PSI - Issue 40

O.N. Belova et al. / Procedia Structural Integrity 40 (2022) 46–60 O.N. Belova, L.V. Stepanova / Structural Integrity Procedia 00 (2022) 000 – 000 O.N. Belova, L.V. Stepanova / Structural Integrity Procedia 00 (2022) 000 – 000

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and higher-order coefficients estimated using the proposed method are compared with finite element analysis (FEA) results, and are found to be in good agreement. © 202 1 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 the 15th International Conference Mechanics, Resource and Diagnostics of materials and structures 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, finite element analysis . 1. Introduction Experimental and computational determination of the stress-strain field in the immediate vicinity of the crack tip in isotropic linear elastic materials has been an area of wide study for many decades and the problem continues to actual and vital nowadays (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 stress distribution in the immediate neighbourhood of a crack tip is obtained experimentally using interference optical methods such as caustic, holography, moire, photoelasticity, speckle interferometry or digital image correlation method. The main goal of this study is to determine the stress field in the vicinity of the crack tip in the plate with two inclined interacting cracks in an isotropic linear elastic material experimentally by the digital photoelasticity method and computationally based on the multi-parameter Williams series expansion considering 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 as in digital image processing procedures and in the technique of the multi-point over-deterministic method are still open. 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 map and isoclinic phase map 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 technique of photoelasticity is being developed in many ways. The most important direction is automation of experimental data collection in interference-optical methods of mechanics (Ramesh and Sasikumar (2020)). Automation is necessary for rapid processing of experimental information. Thus, the vital step in the digital and higher-order coefficients estimated using the proposed method are compared with finite element analysis (FEA) results, and re found to be in good agreement. © 202 1 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 the 15th International Conference Mechanics, Resource and Diagnostics of materials and structures Keywords: Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, optomechanics, digital phototelasticity, digital image processing, isochromatic fringe pa tern, is clinic p se map, fringe analysis, multi-parameter stress field approximat on, finite lement analysis . 1. Introduction Experimental and computational determination of the stress-strain field in the immediate vicinity of the crack tip in isotropic linear elastic materials has been n area of wid tudy for many decades and the problem continues to actual and vital nowadays (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 St p nova ( 20), Patil et al. (2017), Tabanyukhova (2020), Stepano a (2020), Ayatoll hi et al (2011), Stepanova and Dolgikh (2018)). The stress distribution in the immediate eighbourhood of a crack tip is obtained experime tally using interference optical methods such as caustic, holo raphy, moire, photoelasticity, speckle interferometry or digital image correlation method. T e main goal of this stud is t determine the stress field in the vicinity of the crack tip in th plat with two inclined interacting cracks in an isotropic linear ela tic material experimentally by the digital hotoelasticity method and computation lly based on the multi-parameter Williams series expa sion consid rin the higher-order ter s. The use f the multi-param tric representation of the stress, strain and displacement field is not just for academic curiosity but an urgent need in many cas s of engineering interest ((Jobin et al. (2020), Yang et al. (2021), Viv kanandan and Ramesh (2019), Dolgikh and Stepanova (2020), Patil et al. (2017), Tabanyukhova 0 , Stepanov (2020), Ay tolla i 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 differ nt crack d specimens by different authors (Jobin et al (2020), Patil et al (2017), Malikova and Vesely (2014)). Nowadays the multi-point over-det rministic technique for evaluating the multi-parameter stress field is used (Yang et al (2021)). The over-deterministic approach can b based on the experimental evaluation of th stress or displac ment fields, for instance, on the interference-optical methods of measure ents (Dolgikh a d Stepanova (2020)), or on the finite element analysis (Li and Zheng (2021)). However, any questions as in digital image processing procedures and in th t chnique of the multi-point over-deterministic method are still open. Thus, th aim of the contrib tion is to obtain the stress fields near the crack tip based on the stress data obtained experimentally via opti al measurements and to compare the stress field approximati s with the stress fi l derived from finite ele ent analysis. Experimental data such a isochromatic ph se map and isoclinic phase map obtained rom the photoelasticity observation are taken as inputs. It should be noted that digital photoelasticity is an exp rimental technique used b many engineering application to evaluate the stress fields in bodies under mechanical loads (Ramesh (2000), R mesh et al. (1997)). The photoelasticity method is curr ntly undergoing a Renaissa ce (Rame h (2021), Su et al. (2021), Liu et al. (2020)). After being developed and then largely abandon d in 2000-2010, t e photoelasticity method is now in active use and can be consider as a viable technique for d termining stress fields in a structural component. Interest in using the digital photoelasticity is now b ing fueled by possibility of digital processing of the entire s t of exp rimental information. Owing to the increase i computing re ources the digital photoelasticity technique is now one of the powerful tools for investigating the stress field in solid . The advent of computers coupled with developments in digital image proces in has had a great influence in developments of od rn photo lasticity (Su et al (2021), Ramesh and Sasikumar (2020)). Therefore, o e can co clude that the digital ptics revolution in recent years enhanced and empowered innovation in all areas of modern life (Ramesh (2020), Ramesh (2021), Ramesh (2015)) and, particularly, hotoelasticity is a well-dev loped method or reliable measurement of stress and strain distributio s in engineering practice. The technique of photoelasticity is bei developed in many ways. The most important direction is automation of experim ntal data collection in interferenc -optical methods of mechanics (Ramesh and Sasikumar (2020)). Automation is necessary f r rapid proc ssing of experimental information. Thus, the vital step in the digital © 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 the scientific committee of the15th International Conference on Mechanics, Resources and Diagnostics of Materials and Structures.