Non-singular dislocation elastic fields and linear elastic fracture mechanics

Alexander M. Korsunsky

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Citation (Scopus)

Abstract

One of the hallmarks of the traditional linear elastic fracture mechanics (LEFM) is the presence of an (integrable) inverse square root singularity of strains and stresses in the vicinity of the crack tip. It is the presence of this singularity that necessitates the introduction of the concepts of stress intensity factor (and its critical value, the fracture toughness) and the energy release rate (and material toughness). This gives rise to the Griffith theory of strength that includes, apart from applied stresses, the considerations of defect size and geometry. A highly successful framework for the solution of crack problems, particularly in the two-dimensional case, due to Muskhelishvili (1953), Bilby and Eshelby (1968) and others, relies on the mathematical concept of dislocation. Special analytical and numerical methods of dealing with the characteristic 1/r (Cauchy) singularity occupy a prominent place within this theory. Recently, in a different context of dislocation dynamics simulations, Cai et al. (2006) proposed a novel means of removing the singularity associated with the dislocation core, by introducing a blunting radius parameter a into the expressions for elastic fields. Here, using the example of two-dimensional elasticity, we demonstrate how the adoption of the similar mathematically expedient tool leads naturally to a non-singular formulation of fracture mechanics problems. This opens an efficient means of treating a variety of crack problems.

Original languageEnglish
Title of host publicationCurrent Themes in Engineering Science 2009 - Selected Presentations at the World Congress on Engineering - 2009
Pages114-123
Number of pages10
DOIs
Publication statusPublished - 2010
Externally publishedYes
EventWorld Congress on Engineering, WCE - London, United Kingdom
Duration: 1 Jul 20093 Jul 2009

Publication series

NameAIP Conference Proceedings
Volume1220
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

ConferenceWorld Congress on Engineering, WCE
Country/TerritoryUnited Kingdom
CityLondon
Period1/07/093/07/09

Keywords

  • Crack problems
  • Dislocations
  • Eigenstrain
  • Elasticity theory
  • Fracture mechanics

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