The application of discrete dislocation dynamics methods to study materials with realistic yield stresses and realistic cohesive strengths required new algorithms. Here, the limitations of the standard algorithms were discussed, and then new algorithms to overcome these limitations were presented and their successes demonstrated by example. In particular, several improvements to the existing two-dimensional-DD/CZ methodology were implemented which significantly improved the ability to model materials having realistic material properties. These enhancements were a gradient correction in the computation of the dislocation velocity that completely eliminates instabilities and oscillations in the standard forward-Euler approach and also eliminates the need for both an artificial dislocation cut-off velocity and an under-relaxation procedures present in earlier DD implementations. A modified dislocation nucleation algorithm where the Burger’s vector and position of the ‘latent’ dislocation dipole varied linearly with the nucleation time, eliminated spurious jumps in the boundary displacements and stresses. Use of the O’Day-Curtin superposition scheme to correctly capture dislocation interactions with the nonlinear cohesive zone eliminated instabilities in problems with large (realistic) cohesive strengths. A ‘moving mesh method’ captured a priori arbitrary amounts of crack growth while retaining the required fine mesh resolution near the crack tip, which was achieved with almost no additional computational cost. With these new methods, the stability, accuracy and robustness of the discrete dislocation methodology for the study of deformation and fracture was significantly improved.

New Algorithms for Discrete Dislocation Modeling of Fracture. S.S.Chakravarthy, W.A.Curtin: Modelling and Simulation in Materials Science and Engineering, 2011, 19[4], 045009