Crack growth criteria incorporating non-singular stresses: size effect in apparent fracture toughness

Simple criteria accounting for the non-singular stresses at the crack tip are considered. They are based on the comparison of the local stress concentration with the material microstrength. The local stress concentration is estimated either as the magnitude of the conventional elastic stress ahead of the process zone, or by its averaging over the process zone length. When a criterion of this type is used to find the critical load and then the conventional fracture toughness, the latter will be dependent of the crack length. This size effect in fracture toughness manifests itself as an increase (if the non-singular part of the near-tip stress field is positive) or decrease (if the non-singular part is negative) in the apparent fracture toughness as the crack length increases. The obtained dependence is compared with available experimental data. It is also shown that when the load can be resolved into a superposition of elementary loads, the size effect can asymptotically (for long cracks) be presented as a weighted sum of the elementary size effects (i.e. the size effects associated with the elementary loads) with the weights equal to the relative contributions of the elementary loads into the total stress intensity factor.