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A novel dislocation-density-based crystal plasticity model for nanocrystalline face-centered cubic metals is developed based on the thermally-activated mechanism of dislocations depinning from grain boundaries. Dislocations nucleated from grain boundary dislocation sources are assumed to be the primary carriers of plasticity in the nanocrystals. The evolution of the dislocation density thereby involves a competition between the nucleation of dislocations from grain boundary defect structures, such as ledges, and the absorption of dislocations into the grain boundary via diffusion processes. This model facilitates the simulation of plastic deformation in nanocrystalline metals, with consideration of the initial microstructure resulting from a particular processing method, to be computed as a direct result of dislocation-mediated plasticity only. The exclusion of grain boundary-mediated plasticity mechanisms in the formulation of the crystal plasticity model allows for the exploration of the fundamental role dislocations play in nanocrystalline plasticity. The combined effect of average grain size, grain size distribution shape, and initial dislocation density on the mechanical performance and strain-rate sensitivity are explored with the model. Further, the influence of the grain boundary diffusivity on post-yielding strain-hardening behavior is investigated to discern the impact that the choice of processing route has on the resulting deformation response of the material.
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Transmissibility in Interactive Nanocomposite Diffusion: The Nonlinear Double-Diffusion Model
Model analogies and exchange of ideas between physics or chemistry with biology or epidemiology have often involved intersectoral mapping of techniques. Material mechanics has benefited hugely from such interpolations from mathematical physics where dislocation patterning of plastically deformed metals and mass transport in nanocomposite materials with high diffusivity paths such as dislocation and grain boundaries, have been traditionally analyzed using the paradigmatic Walgraef-Aifantis (W-A) double-diffusivity (D-D) model. A long standing challenge in these studies has been the inherent nonlinear correlation between the diffusivity paths, making it extremely difficult to analyze their interdependence. Here, we present a novel method of approximating a closed form solution of the ensemble averaged density profiles and correlation statistics of coupled dynamical systems, drawing from a technique used in mathematical biology to calculate a quantity called the basic reproduction number R0, which is the average number of secondary infections generated from every infected. We show that the R0 formulation can be used to calculate the correlation between diffusivity paths, agreeing closely with the exact numerical solution of the D-D model. The method can be generically implemented to analyze other reaction-diffusion models.
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- Award ID(s):
- 2015317
- PAR ID:
- 10517579
- Publisher / Repository:
- Frontiers
- Date Published:
- Journal Name:
- Frontiers in Applied Mathematics and Statistics
- Volume:
- 8
- ISSN:
- 2297-4687
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3389/fams.2022.852040
