### Abstract

It has previously been shown that crack energy density can be defined in any direction at a crack tip without any restrictions on constitutive equations. The crack energy density, εφ, in an arbitrary direction can be divided into the contributions of each mode (ε_{phi} = ε_{phi}^{I}+ ε_{phi}^{II}+ ε_{phi}^{III}; ε_{phi}^{I}, ε_{phi}^{II} and ε_{phi}^{III} are the contributions of modes I, II and III, respectively), which can be evaluated by path-independent integrals corresponding to each. These are defined for a completely sharp crack as the limits where the notch root radius ρ approaches zero in a notch model. Therefore, it is necessary to use a notch model with a sufficiently small value of ρ in evaluations of the quantities through FEM. In this paper, ε_{phi} and ε_{phi}^{I} are evaluated by path-independent integrals through elastic-plastic finite element analyses varying the value of ρ, and we discuss which of ρ should be adopted in evaluations of them.

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

Pages (from-to) | 1832-1839 |

Number of pages | 8 |

Journal | Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A |

Volume | 55 |

Issue number | 516 |

Publication status | Published - 1989 Aug |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mechanical Engineering

### Cite this

*Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A*,

*55*(516), 1832-1839.

**Fundamental study on the evaluation and applicability as a mixed-mode fracture criterion of crack energy density in an arbitrary direction.** / Utsunomiya, Takao; Watanabe, Katsuhiko.

Research output: Contribution to journal › Article

*Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A*, vol. 55, no. 516, pp. 1832-1839.

}

TY - JOUR

T1 - Fundamental study on the evaluation and applicability as a mixed-mode fracture criterion of crack energy density in an arbitrary direction

AU - Utsunomiya, Takao

AU - Watanabe, Katsuhiko

PY - 1989/8

Y1 - 1989/8

N2 - It has previously been shown that crack energy density can be defined in any direction at a crack tip without any restrictions on constitutive equations. The crack energy density, εφ, in an arbitrary direction can be divided into the contributions of each mode (εphi = εphiI+ εphiII+ εphiIII; εphiI, εphiII and εphiIII are the contributions of modes I, II and III, respectively), which can be evaluated by path-independent integrals corresponding to each. These are defined for a completely sharp crack as the limits where the notch root radius ρ approaches zero in a notch model. Therefore, it is necessary to use a notch model with a sufficiently small value of ρ in evaluations of the quantities through FEM. In this paper, εphi and εphiI are evaluated by path-independent integrals through elastic-plastic finite element analyses varying the value of ρ, and we discuss which of ρ should be adopted in evaluations of them.

AB - It has previously been shown that crack energy density can be defined in any direction at a crack tip without any restrictions on constitutive equations. The crack energy density, εφ, in an arbitrary direction can be divided into the contributions of each mode (εphi = εphiI+ εphiII+ εphiIII; εphiI, εphiII and εphiIII are the contributions of modes I, II and III, respectively), which can be evaluated by path-independent integrals corresponding to each. These are defined for a completely sharp crack as the limits where the notch root radius ρ approaches zero in a notch model. Therefore, it is necessary to use a notch model with a sufficiently small value of ρ in evaluations of the quantities through FEM. In this paper, εphi and εphiI are evaluated by path-independent integrals through elastic-plastic finite element analyses varying the value of ρ, and we discuss which of ρ should be adopted in evaluations of them.

UR - http://www.scopus.com/inward/record.url?scp=0024715416&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024715416&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0024715416

VL - 55

SP - 1832

EP - 1839

JO - Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A

JF - Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A

SN - 0387-5008

IS - 516

ER -