Discrete dislocation dynamics simulations have been generally limited to modeling systems described by isotropic elasticity. Effects of anisotropy on dislocation interactions, which can be quite large, have generally been ignored because of the computational expense involved when including anisotropic elasticity. We present a different formalism of dislocation dynamics in which the dislocations are represented by the deformation tensor, which is a direct measure of the slip in the lattice caused by the dislocations and can be considered as an eigenstrain. The stresses arising from the dislocations are calculated with a fast Fourier transform (FFT) method, from which the forces are determined and the equations of motion are solved. Use of the FFTs means that the stress field is only available at the grid points, which requires some adjustments/regularizations to be made to the representation of the dislocations and the calculation of the force on individual segments, as is discussed hereinafter. A notable advantage of this approach is that there is no computational penalty for including anisotropic elasticity. We review the method and apply it in a simple dislocation dynamics calculation.

Grain growth experiments were performed on Inconel (TM) 718 to investigate the possible correlation of the annealing twin density with grain size and with annealing temperature. Those experiments were conducted at different temperatures in the delta supersolvus domain and under such conditions that only capillarity forces were involved in the grain boundary migration process. In the investigated range, there is a strong inverse correlation of the twin density with the average grain size. On the other hand, the twin density at a given average grain size is not sensitive to annealing temperature. Consistent with previous results for pure nickel, the twin density evolution in Inconel (TM) 718 is likely to be mainly controlled by the propagation of the pre-existing twins of the growing grains; i.e., the largest ones of the initial microstructure. Almost no new twin boundaries are created during the grain growth process itself. Therefore, the twin density at a given average grain size is mainly dependent on the twin density in the largest grains of the initial microstructure and independent of the temperature at which grains grow. Based on the observations, a mean field model is proposed to predict annealing twin density as a function of grain size during grain growth.

Abstract Three-dimensional crystal orientation fields of a copper sample, characterized before and after shock loading using High Energy Diffraction Microscopy, are used for input and validation of direct numerical simulations using a Fast Fourier Transform (FFT)-based micromechanical model. The locations of the voids determined by X-ray tomography in the incipiently-spalled sample, predominantly found near grain boundaries, were traced back and registered to the pre-shocked microstructural image. Using FFT-based simulations with direct input from the initial microstructure, micromechanical fields at the shock peak stress were obtained. Statistical distributions of micromechanical fields restricted to grain boundaries that developed voids after the shock are compared with corresponding distributions for all grain boundaries. Distributions of conventional measures of stress and strain (deviatoric and mean components) do not show correlation with the locations of voids in the post-shocked image. Neither does stress triaxiality, surface traction or grain boundary inclination angle, in a significant way. On the other hand, differences in Taylor factor and accumulated plastic work across grain boundaries do correlate with the occurrence of damage. Damage was observed to take place preferentially at grain boundaries adjacent to grains having very different plastic response.