A thought model for the fracture of brittle solids

1. Problem formulation. The processes governing the fracture of brittle solids are, at present, much less illuminated than those related to plastic deformations. The reason is that it is very difficult to observe the detailed fracture process directly. All one can determine is the load, which acted immediately before fracture started, and the path and nature of the fracture surface. Because during fracture only a very small portion of the body participates in the fracture process the statistical variation of the measurements is much larger than for plastic processes. That fracture is associated with the development of a labile equilibrium state has been generally accepted for a long time. Attempts to derive the fracture strength from known physical parameters of the molecular structure have led to values that are a hundred times larger than those one experiences in laboratory measurements. The most illuminating theory of the processes accompanying brittle fracture is that of A.A. Griffith, who assumes that microscopic cracks preexist in the material, and states that the cracks then propagate when the decrease in the elastic energy during crack propagation equals the work done against the surface tractions as the new surface is generated. GRIFFITH reported on this very lucidly in his talk with the title: “The theory of rupture”, presented at the congress of Mechanics in Delft, 1924. The fracture stress σz is thus proportional to l ET , where E is Young’s modulus, T the surface energy and l the length of the