Issue 66

Ch. F. Markides et alii, Frattura ed Integrità Strutturale, 66 (2023) 233-260; DOI: 10.3221/IGF-ESIS.66.15

Revisiting classical concepts of Linear Elastic Fracture Mechanics - Part I: The closing ‘mathematical’ crack in an infinite plate and the respective Stress Intensity Factors Christos F. Markides National Technical University of Athens, School of Applied Mathematical and Physical Sciences, Department of Mechanics, Lab oratory for Testing and Materials, Zografou Campus, 5 Heroes of Polytechneion Avenue, 157 73, Attiki, Greece markidih@maill.ntua.gr, http://orcid.org/0000-0001-6547-3616 Stavros K. Kourkoulis National Technical University of Athens, School of Applied Mathematical and Physical Sciences, Department of Mechanics, Lab oratory of Biomechanics and Biomedical Physics, Zografou Campus, 5 Heroes of Polytechneion Avenue, 157 73, Attiki, Greece stakkour@central.ntua.gr, http://orcid.org/ 0000-0003-3246-9308

A BSTRACT . This is the first part of a short three-paper series, aiming to revisit some classical concepts of Linear Elastic Fracture Mechanics. The motive of this first paper is to highlight some controversial issues, related to the unnatu ral overlapping of the lips of a ‘mathematical’ crack in an infinite plate loaded by specific combinations of principal stresses at infinity (predicted by the clas sical solution of the respective first fundamental problem), and the closely as sociated issue of negative mode-I Stress Intensity Factor. The problem is con fronted by superimposing to the first fundamental problem of Linear Elastic Fracture Mechanics for an infinite cracked plate (with stress-free crack lips) an ‘inverse’ mixed fundamental problem. This superposition provides naturally acceptable stress and displacement fields, prohibiting overlapping of the lips (by means of contact stresses generated along the crack lips, which force the overlapped lips back to naturally accepted position) and, also, non-negative mode-I Stress Intensity Factors. The solutions of this first paper form the basis for the next two papers of the series, dealing with the respective prob lems in finite domains (recall, for example, the cracked Brazilian disc configu ration) weakened by artificial notches (rather than ‘mathematical’ cracks), by far more interesting for practical engineering applications. K EYWORDS . Linear Elastic Fracture Mechanics, ‘Mathematical’ cracks, Stress Intensity Factors, Stresses, Displacements and Contact stresses, Overlapping crack lips, Complex potentials.

Citation: Markides, Ch.F, Kourkoulis, S.K., Revisiting classical concepts of Linear Elastic Fracture Mechanics-Part I: The closing ‘math ematical’ crack in an infinite plate and the re spective Stress Intensity Factors, Frattura ed Integrità Strutturale, 66 (2023) 233-260.

Received: 10.08.2023 Accepted: 21.08.2023 Online first: 26.08.2023 Published: 01.10.2023

Copyright: © 2023 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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