Over-deterministic method: The influence of rounding numbers on the accuracy of the values of Williams expansion terms

• Main Authors: V. Ru풞icka, L. Malkov�, S. Seitl
• Format: Article
• Language: English
• Published: Gruppo Italiano Frattura 2017-10-01
• Series: Frattura ed Integrità Strutturale
• Subjects: Over-deterministic method; Rounding numbers; Williams� expansion; Fracture mechanics; Stress field
• Online Access: http://www.gruppofrattura.it/pdf/rivista/numero42/numero_42_art_14.pdf

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 squaresbased 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