A theoretical description of the structure of the nonlinear zone in the vicinity of the tip of a dynamic mode I crack

Eran Bouchbinder*, Ariel Livne, Jay Fineberg

*Corresponding author for this work

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

Abstract

The common approach to fracture dynamics, linear elastic fracture mechanics (LEFM), assumes infinitesimal deformation gradients, but, in the vicinity of a crack's tip predicts diverging r-1/2 crack tip strains, a result that appears self-contradictory. We derive the leading nonlinear elastic corrections to these asymptotic fields and show that the resulting theory quantitatively resolves a number of discrepancies raised by recent near-tip measurements of the strain field surrounding a dynamic crack, which are presented in an accompanying paper. We show that no region of r -1/2 dominance exists and "more-divergent" strain terms occur at a finite distance from the tip. In addition, a dynamical length-scale, associated with a nonlinear elastic zone, appears naturally. Where LEFM falls short, the theory provides excellent quantitative agreement with the measured, near-tip, displacement and strain fields. The theory serves as a springboard for the development of a comprehensive theory of fracture dynamics.

Original languageAmerican English
Title of host publication12th International Conference on Fracture 2009, ICF-12
Pages6569-6578
Number of pages10
StatePublished - 2009
Event12th International Conference on Fracture 2009, ICF-12 - Ottawa, ON, Canada
Duration: 12 Jul 200917 Jul 2009

Publication series

Name12th International Conference on Fracture 2009, ICF-12
Volume8

Conference

Conference12th International Conference on Fracture 2009, ICF-12
Country/TerritoryCanada
CityOttawa, ON
Period12/07/0917/07/09

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