Lattice theory of fracture and crack creep

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Abstract
A quasianalytic solution for the atomic displacements of a discrete two‐dimensional lattice containing a crack is obtained. We assume that the force laws are linear up to a critical displacement when the bond snaps, which is the basic assumption of the lattice static approximation. When compared to the classic Griffith continuum description, new results are: (i) a predicted and observable lattice trapping of the crack, (ii) difficulties with the interpretations of the crystal surface energy in a cleavage experiment, and (iii) a predicted characteristic crack creep phenomenon under external constant stress. The present theory shows how two separate ``surface energies'' are inferred from the stress to open and to close a crack, and on our model these energies differ from one another by a large factor of 5.7. The thermodynamic ``surface energy'' is not related to either of these quantities. Experimental verification of the lattice trapping of cracks is thought to be most readily and directly obtained by observations of the creep of a crack under high vacuum conditions.

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