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

Abstract

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

Keywords

• Over-deterministic method
• Rounding numbers
• Williams� expansion
• Fracture mechanics
• Stress field