Lattice theory of fracture and crack creep

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.

Parametrization in Models of Subcritical Glass Fracture: Activation Offset and Concerted Activation

“…This approach is consistent with the approximation of ideally brittle fracture and the lattice trapping understanding of fracture (Hsieh and Thomson, 1973;Lawn et al, 1980;Michalske and Bunker, 1984;Schultz et al, 1994;Zhu et al, 2004). Putting Eqs 5 and 6 together yields:…”

Effects of atoms on brittle fracture

“…The three-dimensional situation is different. The process of creep becomes more complex; portions of the crack line move ahead unevenly because of thermal fluctuations, and eventually the rest of the crack line follows (Hsieh and Thomson, 1973, Sinclair, 1975, Markworth and Hirth, 1981, Lin and Hirth, 1982, Thomson et al 1987, Marder, 1998. Just as thermal fluctuations have a harder time moving a stationary crack front forward in three dimensions than two, they probably have a more difficult time disrupting a rapidly moving front.…”

Attractive and repulsive cracks in a heterogeneous material

“…Characterization of rupture properties very often involve the growth of a dominant crack. For instance, there is an extensive literature, both experimental and theoretical, discussing the slow growth dynamics of a single crack along a straight path in brittle [1,2,3,4,5,6,7] or visco-plastic materials [8,9,10,11,12,13,14,15]. However, in many practical situations, the crack path is not straight.…”