Some exact results for the velocity of cracks propagating in non-linear elastic models

Details Some exact results for the velocity of cracks propagating in non-linear elastic models Some exact results for the velocity of cracks propagating in non-linear elastic models

2006-04-03

arxiv.org/abs/cond-mat/0604056v1

Physics

Condensed Matter

Materials Science

9 pages, 13 figures

Scientific paper

10.1103/PhysRevE.74.016106

We analyze a piece-wise linear elastic model for the propagation of a crack in a stripe geometry under mode III conditions, in the absence of dissipation. The model is continuous in the propagation direction and discrete in the perpendicular direction. The velocity of the crack is a function of the value of the applied strain. We find analytically the value of the propagation velocity close to the Griffith threshold, and close to the strain of uniform breakdown. Contrary to the case of perfectly harmonic behavior up to the fracture point, in the piece-wise linear elastic model the crack velocity is lower than the sound velocity, reaching this limiting value at the strain of uniform breakdown. We complement the analytical results with numerical simulations and find excellent agreement.

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