### Abstract

We present a new numerical path independent Ê-integral for calculating the stress intensity factors using a known auxiliary solution. The integral is path independent in the similar manner to the well known domain independent M-integral for calculating the stress intensity factors. The E-integral is, however, path independent even if the path contains any number of crack-tip and the integral may obtain the stress intensity factors at the onset of crack kinking by the path independent integral ; therefore, the integral path can be far from the crack-tip around which the numerical solution has noticeable error : The domain M-integral may not obtain the stress intensity factors at the onset of crack kinking and may be very difficult to obtain the stress intensity factors when there exist small cracks in the neighborhood of the crack-tip. For illustrative purposes, by using finite element method, numerical examples obtaining the stress intensity factors are presented for an extending straight crack and a kinking crack.

Original language | English |
---|---|

Pages (from-to) | 1031-1036 |

Number of pages | 6 |

Journal | Zairyo/Journal of the Society of Materials Science, Japan |

Volume | 60 |

Issue number | 11 |

DOIs | |

Publication status | Published - 2011 Nov 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Domain M-integral
- Kinking crack
- Path Ê-integral
- Stress intensity factor

### ASJC Scopus subject areas

- Materials Science(all)
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering

### Cite this

*Zairyo/Journal of the Society of Materials Science, Japan*,

*60*(11), 1031-1036. https://doi.org/10.2472/jsms.60.1031

**The finite element method analysis for the stress intensity factors using a path independent Ê-integral formula.** / Yatomi, Chikayoshi; Ueda, Takuya; Takagi, Shintaro; Abe, Takahiro.

Research output: Contribution to journal › Article

*Zairyo/Journal of the Society of Materials Science, Japan*, vol. 60, no. 11, pp. 1031-1036. https://doi.org/10.2472/jsms.60.1031

}

TY - JOUR

T1 - The finite element method analysis for the stress intensity factors using a path independent Ê-integral formula

AU - Yatomi, Chikayoshi

AU - Ueda, Takuya

AU - Takagi, Shintaro

AU - Abe, Takahiro

PY - 2011/11/1

Y1 - 2011/11/1

N2 - We present a new numerical path independent Ê-integral for calculating the stress intensity factors using a known auxiliary solution. The integral is path independent in the similar manner to the well known domain independent M-integral for calculating the stress intensity factors. The E-integral is, however, path independent even if the path contains any number of crack-tip and the integral may obtain the stress intensity factors at the onset of crack kinking by the path independent integral ; therefore, the integral path can be far from the crack-tip around which the numerical solution has noticeable error : The domain M-integral may not obtain the stress intensity factors at the onset of crack kinking and may be very difficult to obtain the stress intensity factors when there exist small cracks in the neighborhood of the crack-tip. For illustrative purposes, by using finite element method, numerical examples obtaining the stress intensity factors are presented for an extending straight crack and a kinking crack.

AB - We present a new numerical path independent Ê-integral for calculating the stress intensity factors using a known auxiliary solution. The integral is path independent in the similar manner to the well known domain independent M-integral for calculating the stress intensity factors. The E-integral is, however, path independent even if the path contains any number of crack-tip and the integral may obtain the stress intensity factors at the onset of crack kinking by the path independent integral ; therefore, the integral path can be far from the crack-tip around which the numerical solution has noticeable error : The domain M-integral may not obtain the stress intensity factors at the onset of crack kinking and may be very difficult to obtain the stress intensity factors when there exist small cracks in the neighborhood of the crack-tip. For illustrative purposes, by using finite element method, numerical examples obtaining the stress intensity factors are presented for an extending straight crack and a kinking crack.

KW - Domain M-integral

KW - Kinking crack

KW - Path Ê-integral

KW - Stress intensity factor

UR - http://www.scopus.com/inward/record.url?scp=84863406658&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863406658&partnerID=8YFLogxK

U2 - 10.2472/jsms.60.1031

DO - 10.2472/jsms.60.1031

M3 - Article

AN - SCOPUS:84863406658

VL - 60

SP - 1031

EP - 1036

JO - Zairyo/Journal of the Society of Materials Science, Japan

JF - Zairyo/Journal of the Society of Materials Science, Japan

SN - 0514-5163

IS - 11

ER -