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.

On the Origin of Plastic Deformation and Surface Evolution in Nano-Fretting: A Discrete Dislocation Plasticity Analysis

Discrete dislocation plasticity (DDP) calculations were carried out to investigate a single-crystal response when subjected to nano-fretting loading conditions in its interaction with a rigid sinusoidal asperity. The effects of the contact size and preceding indentation on the surface stress and profile evolution due to nano-fretting were extensively investigated, with the aim to unravel the deformation mechanisms governing the response of materials subjected to nano-motion. The mechanistic drivers for the material’s permanent deformations and surface modifications were shown to be the dislocations’ collective motion and piling up underneath the contact. The analysis of surface and subsurface stresses and the profile evolution during sliding provides useful insight into damage and failure mechanisms of crystalline materials subject to nano-fretting; this can lead to improved strategies for the optimisation of material properties for better surface resistance under micro- and nano-scale contacts.