Lattice and continuum predictions of cracktip stability
Abstract
The stability of a crack which has a nonlinear core emerging from the tip onto the plane ahead of the crack is investigated in terms of K_{I}K_{II} loading. The principal focus is to address a paradox that the Griffith relation, G=2γ_{s}, permits equilibrium cracks to exist in pure modeII loading, yet under such conditions there would be insufficient tensile force to pull atoms apart to maintain free surfaces. Using a Peierlstype framework developed by Rice [J. Mech. Phys. Solids 40, 239 (1992)], a continuum analysis of a crack with a nonlinear core ahead of the crack tip is presented to demonstrate that, indeed, the crackcore structure is stable to selfsimilar translation when the Griffith condition is met. However, the portions of the Griffith curve which have a sufficient fraction of modeII loading—approximately ‖K_{II}‖/K_{I}≥0.4 for the particular bonding properties considered here, are unattainable because dislocation emission intervenes. Corresponding studies of an equilibrium crack in a 2D hexagonal lattice demonstrate that there is a band of K_{I}K_{II} values within which the crack is stable. The band is approximately centered on the Griffith curve and extends to critical K_{II} values comparable to those at which the continuum model predicts dislocation emission to intervene. The finite width of the band occurs due to lattice trapping, and that width is observed to broaden as K_{II} is increased. In this context, the continuum model represents the case of zero trapping. Consequently, a satisfactory explanation of the Griffith crack paradox is that pure modeII equilibrium cracks are unattainable because dislocation emission from the crack tip intervenes before the pure modeII Griffith value can be reached.
 Publication:

Journal of Applied Physics
 Pub Date:
 July 1994
 DOI:
 10.1063/1.357759
 Bibcode:
 1994JAP....76..843A
 Keywords:

 Continuum Modeling;
 Crack Tips;
 Crystal Lattices;
 Griffith Crack;
 Stability;
 Trapping;
 Crystal Dislocations;
 Loads (Forces);
 Nonlinearity;
 SolidState Physics