PSI - Issue 26

Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2019) 000 – 000 Available online at www.sciencedirect.com ScienceDirect il l li i i

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ScienceDirect

Procedia Structural Integrity 26 (2020) 53–62

The 1 st Mediterranean Conference on Fracture and Structural Integrity, MedFract1 Edge-cracked beams under four-point bending: Approximate analytic solutions for stresses and displacements h 1 t

Christos F. Markides, Ermioni D. Pasiou, Stavros K. Kourkoulis* National Technical University of Athens, Department of Mechanics, Laboratory for Testing and Materials, Theocaris Building, Zografou Campus, 157 73, Athens, Greece , , , , , , ,

Abstract

© 2020 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 MedFract1 organizers An approximate analytic solution for the stress- and displacement-field developed in a notched prismatic beam under four-point bending test is presented. The solution is obtained a dopting Muskhelishvili’s complex potentials technique . As a first step, the complex potentials are obtained and then the stresses and displacements are calculated all over central part of the beam. As an example, the solution is applied for a PMMA beam. Then, the analytical results for the strains are qualitatively compared against experimental data for a notched marble beam, obtained from literature. The comparison is quite satisfactory. The limitations of the analysis are discussed and means to overcome them are finally proposed. © 2020 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 MedFract1 organizers Keywords: Four-point bending; notched beams; complex potentials; stress field; displacement field 2 T This is an ope ccess

1. Introduction

Bending tests, either in the form of three- or four-point bending, are quite often used in laboratory protocols due to their relatively easy experimental implementation as well as due to the simple analytic formulae describing approximately the stress and displacement fields. However, the exact distribution of stresses and displacements in a prismatic beam subjected to the action of concentrated loads is an extremely difficult problem and closed-form solutions do not as yet

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* Corresponding author. Tel.: +30 210772 1263; fax: +30210772 1302. E-mail address: stakkour@central.ntua.gr . .

2452-3216 © 2020 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 MedFract1 organizers

2452-3216 © 2020 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 MedFract1 organizers 10.1016/j.prostr.2020.06.008