determining stress fields in a structural component. Interest in using the digital photoelasticity is now being fueled by possibility of digital processing of the entire set of experimental information. Owing to the increase in computing resources the digital photoelasticity technique is now one of the powerful tools for investigating the stress field in solids. The advent of computers coupled with developments in digital image processing has had a great influence in developments of modern photoelasticity (Su et al (2021), Ramesh and Sasikumar (2020)). Therefore, one can conclude that the digital optics revolution in recent years enhanced and empowered innovation in all areas of modern life (Ramesh (2020), Ramesh (2021), Ramesh (2015)) and, particularly, photoelasticity is a well-developed method for reliable measurement of stress and strain distributions in engineering practice. The photoelasticity method which is the classical experimental method in solid mechanics is being developed in many ways. One of the most important direction is automation of experimental data collection in interference-optical 889