PSI - Issue 39

ScienceDirect Structural Integrity Procedia 00 (2021) 000–000 Structural Integrity Procedia 00 (2021) 000–000 Available online at www.sciencedirect.com Available online at www.sciencedirect.com ScienceD rect Available online at www.sciencedirect.com ScienceDirect

www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia

Procedia Structural Integrity 39 (2022) 761–769

© 2021 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 CP 2021 – Guest Editors Abstract The study is aimed at experimental and numeric determination of the higher order coefficients of the Williams power expansion for the near crack-tip fields in isotropic linear elastic materials by two approaches. The first one is based on the experimental method of holographic interferometry, the second one is relied on the finite element analysis. The main problem and difficulty are accurate extracting the coefficients from the whole set of experimental data. To obtain the higher order coefficients of the Williams expansion the program tool which is designed for digital image processing of the experimental fringe patterns. As the first step the plate with the horizontal central crack has been chosen since this cracked geometry is thoroughly studied and the coefficients of the higher order terms are known. The stress intensity factors, T-stress and higher order coefficients are extracted and compared with the theoretical values. Then the mixed mode loading is considered. Using holographic interferometry a lot of tests with the inclined cracks were performed. It is shown that the digital holographic method and the developed programming tool allow us to find the coefficients with high accuracy. The results of digital image processing of the experimental data have been verified and confirmed by the finite element analysis. © 2021 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 CP 2021 – Guest Editors 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. 7th International Conference on Crack Paths Holographic interferometry experiments and numerical analyses of the stress field on the Williams series expansion: higher – order terms O.N. Belova a , L.V. Stepanova a * a Department of Mathematical Modelling in Mechanics, Samara National Research University, Moskovskoye shosse, 34, 443086, Samara, Russia Abstract The study is aimed at experimental and numeric determination of the higher order coefficients of the Williams power expansion for the near crack-tip fields in isotropic linea elas ic aterials by two appr aches. The first ne is based on the xperimental method of holographic nterferome y, the second one is relied on the finite element analysis. The main problem and difficulty are accurate extracting t e coefficients from the whole set of exp rimental data. To obtain the h gher order coefficients of the Williams expansion the pro ram t ol which is designed f r digital image processing of the experimental fring patterns. As the first step the plate with horizontal central crack has been chosen since this racked geometry is thoroughly studied and the coefficients of the higher order terms re k own. The stress i tensity factors, T-st ess and high order coefficients ar extracted and compared with the theor tical values. The the mix d mode loading is con id red. Usin hol graphic interferom try a lot of tests with the inclined cracks were performed. It is shown that the digital hol graphic method and the developed programming tool allow us to find the oefficients with high accuracy. The results of digital image proc ssing of the experimental dat have been verified and confirmed by th finite element analysis. © 2021 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 u der re ponsibility of CP 2021 – Guest Editors Keywords: Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm; optomechanics, digital phototelasticity; digital image processing; isochromatic fringe pattern, isoclinic p ase map, fringe analysis; multi-parameter stress field approximation; higher-order terms; finite element analysis; numerical simulation. 7th International Conference on Crack Paths Holographic interferometry experiments and numerical analyses of the stress field on the Williams series expansion: higher – order terms O.N. Belova a , L.V. Stepanova a * a Department of Mathematical Modelling in Mechanics, Samara National Research University, Moskovskoye shosse, 34, 443086, Samara, Russia

* Corresponding author. Tel.: +7 9277522102; fax:+7 8462674370. E-mail address: Stepanova.lv@ssau.ru * Corresponding author. Tel.: +7 9277522102; fax:+7 8462674370. E-mail address: Stepanova.lv@ssau.ru

2452-3216 © 2021 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 CP 2021 – Guest Editors 2452-3216 © 2021 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 CP 2021 – Guest Editors

2452-3216 © 2021 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 CP 2021 – Guest Editors 10.1016/j.prostr.2022.03.150