Last modified: 2016-06-05
Abstract
At the mesoscale, plastic deformation is facilitated by the motion of dislocations and is strongly dependent on the local crystallographic orientation. In polycrystalline materials, the mismatch between adjacent crystals inhibits the inter-granular dislocation mobility, reduces plastic strain homogeneity and significantly influences the hardening and softening stress-strain behavior. Studies have shown that inter-granular slip transmission is possible at high stresses, involving a complex combination of dislocation absorption, junction formation and nucleation interactions with the intrinsic grain boundary dislocations. These effects are thought to contribute significantly to the behavior of dislocation pile-ups and could explain the predominant mechanisms influencing the properties of nanocrystalline materials. Modelling the mesoscale microstructure-property relationships, observed in real materials, would be very useful to guide future developments in the field of grain boundary engineering.
Dislocation dynamics (DD) simulations are a promising framework for computational modelling to provide insights about phenomena that can only be explained from the intermediate scale between atomistic and macro scales. However, a robust framework for modelling dislocation interactions with internal microstructure such as grain boundaries (GBs) has yet to be achieved for 3D models of DD at the meso-scale. Atomistic studies have shown that GBs cannot be assumed to act purely as an inertial damper between two regions with identical crystallography [1], or as an impenetrable barrier [2, 3]. The primary aim of the present study was to establish a sufficiently ‘generic’ framework to enable the modelling of various GB structures, polycrystal geometries and crystallographic orientations. The framework described is effective for studying GB-dislocation interactions (including inter-granular effects) and the approach for partitioning the DD simulation domain also provides an ideal future basis for modelling precipitate-hardened materials.
To achieve a robust method to differentiate between crystal regions, the present framework utilizes a mesh-based partitioning system. The simulation domain is meshed and “region IDs” are assigned to individual mesh elements. GBs are recognized as internal surfaces separating regions with different “IDs”. This flexible construction allows modeling of an arbitrary number of grains and grain orientation. Within each grain, slip systems are determined by the grain orientation, and grain boundary dislocations are created to accommodate the grain misorientation. These special dislocations are either of sessile or glissile character, depending on the grain boundary structure. The glissile structure cases allow for grain boundary sliding. An algorithm was developed to re-position any dislocations which would otherwise cross the mesh-region interface to exactly intersect the GB plane. Dislocations in the GB are constrained to glide in the GB plane. Atomistically informed criteria for “slip transmission” are implemented. In particular, ‘Slip transmission’ was enabled by simulating dislocation nucleation in the adjacent crystal if the local Peach Koehler force on the secondary slip system exceeds the threshold value (obtained with atomistic studies).
GBs contain intrinsic dislocations (GBDs) which must be considered carefully, particularly when attempting to model inter-granular interactions with mobile lattice dislocations. A dislocation extraction algorithm was used to analyze the atomistic structure of a low angle grain boundary and identify the appropriate spacing of GBDs within the DD simulation bi-crystal model. This work provides a means to study multi-grain deformation processes governed by dislocations that “pile-up” at grain boundaries, in detail beyond feasible limits of experiments.