Physics – Condensed Matter – Materials Science
Scientific paper
2008-07-30
Phys. Rev. Lett. 101, 264302 (2008)
Physics
Condensed Matter
Materials Science
4 pages, 2 figures, second of a two-paper series (theory); no change in content, minor textual revisions
Scientific paper
10.1103/PhysRevLett.101.264302
The common approach to crack dynamics, linear elastic fracture mechanics (LEFM), assumes infinitesimal strains and predicts a $r^{-1/2}$ strain divergence at a crack tip. We extend this framework by deriving a weakly nonlinear fracture mechanics theory incorporating the leading nonlinear elastic corrections that must occur at high strains. This yields strain contributions "more-divergent" than $r^{-1/2}$ at a finite distance from the tip and logarithmic corrections to the parabolic crack tip opening displacement. In addition, a dynamic length-scale, associated with the nonlinear elastic zone, emerges naturally. The theory provides excellent agreement with recent near-tip measurements that can not be described in the LEFM framework.
Bouchbinder Eran
Fineberg Jay
Livne Ariel
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