A mathematical model for the embrittlement of a long elastic-plastic crack by a relatively small, misfitting inclusion is presented. The model makes direct contact with the Dugdale-Bilby-Cottrell-Swinden model as a limiting case. The particular case of an oxide inclusion with a triangular cross-section at the tip of an intergranular crack in the Ni-based superalloy RR1000 at 650 • C is considered. The positive misfit of the intrusion provides an additional tensile load on the crack tip and on the plastic zone, raising the local stress intensity factor k I and the crack tip opening displacement Δu above those when the inclusion is replaced by a dislocation-free zone of the same length. It is shown that for a given misfit strain and inclusion shape, the enhancement of k I and Δu is controlled Electronic supplementary material The online version of this article (https://doi.

A unified theory captures both brittle and ductile fracture. The fracture toughness is proportional to the applied stress squared and the length of the crack. For purely brittle solids this criterion is equivalent to Griffith's theory. In other cases it provides a theoretical basis for the Irwin-Orowan formula. For purely ductile solids the theory makes direct contact with the Bilby-Cottrell-Swinden model. The toughness is highest in ductile materials because the shielding dislocations in the plastic zone provide additional resistance to crack growth. This resistance is the force opposing dislocation motion, and the Peach-Koehler force overcomes it. A dislocationfree zone separates the plastic zone from and the tip of the crack. The dislocation-free zone is finite because molecular forces responsible for the cohesion of the surfaces near the crack tip are not negligible. At the point of crack growth the length of the dislocation-free zone is constant and the shielding dislocations advance in concert. As in Griffith's theory the crack is in unstable equilibrium. The theory shows that a dimensionless variable controls the elastoplastic behaviour. A relationship for the size of the dislocation-free zone is derived in terms of the macroscopic and microscopic parameters that govern the fracture.