Monte Carlo-discrete dislocation dynamics: A technique for studying the formation and evolution of dislocation structures

A novel Monte Carlo (MC) based solver for discrete dislocation dynamics (DDD) has been developed, by which dislocation lines are inserted to the system in succession subject to a user-defined acceptance criterion. Utilizing this solver, dislocation structure evolution can be examined in a controlled fashion that is not possible using conventional DDD methods. The outcomes of the MC-DDD simulations establish for the first time that dislocation wall structures can adopt a characteristic width that naturally arises from elastic interactions within the network. This characteristic width does not alter as additional dislocation lines are inserted and the density in the wall increases, meaning it is independent of the mean dislocation spacing. However, the wall width is influenced by the acceptance criterion used during MC steps; the wall gets thinner as the interactions within the wall become more attractive. Finally, we demonstrate that algorithmic aspects of MC-DDD simulations can provide insights into structure evolution. Overall, this new MC-DDD technique will allow systematic studies of dislocation structures, providing unprecedented insight into the underlying mechanics.

FFT based approaches in micromechanics: fundamentals, methods and applications

FFT methods have become a fundamental tool in computational micromechanics since they were first proposed in 1994 by H. Moulinec and P. Suquet for the homogenization of composites. From that moment on many dierent approaches have been proposed for a more accurate and efficient resolution of the non- linear homogenization problem. Furthermore, the method has been pushed beyond its original purpose and has been adapted to many other problems including continuum and discrete dislocation dynamics, multi-scale modeling or homogenization of coupled problems as fracture or multiphysical problems. In this paper, a comprehensive review of FFT approaches for micromechanical simulations will be made, covering the basic mathematical aspects and a complete description of a selection of approaches which includes the original basic scheme, polarization based methods, Krylov approaches, Fourier-Galerkin and displacement-based methods. The paper will present then the most relevant applications of the method in homogenization of composites, polycrystals or porous materials including the simulation of damage and fracture. It will also include an insight into synergies with experiments or its extension towards dislocation dynamics, multi-physics and multi-scale problems. Finally, the paper will analyze the current limitations of the method and try to analyze the future of the application of FFT approaches in micromechanics.

The Effect of Multipoles on the Elasto-Plastic Properties of a Crystal: Theory and 3D Dislocation Dynamics Modeling

Plastic deformation in metals is dominated by the interactions among dislocations and other defects inside the crystal. A large number of dislocation multipoles (dipoles, tripoles, quadrupoles, etc.) can form during plastic deformation. Depending on the relative position and the orientation of the dislocations, interactions in and between multipoles can change the elastoplastic properties of a material. The authors of this article investigate the effect of dislocation multipoles on the elastoplastic properties of a material. This is performed under different multipole configurations (i.e. the distance between active glide planes and the signs of the dislocations) using a 3D Discrete Dislocation Dynamics (DDD) code. The simulations show that multipoles exhibit a hardening/softening effect when the sign of the dislocations involved is the same, and a hardening effect only when the dislocations are of opposite sign to nearby ones. The distance between the two neighboring dislocations was also affecting the proportional limit for the material. Such hardening or flow stress results, as in this study, can be incorporated into larger-scale modeling work.