2.1. Asymptotic Analysis of Size Effect in Structures with Notches or Large Cracks

The scaling properties for the nominal strength ? _N of a structure containing a notch or a stably grown large crack can be most generally deduced by an asymptotic analysis of the energy release (Ba ant 1997a). We will now outline it briefly, restricting attention to two-dimensional similarity although the case of three-dimensional similarity could be analyzed similarly. The fracture may be characterized by the dimensionless variables ? ₀ = a ₀/ D, ? = a/ D, ? = c _f/ D, in which a = the total crack length which gives (according to LEFM) the same specimen compliance as the actual crack with its fracture process zone; a ₀ = length of the traction-free crack or the notch; c _f = a - a ₀ = effective size of the fracture process zone (or the effective length of the R-curve); and D is the characteristic size (dimension) of the structure, for example taken as the depth of the notched three-point bend beam shown in Fig. 2.1.

Figure 2.1: Similar structures with large cracks and function ?

Note that in our analysis the interpretation in the sense of a cohesive crack or an R-curve model is not essential. We can equally well assume that c _f is in general any kind of material length, for example c _f = G