Issue 42

V. Růžička et alii, Frattura ed Integrità Strutturale, 42 (2017) 128-135; DOI: 10.3221/IGF-ESIS.42.14 128 Focused on Mechanical Fatigue of Metals Over-deterministic method: The influence of rounding numbers on the accuracy of the values of Williams’ expansion terms Vladimír Růžička Brno University of Technology, Faculty of Civil Engineering, Institute of Structural Mechanics, Veveří 331/95, 602 00 Brno, Czech Republic ruzicka@musicer.net Lucie Malíková, Stanislav Seitl Academy of Sciences of the Czech Republic, Institute of Physics of Materials, v. v. i., Žižkova 22, 616 62 Brno, Czech Republic malikova.l@fce.vutbr.cz , http://orcid.org/0000-0001-5868-5717 seitl@ipm.cz, http://orcid.org/0000-0002-4953-4324 A BSTRACT . A study on the accuracy of the values of Williams’ expansion terms influenced by rounding numbers is presented. The results are presented taking into account a three-point bend single edge notched beam . Crack tip stress tensor components are expressed using the linear elastic fracture mechanics (LEFM) theory in this work, more precisely via its multi-parameter formulation, i.e. by Williams’ power series (WPS). Determination of the coefficients of the terms of this series is performed using the least squares- based regression technique known as the over-deterministic method (ODM), for which displacements data obtained numerically in software ANSYS are taken as inputs. The values of Williams’ expansion terms based on the displacement data obtained are calculated by using various levels of rounding numbers and the results are compared and discussed. K EYWORDS . Over-deterministic method; Rounding numbers; Williams’ expansion; Fracture mechanics; Stress field. Citation: Ruzicka,V., Malikova, L., Seitl, S., Over-deterministic method: The influence of rounding numbers on the accuracy of the values of Williams’ expansion terms, Frattura ed Integrità Strutturale, 42 (2017)128-135. Received: 10.06.2017 Accepted: 16.06.2017 Published: 01.10.2017 Copyright: © 2017 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. I NTRODUCTION ometimes it is necessary to describe the crack-tip stress field by means of more than only one singular term (the well- known stress intensity factor, see e.g. [1-4] or two-parameter fracture mechanics, see e.g. [5-10]) of Williams’ expansion (WE). It has been shown that so-called multi-parameter fracture mechanics can be helpful when the fracture process occurs in the more extensive surroundings of the crack tip, see for material like concrete [11-19]. Then, a particular number of the WE terms needs to be taken into account for a more complex fracture analysis. In this paper, the focus is devoted to investigations into the accuracy of the higher-order terms of the WE when various types of rounding S