PSI - Issue 43

Available online at www.sciencedirect.com Structural Int grity Procedia 00 (2022) 000 – 000 Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2022) 000 – 000 Available online at www.sciencedirect.com ScienceDirect

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Procedia Structural Integrity 43 (2023) 252–257

© 2023 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 the responsibility of MSMF10 organizers. Abstract The answer of the thin, infinite, central cracked plate, subjected to in-plane loading, is investigated. The plate is made from a ductile metallic material. The two pairs of the concentrate forces, F, act on the crack surface in the direction perpendicular to it. The other edges of the plate, at infinity, are free of loading. The forces, F, open the crack and they are monotonously increased. The small plastic zones around crack tips will appear. It is assumed an isotropic and non-linear strain hardening of a plate material which can be good described by the Ramberg-Osgood ´s equation. The investigations were carried out for the several different values of the strain hardening exponent n which is changed among the discrete values n = 2, 3, 4, 5, 7, 10, 15, 25, 50 and 1000. One well-known cohesive model (Dugdale´s model) was applied in the crack tip plasticity investigating. It was assumed that the cohesive stresses within the plastic zone are changed according to non-linear law. Also, a new algorithm was established which enables direct calculation of plastic zone magnitude depending on the magnitude of external loads. The contemporary mathematical tools, like the software package Wolfram Mathematica, were used. The solutions are presented through the special, Gamma and the Hypergeometric functions. © 20 23 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under the responsibility of MSMF10 organizers. Keywords: Elastic plastic fracture mechanics; cohesive stress; isotropic and non-linear strain hardening material; Ramberg- Osgood´s equation; strain hardening exponent; stress intensity coefficient; plastic zone magnitude around crack tip; analytical methods; Green functions method, Wolfram Mathematica. 10th International Conference on Materials Structure and Micromechanics of Fracture Cohesive Model Application in the Assessment of Plastic Zone Magnitude for One Particular Case of Crack Loading Dragan Pustaić a, * , Martina Lovrenić - Jugović b a Univer ity of Zagreb, Faculty of Mech ical Engineering and Naval A chitecture, Institute of Applied Mechanics, Ivana L čića 5, 10 000 Zagreb, Croatia b University of Zagreb, Faculty of M tallurgy, Department of Mechanical Metallurgy, Aleja narodnih heroja 3, 44 000 Sisak, Croatia Abstract The answer of the thin, infinite, cen ral ra ked plate, subjected o i -plane loading, is vestigated. The plate is m de from a ductile metallic materi l. The two pairs of th concentrate forces, F, act on the crack surf ce in the direction perpendicular to it. other edges of th plate, at infinity, are free of loading. The force , F, open the crack and they are monotonously increased. T e sm ll plastic zones around crack tips will appear. It is assumed an isotrop c nd non-line strain hardening of a plate material which can be good described by the Ramberg-Osgood ´s equation. The inv stigatio s were carried out for the several different values of the strain hardening exponent n which is changed among the discrete values n = 2, 3, 4, 5, 7, 10, 15, 25, 50 and 1000. On well-known cohesive model (Dugdale´s model) w s applied in the crack tip plasticity inv stigating. It was assumed that the ohesive tresses within the plastic zone are cha ge according to on-linear law. Also, a ew algorit m was established which enables direct calculation of plastic zone m gnitude depending on the magnitude of external loads. The contemporary mathematical tools, lik the softwar package Wolfram Mathematica, were used. The solutions are presented through the special, Gamma and the Hypergeometric functions. © 20 23 The Authors. Published by Elsevier B.V. This is an ope access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under the responsibility of MSMF10 organizers. Keywords: Elastic lastic fracture m chani s; cohesive stress; isotropic and non-linear strain harde ing material; Ramberg- Osgood´s equati n; strain hardening exponent; stress intensity coefficient; plastic zone magnitude around crack tip; analytical methods; Green functions method, Wolfram Mathematica. 10th International Conference on Materials Structure and Micromechanics of Fracture Cohesive Model Application in the Assessment of Plastic Zone Magnitude for One Particular Case of Crack Loading Dragan Pustaić a, * , Martina Lovrenić - Jugović b a University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Institute of Applied Mechanics, Ivana Lučića 5, 10 000 Zagreb, Croatia b University of Zagreb, Faculty of Metallurgy, Department of Mechanical Metallurgy, Aleja narodnih heroja 3, 44 000 Sisak, Croatia

* Corresponding author. Tel.: +0-385-1-6168-108; fax: +0-385-1-6168-187. E-mail address: dragan.pustaic@fsb.hr * Correspon ing author. Tel.: +0-385-1-6168-108; fax: +0-385-1-6168-187. E-mail address: dragan.pustaic@fsb.hr

2452-3216 © 2023 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 the responsibility of MSMF10 organizers. 2452-3216 © 2023 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 the responsibility of MSMF10 organizers.

2452-3216 © 2023 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 the responsibility of MSMF10 organizers. 10.1016/j.prostr.2022.12.267