Abstract
The Continuum Dislocation Dynamics (CDD) theory and the Discrete Dislocation Dynamics (DDD) method are compared based on concise mathematical formulations of the coarse graining of discrete data. A numerical tool for converting from a discrete to a continuum representation of a given dislocation configuration is developed, which allows to directly compare both simulation approaches based on continuum quantities (e.g. scalar density, geometrically necessary densities, mean curvature). Investigating the evolution of selected dislocation configurations within analytically given velocity fields for both DDD and CDD reveals that CDD contains a surprising number of important microstructural details.
Highlights
Applications with high densities and/or high accumulated plastic strains benefit from continuum dislocation dynamics models (e.g. [37,38,39,40,41])
We developed a systematic method for averaging geometrical properties of discrete dislocation lines which allows for a direct comparison of discrete and continuum descriptions of evolving dislocation microstructures
Particular care was taken to formulate the numerical approximation such that discrete and continuous formulations are at all times consistent with each other
Summary
The computational cost of DDD scales with the number of dislocations considered and is computationally expensive when it comes to large numbers of interacting dislocations (large referring e.g. to a density of ⩾1013m−2 in a volume of ⩾(10 μm)3) To overcome these limitations, one might seek continuous density-based descriptions as alternative to the representation of dislocations as discrete objects. Reducing dislocation microstructure to distinct ‘types’ of e.g. geometrically necessary and statistically stored dislocations (GNDs and SSDs) allows strain gradient based continuum methods [21,22,23] to become independent of the number of interacting dislocations These approaches result in a substantial gain in terms of tractable length and time scales which makes them interesting for engineering applications. Applications with high densities and/or high accumulated plastic strains benefit from continuum dislocation dynamics models (e.g. [37,38,39,40,41])
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