A study on the approximation of the displacement field in the vicinity of a crack tip in a compact tension specimen made from Al 2024‐T351 is presented. Components of displacements vector are expressed using the linear elastic fracture mechanics theory via Williams' power series multi‐parameter formulation. Determination of the coefficients of the terms of this series is performed using a least squares‐based regression technique known as over deterministic method for which displacements data obtained experimentally via optical measurements are taken as inputs. The displacement fields reconstructed are discussed, and several conclusions are drawn regarding the number of the Williams' power series terms considered and the region where the displacement are investigated.

Multi-parameter fracture mechanics is nowadays quite extensively applied when cracked structures/specimens are investigated. The reason was that it has been shown that it can be helpful and bring results that are more accurate when for describing of fracture processes a larger region around the crack tip is used. This can be typical for material like concrete or other materials with quasi-brittle behaviour. Various relative crack length configurations were chosen in order to investigate the importance of the higher-order terms of the Williams expansion (WE) on the crack-tip stress field distribution in Wedge splitting test specimen. The higher-order terms were calculated by means of the over-deterministic method from displacements of nodes around the crack tip obtained by a finite element analysis in different radial distances from the crack tip. The effect of the constraint level (second member of WE) was investigated. Although the third and higher terms of the Williams series are very often neglected, their influence on the opening stress values was investigated and discussed.

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.

A study on the accuracy of the approximation of the displacement field around of crack tip in a sample made from bridge steel (S355) is main objective of contribution. Linear elastic fracture mechanics (LEFM) theory in framework of multi-parameter formulation, i.e. postulated by Williams is used to determine of coefficients of Williams power series terms. Over deterministic method was used to calculate the terms based on the least squares regression technique, applied on data from numerical simulation and experiment on S355 steel grades. Comparison between the stress fields (by principal stress  1 and von Mises stress  HMH) obtain from experimental measurement DIC, Hybrid method and obtain from reconstruction by using various number of Williams power terms are quantified in order to get key information around the crack tip region on bridge steel specimens.