Issue 39

J. Sobek et alii, Frattura ed Integrità Strutturale, 39 (2017) 129-142; DOI: 10.3221/IGF-ESIS.39.14 129 Focussed on Modelling in Mechanics Analysis of accuracy of Williams series approximation of stress field in cracked body – influence of area of interest around crack-tip on multi-parameter regression performance J. Sobek, P. Frantík, V. Veselý Brno University of Technology, Faculty of Civil Engineering, Institute of Structural Mechanics, Brno, Czech Republic sobek.j@fce.vutbr.cz, http://orcid.org/0000-0003-4215-1029 kitnarf@centrum.cz vesely.v1@ fce.vutbr.cz , http://orcid.org/0000-0002-7723-971X A BSTRACT . A study on the accuracy of an approximation of the stress field in a cracked body is presented. Crack-tip stress tensor is 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 coefficients of terms of this series is performed using a least squares-based regression technique known as over-deterministic method (ODM) for which results from finite element (FE) method computation are usually taken as inputs. Main attention is paid to a detailed analysis of a suitable selection of FE nodes whose results serve as the inputs to the employed method. Two different ways of FE nodal selection are compared – nodes selected from the crack tip vicinity lying at a ring of a certain radius versus nodes selected more or less uniformly from a specified part of the test specimen body. Comparison of these approaches is made with the help of procedures developed by the authors which enable both the determination of the coefficients of terms of the analytical WPS approximation of the stress field based on the FE results and the backward reconstruction of the field (again using WPS) from those determined terms’ coefficients/functions. The wedge-splitting test (WST) specimen with a crack is taken as example for the study. K EYWORDS . Multi-parameter fracture mechanics; Williams power series; Crack-tip fields; Over-deterministic method; Higher order terms. Citation: Sobek, J., Frantík, P., Veselý, V., Analysis of accuracy of Williams series approximation of stress field in cracked body – influence of area of interest around crack- tip on multi-parameter regression performance, Frattura ed Integrità Strutturale, 39 (2017) 129-142. Received: 20.07.2016 Accepted: 19.09.2016 Published: 01.01.2017 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 etermination of the higher order terms of Williams power series [1] approximating the fields of stress and displacements in a cracked body is of substantial interest of the presented work. Particular motivation of it is represented by the need for capturing the crack-tip fields in a farther distance from the crack tip. D