PSI - Issue 74

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

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Procedia Structural Integrity 74 (2025) 70–76

Eleventh International Conference on Materials Structure and Micromechanics of Fracture Assessment of the plastic zone magnitude around the crack tip with uniformly distributed, continuous load acting over the crack surface Eleventh International Conference on Materials Structure and Micromechanics of Fracture Assessment of the plastic zone magnitude around the crack tip with uniformly distributed, continuous load acting over the crack surface

Dragan Pustaić a , Martina Lovrenić - Jugović a,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 Dragan Pustaić a , Martina Lovrenić - Jugović a,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

© 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 the responsibility of Libor Pantělejev © 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 the responsibility of Libor Pant ě lejev Keywords: Dugdale´s cohesive model; straight crack in the plate; uniformly distributed, continuous loading over the crack surface; isotropic and non-linear hardening of a plate material; strain hardening exponent; stress intensity factor; plastic zone magnitude around a crack tip; exact analytical solution. Abstract The thin, infinite plate contains a discontinuity in form of straight crack of the length, 2 a . The uniformly distributed, continuous loading, p 0 , acts across the crack surface and is successively and gradually increasing. The loading, p 0 , acts in-plane of the plate (same as the crack) and opens the crack. The plane state of stress, ( σ x , σ y , τ xy ), is assumed in the plate. The plate is made of homogeneous and ductile metallic material which is, at the plastic deformation, isotropic and non-linear hardened in accordance with the Ramberg-Osgood´s hardening law. At the crack loading, the small plastic zones around its tips are formed, which are spread with increasing of the load, p 0 . The goal of this article was to investigate the correlation between the increase of loading, p 0 , and the increase of the plastic zone magnitude, r p . The problem was solved fully exactly in analytical way. In order to solve the problem the cohesive Dugdale´s model was used. The original expressions for the stress intensity factors (SIFs) from the external loads, K ext , and from the cohesive stresses, K coh , were derived. The solutions are given through the special Gamma, the Hypergeometric and the inverse trigonometric functions . All numerical computations and diagrams were done by using the mathematical software Wolfram Mathematica. © 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 the responsibility of Libor Pant ě lejev Keywords: Dugdale´s cohesive model; straight crack in the plate; uniformly distributed, continuous loading over the crack surface; isotropic and non-linear hardening of a plate material; strain hardening exponent; stress intensity factor; plastic zone magnitude around a crack tip; exact analytical solution. Abstract The thin, infinite plate contains a discontinuity in form of straight crack of the length, 2 a . The uniformly distributed, continuous loading, p 0 , acts across the crack surface and is successively and gradually increasing. The loading, p 0 , acts in-plane of the plate (same as the crack) and opens the crack. The plane state of stress, ( σ x , σ y , τ xy ), is assumed in the plate. The plate is made of homogeneous and ductile metallic material which is, at the plastic deformation, isotropic and non-linear hardened in accordance with the Ramberg-Osgood´s hardening law. At the crack loading, the small plastic zones around its tips are formed, which are spread with increasing of the load, p 0 . The goal of this article was to investigate the correlation between the increase of loading, p 0 , and the increase of the plastic zone magnitude, r p . The problem was solved fully exactly in analytical way. In order to solve the problem the cohesive Dugdale´s model was used. The original expressions for the stress intensity factors (SIFs) from the external loads, K ext , and from the cohesive stresses, K coh , were derived. The solutions are given through the special Gamma, the Hypergeometric and the inverse trigonometric functions . All numerical computations and diagrams were done by using the mathematical software Wolfram Mathematica.

* Corresponding author. Tel.: +0-385-1-48-54-168; fax: +0-000-000-0000 . E-mail address: dragan.pustaic@fsb.unizg.hr * Corresponding author. Tel.: +0-385-1-48-54-168; fax: +0-000-000-0000 . E-mail address: dragan.pustaic@fsb.unizg.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 the responsibility of Libor Pant ě lejev 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 the responsibility of Libor Pant ě lejev

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 the responsibility of Libor Pantělejev 10.1016/j.prostr.2025.10.036