# A simple path-independent integral for calculating mixed-mode stress intensity factors

Zhiliang Zhang, Timo Mikkola

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)

### Abstract

A path‐independent integral is introduced for calculating stress intensity factors. The derivation of the integral is based on the application of the known Bueckner's fundamental field solution for a crack in an infinite body and on the reciprocal theorem. The method was applied to two‐dimensional linear elastic mixed‐mode crack problems. The key advantage of the present path‐independent integral is that the stress intensity factor components for any irregular cracked geometry under any kind of loading can be easily obtained by a contour integral around the crack tip. The method is simple to implement and only the far field displacements and tractions along the contour must be known. The required stress analysis can be made by using any analytical or numerical method, e.g. the finite element method, without special consideration of the modelling of crack tip singularity. The application of this integral is also independent of the crack type, that is, there is no difference between an edge crack and an embedded crack, provided that the crack tip asymptotic behaviour exists.
Original language English 1041-1049 9 Fatigue & Fracture of Engineering Materials & Structures 15 10 https://doi.org/10.1111/j.1460-2695.1992.tb00030.x Published - 1992 A1 Journal article-refereed

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Stress intensity factors
Cracks
Crack tips
Stress analysis
Numerical methods
Finite element method
Geometry

### Cite this

@article{b6d95f7eaf0d4695b75730d8ab4edbd0,
title = "A simple path-independent integral for calculating mixed-mode stress intensity factors",
abstract = "A path‐independent integral is introduced for calculating stress intensity factors. The derivation of the integral is based on the application of the known Bueckner's fundamental field solution for a crack in an infinite body and on the reciprocal theorem. The method was applied to two‐dimensional linear elastic mixed‐mode crack problems. The key advantage of the present path‐independent integral is that the stress intensity factor components for any irregular cracked geometry under any kind of loading can be easily obtained by a contour integral around the crack tip. The method is simple to implement and only the far field displacements and tractions along the contour must be known. The required stress analysis can be made by using any analytical or numerical method, e.g. the finite element method, without special consideration of the modelling of crack tip singularity. The application of this integral is also independent of the crack type, that is, there is no difference between an edge crack and an embedded crack, provided that the crack tip asymptotic behaviour exists.",
author = "Zhiliang Zhang and Timo Mikkola",
year = "1992",
doi = "10.1111/j.1460-2695.1992.tb00030.x",
language = "English",
volume = "15",
pages = "1041--1049",
journal = "Fatigue & Fracture of Engineering Materials & Structures",
issn = "8756-758X",
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A simple path-independent integral for calculating mixed-mode stress intensity factors. / Zhang, Zhiliang; Mikkola, Timo.

In: Fatigue & Fracture of Engineering Materials & Structures, Vol. 15, No. 10, 1992, p. 1041-1049.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - A simple path-independent integral for calculating mixed-mode stress intensity factors

AU - Zhang, Zhiliang

AU - Mikkola, Timo

PY - 1992

Y1 - 1992

N2 - A path‐independent integral is introduced for calculating stress intensity factors. The derivation of the integral is based on the application of the known Bueckner's fundamental field solution for a crack in an infinite body and on the reciprocal theorem. The method was applied to two‐dimensional linear elastic mixed‐mode crack problems. The key advantage of the present path‐independent integral is that the stress intensity factor components for any irregular cracked geometry under any kind of loading can be easily obtained by a contour integral around the crack tip. The method is simple to implement and only the far field displacements and tractions along the contour must be known. The required stress analysis can be made by using any analytical or numerical method, e.g. the finite element method, without special consideration of the modelling of crack tip singularity. The application of this integral is also independent of the crack type, that is, there is no difference between an edge crack and an embedded crack, provided that the crack tip asymptotic behaviour exists.

AB - A path‐independent integral is introduced for calculating stress intensity factors. The derivation of the integral is based on the application of the known Bueckner's fundamental field solution for a crack in an infinite body and on the reciprocal theorem. The method was applied to two‐dimensional linear elastic mixed‐mode crack problems. The key advantage of the present path‐independent integral is that the stress intensity factor components for any irregular cracked geometry under any kind of loading can be easily obtained by a contour integral around the crack tip. The method is simple to implement and only the far field displacements and tractions along the contour must be known. The required stress analysis can be made by using any analytical or numerical method, e.g. the finite element method, without special consideration of the modelling of crack tip singularity. The application of this integral is also independent of the crack type, that is, there is no difference between an edge crack and an embedded crack, provided that the crack tip asymptotic behaviour exists.

U2 - 10.1111/j.1460-2695.1992.tb00030.x

DO - 10.1111/j.1460-2695.1992.tb00030.x

M3 - Article

VL - 15

SP - 1041

EP - 1049

JO - Fatigue & Fracture of Engineering Materials & Structures

JF - Fatigue & Fracture of Engineering Materials & Structures

SN - 8756-758X

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ER -