We have developed static discrete dislocation-based Boundary Element Method simulations to understand the mechanics of complex crack geoetries at the microstructural length scale. Earlier work made use of closed form analytical solutions for the continuous distribution of dislocation density needed to represent a crack and the associated plastic zone at the crack tip. This had the virtue of rapid calculation but the very significant limit in that only very simple geometries could be considered.
The boundary elements consist of dislocation dipoles and a central stress evaluation point. The Burgers vectors of the dipoles are solved for by imposing the stress free boundary conditions for BEM along the crack, and fixed yield stress (in shear) for BEMs representing slip bands.
We have evaluated multiply kinked and branched cracks that are often found in intergranular stress corrosion cracking. A monte-carlo approach was used to evaluate IGSCC crack growth rate laws by fitting the distribution of short crack depths coming from multiple instantiations of the simulation to that found experimentally.
