PSI - Issue 68

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Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2025) 000–000 Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2025) 000–000 ScienceDirect

www.elsevier.com/locate/procedia

ScienceDirect

Procedia Structural Integrity 68 (2025) 16–23

European Conference on Fracture 2024 A novel Approach for Determining and Analyzing the Magnitude of the Plastic Zone around a Crack Tip: an Algorithm for an approximate analytical Solution Dragan Pustaić a *, Martina Lovrenić-Jugović b a University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Ivana Lučića 5, 10 000 Zagreb, Croatia b University of Zagreb, Faculty of Metallurgy, Aleja narodnih heroja 3, 44 000 Sisak, Croatia Abstract The straight crack of the length 2 a, in the thin, infinite plate is considered. A thin plate is assumed, in which a plane state of stress is occurred, which means that only the stress components, σ x , σ y and τ xy , [MPa], are different from zero, while all the other components of the stress tensor, σ ij , are equal to zero. Two pairs of the concentrated forces, F , act on the crack surface, they are monotonously increased and open the crack. The forces, F , are acting in-plane and are related to the unit of a plate thickness, [N/m]. The plate is made of a ductile metal material. When loading the plate, the plastic zones are formed around crack tips. It is assumed that the plate material is hardened at the plastic deformation. An isotropic and non-linear strain hardening is assumed, in accordance with Ramberg-Osgood´s hardening law. The investigation of the plastic zone magnitude is in the focus of this article, value is determined according to the premises of a well-known cohesive model (Dugdale´s model). The analytical methods were used in the analysis. The fully exact analytical solution was found while afterwards an assumption about small plastic zone around the crack tip was introduced and the approximate solution was found. The comparison of the exact and approximate analytical solution was in the focus of interest of this article. Also, the assessment of the accuracy of the approximate solution was of interest, for which much simpler mathematical apparatus is necessary. © 2025 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 ECF24 organizers European Conference on Fracture 2024 A novel Approach for Determining and Analyzing the Magnitude of the Plastic Zone around a Crack Tip: an Algorithm for an approximate analytical Solution Dragan Pustaić a *, Martina Lovrenić-Jugović b a University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Ivana Lučića 5, 10 000 Zagreb, Croatia b University of Zagreb, Faculty of Metallurgy, Aleja narodnih heroja 3, 44 000 Sisak, Croatia Abstract The straight crack of the length 2 a, in the thin, infinite plate is considered. A thin plate is assumed, in which a plane state of stress is occurred, which means that only the stress components, σ x , σ y and τ xy , [MPa], are different from zero, while all the other components of the stress tensor, σ ij , are equal to zero. Two pairs of the concentrated forces, F , act on the crack surface, they are monotonously increased and open the crack. The forces, F , are acting in-plane and are related to the unit of a plate thickness, [N/m]. The plate is made of a ductile metal material. When loading the plate, the plastic zones are formed around crack tips. It is assumed that the plate material is hardened at the plastic deformation. An isotropic and non-linear strain hardening is assumed, in accordance with Ramberg-Osgood´s hardening law. The investigation of the plastic zone magnitude is in the focus of this article, value is determined according to the premises of a well-known cohesive model (Dugdale´s model). The analytical methods were used in the analysis. The fully exact analytical solution was found while afterwards an assumption about small plastic zone around the crack tip was introduced and the approximate solution was found. The comparison of the exact and approximate analytical solution was in the focus of interest of this article. Also, the assessment of the accuracy of the approximate solution was of interest, for which much simpler mathematical apparatus is necessary. © 2025 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 ECF24 organizers © 2025 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 ECF24 organizers

* Corresponding author. Tel.: +385 1 48 54 168; fax: +0-000-000-0000 . E-mail address: dragan.pustaic@fsb.hr

2452-3216 © 2025 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 ECF24 organizers 2452-3216 © 2025 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 ECF24 organizers * Corresponding author. Tel.: +385 1 48 54 168; fax: +0-000-000-0000 . E-mail address: dragan.pustaic@fsb.hr

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