### 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, ε_{φ}, in an arbitrary direction can be divided into the contributions of each mode (ε_{φ}= ε^{I} _{φ}+ε^{II} _{φ}+ε^{III} _{φ};ε^{I} _{φ},ε^{II} _{φ}and ε^{III} _{φ} 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_{φ} and ε^{I} _{φ} 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. Moreover, by applying these results to an experimental result of ductile fracture under a mixed mode, we show that ε^{I} _{φ} is a potential parameter for expressing elastic-plastic fracture criterion under a mixed mode.

Original language | English |
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Pages (from-to) | 1832-1840 |

Number of pages | 9 |

Journal | Transactions of the Japan Society of Mechanical Engineers Series A |

Volume | 55 |

Issue number | 516 |

DOIs | |

Publication status | Published - 1989 Jan 1 |

### Keywords

- Crack Energy Density
- Finite Element Method
- Fracture Criterion
- Fracture Mechanics
- Mixed-mode Crack
- Path-independent Integral

### ASJC Scopus subject areas

- Materials Science(all)
- Mechanics of Materials
- Mechanical Engineering

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## Cite this

*Transactions of the Japan Society of Mechanical Engineers Series A*,

*55*(516), 1832-1840. https://doi.org/10.1299/kikaia.55.1832