Mode I crack analysis in single crystals with anisotropic discrete dislocation plasticity:I. Formulation and crack growth

Analyses of monotonic loading of a plane-strain mode I crack in an fcc single crystal under small-scale yielding are carried out using discrete dislocation plasticity (DDP) incorporating anisotropic elasticity. Two crystallographically symmetric crack orientations are considered where plane-strain plastic deformation is achieved by the nucleation and glide of edge dislocations on three effective slip systems. A cohesive surface ahead of the initial crack tip, endowed with the universal binding law, allows for the crack to grow. Simulations are carried out in an incremental way, using the superposition of the singular fields of dislocations in an anisotropic half-space and image fields that enforce boundary conditions and the cohesive properties. Considering a wide range of DDP parameters, i.e. source and obstacle densities, the dependence of fracture characteristics on these parameters is demonstrated. The crack growth resistance is found to be orientation-dependent and slightly smaller if the elastic anisotropy of the crystal is taken into consideration. Investigations of plastic dissipation and dislocation density evolution reveal that the dislocation structure evolving around the crack tip plays a key role in the fracture process.