Williams expansion-based approximation of the stress field in an Al 2024 body with a crack from optical measurements

S Seitl,P Frantík,J Sobek,L Malíkova,P Lopez-Crespo

doi:10.3221/igf-esis.41.43

Abstract

A study on the approximation of the stress field in the vicinity of crack tip in a compact tension specimen made from Al 2024-T351 is presented. 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 coefficients of terms of this series is performed using a least squares-based regression technique known as over deterministic method (ODM) for which displacements data obtained experimentally via optical measurements are taken as inputs. The stress fields reconstructed based on the displacement data obtained experimentally by means of optical measurements are verified by means of the stress field approximations derived for the normalized CT specimen via hybrid elements.

Highlights

C haracterization of crack tip stresses has been an area of active research for many decades; see short state-of-art in [1, 2] presenting an over-deterministic least squares technique to evaluate the mixed-mode multi-parameter stress field by photo- elasticity underlining the fact that the use of a multi-parametric representation is not just for academic curiosity but a necessity in some cases of engineering interest
I n the first step of the verification process, the stress intensity factor (SIF) values were compared
The values obtained directly from the fracture tests are compared to values calculated from the displacements measured via Digital Image Correlation technique (DIC) and to values obtained by Bednář and Knésl by means of the hybrid crack elements [5]

Summary

Introduction

C haracterization of crack tip stresses has been an area of active research for many decades; see short state-of-art in [1, 2] presenting an over-deterministic least squares technique to evaluate the mixed-mode multi-parameter stress field by photo- elasticity underlining the fact that the use of a multi-parametric representation is not just for academic curiosity but a necessity in some cases of engineering interest This fact is underlined by Ayatollahi et al in [3] who used displacement fields obtained from finite element analysis and provided a specific algorithm for fast determination of the unknown parameters. Note that this work is only a part of the extensive ongoing research of the authors on the application of this multi-parameter approach in more advanced fracture mechanics tasks

Methods

Results

Conclusion