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.

Notes:

12th International Conference on Fracture 2009, ICF-12 ; Conference date: 12-07-2009 Through 17-07-2009