Stress correlations of dislocations in a double-pileup configuration: a continuum dislocation density approach – complas XII

Dislocation motion in the crystal lattice of materials is the basis for macroscopic plasticity. While continuum models for describing the role of dislocations in plasticity have existed for decades, only recently have the mathematical tools become available to describe ensembles of moving, oriented lines. These tools have allowed for the creation of a Continuum Dislocation Dynamics (CDD) theory describing a second-order dislocation density tensor, a higher order analog of the classical dislocation density tensor, and its evolution in time. In order to reduce the computational complexity of the theory, a simplified theory has also been developed, which more readily allows for a numerical implementation, useful for describing larger systems of dislocations. In order to construct a self-consistent implementation, several issues have to be resolved including calculation of the stress field of a system of dislocations, coarse graining, and boundary values. The present work deals with the implementation including treatment of the near- and far-field stresses caused by the dislocation density tensor as well as boundary value considerations. The implementation is then applied to a few simple benchmark problems, notably the double pileup of dislocations in 1D. Applications to more general problems are considered, as well as comparisons with analytical solutions to classical dislocation problems. Focus is placed on problems where analytical solutions as well as simulations of discrete dislocations are known which act, along with experimental results, as the basis of comparison to determine the validity of the results