Abstract
Continuum models of dislocation plasticity require constitutive closure assumptions, e.g., by relating details of the dislocation microstructure to energy densities. Currently, there is no systematic way for deriving or extracting such information from reference simulations, such as discrete dislocation dynamics (DDD) or molecular dynamics. Here, a novel data-mining approach is proposed through which energy density data from systems of discrete dislocations can be extracted. Our approach relies on a systematic and controlled coarse-graining process and thereby is consistent with the length scale of interest. For data-mining, a range of different dislocation microstructures that were generated from 2D and 3D DDD simulations, are used. The analyses of the data sets result in energy density formulations as a function of various dislocation density fields. The proposed approach solves the long-standing problem of voxel-size dependent energy calculation during coarse graining of dislocation microstructures. Thus, it is crucial for any continuum dislocation dynamics simulation.
Highlights
Plasticity in crystalline materials originates from the collective movement of dislocations
This is because the dislocation microstructure mainly consists of statistically stored dislocations (SSDs), the coarse graining process can result in a complete loss of the dipole information due to the fact that the dipole has no contribution to α1i 3 in (29), i.e., no long range stress, no contribution to the strain energy density
It can be seen that for dislocation microstructure created through tension, the energy contribution of the geometrically necessary dislocations (GND) term decreases with increasing voxel sizes: when the voxel size is larger than 40b, the contribution is negligible compared to the dislocation density term
Summary
Plasticity in crystalline materials originates from the collective movement of dislocations. The so-called continuum dislocation dynamics (CDD) proposed by Hochrainer and coworkers [12, 13, 14] has introduced dislocation density and density-like variables along with their evolution equations which advanced the development of a general continuum description of 3D curved dislocations The shortcoming of this theory up to now is that no systematic approach for relating the averaged dislocation microstructure to the velocity, by which dislocation densities move, exists. Our approach solves the long-standing problem of the “mesh-dependency” during the coarse graining of dislocation microstructures: given the desired voxel size, our results are able to recover the lost, mesh-dependent strain energy density during the coarse graining, provide the accurate strain energy density that is effectively independent of the chosen voxel size This is an important prerequisite for the “dynamic closure” of a continuum dislocation dynamics framework. Data-mining of dislocation microstructures: concepts for coarse-graining of internal energies
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