Brittle fracture: thermodynamic refinement of the Griffith problem

Abstract

The purpose of the work is (a) a rigorous formulation of the brittle fracture problem from the thermodynamic point of view and (b) widening the theory by accounting for not only surface tension, but also the line tension of a crack. A proper thermodynamic formulation of the Griffith problem is attained by introducing generalized Gibbs energy as a thermodynamic potential, both the 2d and 3d cases being included. Thermodynamic line tension is introduced as a new characteristic of a crack originating from changing surface tension near the crack tip, which can be of certain significance for nanocracks. The criterion of rupture is reformulated in the context of line tension. As an example, a detailed calculation of the surface and line tensions of a crack is performed for a molecular solid with dispersion forces. The effect of line tension on the ultimate strength is shown to be twice as much in the 3d case as compared with the 2d case.