Surface thermodynamics of cracks

Although a crack is a typical detail of a real solid, the theory of cracks in surface science was reduced to studying flat-parallel slits for a long time. The last decade has brought a number of new results related to the thermodynamic and surface science fundamentals of wedge-shaped cracks including the crack line tension. These results, essentially correcting and developing the theory of cracks, could not yet be included in the previous reviews of the author [A.I. Rusanov, Surf. Sci. Rep. 23 (1996) 173–247 and A.I. Rusanov, Surf. Sci. Rep. 58 (2005) 111–239] and make a subject for reviewing in this paper. Surface characteristics of a crack are described including the crack line tension as a new property that can be important for nanocracks. General thermodynamic relationships are derived, and the calculation of the thermodynamic surface and line tensions for solids with dispersion forces is given as an example. The dependence of the crack line tension on the crack size is analyzed for the conformal change (when a crack changes its size with maintaining its geometrical similarity) and the depth growth (when the distance between the crack lips is fixed). The latter has been found to be more favorable energetically. Since the presence of a crack is more probable for a loaded body, a general and rigorous approach to the thermodynamic description of loaded solids is presented including correcting earlier mistakes and terminology. The thermodynamic consideration presented outputs a useful contribution to the theory of solid strength. A generalized brittle fracture criterion is deduced and the ultimate strength is calculated for both the above mechanisms of the crack growth. The influence of the line tension on the ultimate strength is estimated both for the 2d and 3d cases.