PSI - Issue 28

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

www.elsevier.com/locate/procedia

ScienceDirect

Procedia Structural Integrity 28 (2020) 710–719

© 2020 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 the European Structural Integrity Society (ESIS) ExCo Abstract Although more than fifteen years have passed since the flattened Brazilian disc test was introduced, analytic studies on the respective stress field are scarce, mainly due to difficulties related to the shape of its boundary. In this context, an alternative mathematical formulation, providing a full-field solution for the distribution of stresses in the flattened Brazilian disc, is here proposed, based on the configuration of an intact circular disc, under a large number of equal point forces, arranged at equal distances along two symmetric parallel chords of the disc. Considering each point force as the resultant of stresses acting on an eliminated hole, a great number of such forces implies the introduction of a large number of small holes, dividing the uniform disc into three distinct parts; the one between the two chords is to stand as the flattened disc under uniform compression. This particular problem for the uniform disc is here solved with the aid of Muskhelishvili’s complex potential technique, providing a closed-form, full-field solution for the stresses on the as above “truncated” disc, and thus, in a first approximation, on the flattened Brazilian disc. The analysis, apart from highlighting the advantage of the flattened against the classical intact Brazilian disc (regarding the reduction of stress concentration along the disc loading platen contact region), revealed, also, that the pressure on the flat edges of the flattened disc should be non-uniform in order to better approximate the experimental reality. In this direction, a numerical model was developed, indicating the proper non uniform distribution of pressure that should be applied along the flat edges of the flattened Brazilian disc, in order for these edges to remain plane after deformation, in accordance to the laboratory implementation of the experiment. © 2020 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 the European Structural Integrity Society (ESIS) ExCo Keywords: Flattened Brazilian disc;Tensile strength; Complex potentials; Stress and displacement fields 1st Virtual European Conference on Fracture Mathematical formulation of an analytic approach to the stress field in a flattened Brazilian disc Christos F. Markides, Stavros K. Kourkoulis* National Technical University of Athens, School of Applied Mathematical and Physical Sciences, Department of Mechanics, Laboratory for Testing and Materials, Theocaris Building, Zografou Campus, 157 73, Greece

* Corresponding author. Tel.: +30 210 7721263; fax: +30 210 7721302. 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 (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the European Structural Integrity Society (ESIS) ExCo

2452-3216 © 2020 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 the European Structural Integrity Society (ESIS) ExCo 10.1016/j.prostr.2020.10.082