A Continuum Model for Dislocation Pile-up Problems

A 2-d dislocation pile-up model is developed to solve problems with arrays of edge dislocations on one or multiple slip planes. The model developed in this work has four unique features: 1) As a continuum mechanics model, it captures the discrete behaviors of dislocations including the region near pile-up boundaries. 2) It allows for a general distribution of dislocations and applied boundary conditions. 3) The computational complexity does not quadratically scale with increased number of dislocations. 4) The effect of anisotropy and stacking fault energy can be naturally modeled. Pile-ups against a lock under shear load are extensively investigated, which shows the dependence of near-lock piles distribution on the total number of dislocations. The stacking fault energy effect is found to be positively correlated to the length of an equilibrated pileup. The stress intensity near a bi-metallic interface is studied for both isotropic material and anisotropic materials. The model is validated by reproducing the solutions of problems for which analytical solutions are available. More complicated phenomena such as interlacing and randomly distributed dislocations are also simulated.