Some remarks upon fracture mechanics

Kari Santaoja

Research output: Book/ReportReport

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 languageEnglish
Place of PublicationEspoo
PublisherVTT Technical Research Centre of Finland
Number of pages77
ISBN (Print)951-38-4078-6
Publication statusPublished - 1992
MoE publication typeNot Eligible

Publication series

SeriesVTT Publications
Number100
ISSN1235-0621

Fingerprint

fracture mechanics
J integral
crack tips
cracks
continuums
momentum
elastic deformation
dissipation
examination
energy dissipation
kinetic energy
potential energy
moments

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

Cite this

Santaoja, K. (1992). Some remarks upon fracture mechanics. Espoo: VTT Technical Research Centre of Finland. VTT Publications, No. 100
Santaoja, Kari. / Some remarks upon fracture mechanics. Espoo : VTT Technical Research Centre of Finland, 1992. 77 p. (VTT Publications; No. 100).
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Santaoja, K 1992, Some remarks upon fracture mechanics. VTT Publications, no. 100, VTT Technical Research Centre of Finland, Espoo.

Some remarks upon fracture mechanics. / Santaoja, Kari.

Espoo : VTT Technical Research Centre of Finland, 1992. 77 p. (VTT Publications; No. 100).

Research output: Book/ReportReport

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AB - 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.

KW - theories

KW - mathematical models

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KW - crack propagation

KW - crack initiation

KW - momentum

KW - kinetic energy

KW - potential energy

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KW - singular integral equations

KW - integral equations

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M3 - Report

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Santaoja K. Some remarks upon fracture mechanics. Espoo: VTT Technical Research Centre of Finland, 1992. 77 p. (VTT Publications; No. 100).