Multi-parameter approximation of stress field in a cracked specimen using purpose-built Java applications

V Veselý,P Frantík,T Pail,S Seitl,D Tesa,J Sobek

doi:10.3221/igf-esis.33.16

Abstract

A quality of multi-parameter approximation of the stress and displacement fields around a crack tip in a non-brittle material test specimen is studied in the paper. The stress field approximation using Williams power series is intended to be utilized for estimation of the nonlinear zone extent which potentially plays a role within methods for determination of true values of fracture parameters of materials exhibiting nonlinear failure. Considering the fact that in the case of elastic-plastic and especially quasi-brittle materials the size of this zone is substantial in comparison to the specimen dimensions, it is necessary to take a large region around the crack tip into account for this task. An automatic utility created to determine the values of coefficients of the higher order terms of Williams power series by usage of over-deterministic method applied on results of finite element analysis of arbitrary mode I test geometry is one of the tested procedures. The second one provides a backward reconstruction of the crack-tip stress field analytically by means of truncated Williams expansion. The developed procedures are based on the support of Java programming language and considerably simplify analyses of the mechanical fields’ description in a farther distance from the crack-tip. The presented research is focused on optimization of selection of FE nodal results for improvement of accuracy of the approximation.

Highlights

The concept of fracture process zone (FPZ) has been introduced into analysing fracture behaviour of nonlinearly failing materials already several decades ago [1,2,3]
Multi-parameter fracture mechanics is employed as the proportion of sizes of the FPZ and the whole specimen is much larger in the case of the quasi-brittle materials than e.g. plastic zone in metals [4], and the stress field farther from the crack trip must be described precisely
Main focus of the contribution is on testing of two own developed automatic utilities; the first enables computation of values of coefficients of the higher order terms of Williams power series using the over-deterministic method (ODM) applied to results of FEM analysis, the second provides analytical approximation of the stress field in the cracked body via truncated Williams power expansion taking into account the values of coefficients of the higher order terms calculated using the first programmed application

Summary

Introduction

The concept of fracture process zone (FPZ) has been introduced into analysing fracture behaviour of nonlinearly failing (especially softening) materials already several decades ago [1,2,3]. The influence of the number of terms considered for the power series reconstruction of stress field as well as the way of selection of the FEM nodes for the calculation of the values of coefficients of those terms are investigated in the paper.

Results

Conclusion