### Abstract

This work studies the basics of fracture mechanics. The
theory proposed by
Griffith is
derived starting from the examination of the momentum and
moment of momentum
principles. A condition for crack growth is formulated.
This equation also
contains the
influence of kinetic energy and continuum dissipation.
The condition is
expressed in the
rate form i.e. it describes the response of a continuum
in the case of a
running crack. In
the special case, the derived condition reduces to that
proposed by Griffith.
The present investigation derives 7 sufficient conditions
for the path
independency of the
J-integral.
The mathematical treatment of unbounded functions (due to
the crack tip) is
also
considered, This study examines the relation between the
J-integral and the
potential
energy. The present work brings out a new result: If a
pure elastic deformation
and crack
tip singularity is assumed a previously not derived term
has to be added to the
above
mentioned relationship. A computed example which studies
the mode I of cracking
and
assumes a linear elastic, isotropic material behaviour
shows that the value of
this new
term equals that of the J-integral.

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

Place of Publication | Espoo |

Publisher | VTT Technical Research Centre of Finland |

Number of pages | 77 |

ISBN (Print) | 951-38-4078-6 |

Publication status | Published - 1992 |

MoE publication type | Not Eligible |

### Publication series

Series | VTT Publications |
---|---|

Number | 100 |

ISSN | 1235-0621 |

### Keywords

- theories
- mathematical models
- fracture mechanics
- cracking (fracturing)
- crack propagation
- crack initiation
- momentum
- kinetic energy
- potential energy
- continuum mechanics
- singular integral equations
- integral equations
- Griffith crack

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## Cite this

Santaoja, K. (1992).

*Some remarks upon fracture mechanics*. VTT Technical Research Centre of Finland. VTT Publications, No. 100