PSI - Issue 23

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Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2019) 000 – 000 Structural Integrity Procedia 00 (2019) 000 – 000

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Procedia Structural Integrity 23 (2019) 27–32

© 2019 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 responsibility of the scientific committee of the ICMSMF organizers © 201 9 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 responsibility of the scientific committee of the IC MSMF organizers. Keywords: Elastic plastic fracture mechanics; cohesive stress; isotropic and non-linear strain hardening material; strain hardening exponent; plastic zone magnitude around crack tip. The thin infinite central c acked plat , made of ductile met lli mat ri l, is observed. The p ate is loaded with uniformly distr bute c tinuous lo ding, according to the Fig. 1a. The small plastic zon s a ound crack tips will appear. It is assumed an isotropic a d non-linear strain hardening of a plate material whic can be goo described by the Ramberg-Osgood equation. The i vestigations were carried out for the several discre values of the strain hardening exponent n , i.e. for n = 3, 5, 7, 10, 25, 50 nd 1000. The magn tude f plastic z ne is investigated on the basis of t e premises of t e Dugdale´s cohesive mod l. I the frame of applied coh sive model, the problem is formulated fully xact. The analytical methods wer applied. Our intention is to c ntribute in a mor a curate mathematical descripti n of the phen mena occurring within the cohesive zones and to solve he roblems, in so call d closed-form, with ut any additional assumptions, s for example, about small plastic zones (SSY), elas ic-perfectly lastic material and so on. The commercial software Wolfram Mathematica 7.0 is used and the solutions are presented through the special, the Gamma and the Hypergeometric functions . © 201 9 The Authors. Published by Elsevier B.V. This is an ope acces article under CC BY-NC-ND lic nse (http://creativecommon org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the IC MSMF organizers. Keywords: Elastic plastic fracture mechanics; cohesive stress; isotropic and non-linear strain hardening material; strain hardening exponent; plastic zone magnitude around crack tip. 9th International Conference on Materials Structure and Micromechanics of Fracture More accurate mathematical description in the assessment of plastic zone magnitude around the crack tip 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 The thin infinite central cracked plate, made of ductile metallic material, is observed. The plate is loaded with uniformly distributed continuous loading, according to the Fig. 1a. 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 equation. The investigations were carried out for the several discrete values of the strain hardening exponent n , i.e. for n = 3, 5, 7, 10, 25, 50 and 1000. The magnitude of plastic zone is investigated on the basis of the premises of the Dugdale´s cohesive model. I n the frame of applied cohesive model, the problem is formulated fully exact. The analytical methods were applied. Our intention is to contribute in a more accurate mathematical description of the phenomena occurring within the cohesive zones and to solve the problems, in so called closed-form, without any additional assumptions, as for example, about small plastic zones (SSY), elastic-perfectly plastic material and so on. The commercial software Wolfram Mathematica 7.0 is used and the solutions are presented through the special, the Gamma and the Hypergeometric functions . 9th International Conference on Materials Structure and Micromechanics of Fracture More accurate mathematical description in the assessment of plastic zone magnitude around the crack tip 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 Lučić 5, 10 000 Zagreb, Croati b University of Zagreb, Faculty of M tallurgy, Department of Mechanical Metallurgy, Aleja narodnih heroja 3, 44 000 Sisak, Croatia Abstract Abstract

* 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 © 2019 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 responsibility of the scientific committee of the IC MSMF organizers. 2452-3216 © 2019 The Authors. Published by Elsevier B.V. This is an ope acces article under CC BY-NC-ND lic nse (http://creativecommon org/licenses/by-nc-nd/4.0/)

Peer-review under responsibility of the scientific committee of the IC MSMF organizers.

2452-3216 © 2019 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 responsibility of the scientific committee of the ICMSMF organizers 10.1016/j.prostr.2020.01.058