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Composite Grain Model
Hardening Due to Grain Boundaries
A polycrystal plasticity model is used to predict the unique rolling texture of Cu/Nb nanostructured multilayers. The interface between the Cu and Nb layers is accounted for by computing the aggregate response of composite grains using a viscoplastic self-consistent (VPSC) scheme, which satisfies the compatibility and equilibrium requirements. An unconventional interface hardening effect involving edge dislocations is created by the symmetric slip conditions imposed by layer confinement.
Composite Grain Model
Rolling Textures
Rolling textures of Cu/Nb multilayers after 50% reduction in thickness. (a) X-ray diffraction pole figures, (b) Pole figures using composite grain model with assumption of latent hardening.
Hardening Effect Due to Interface Dislocation Reactions
Conclusions:
The interface hardening and relaxation of shear strains at the boundary provide a continuum approximation of the detailed mechanism of slip transfer.
The interaction between the glide and interface dislocations promotes hardening on slip systems responsible for the rotation of the Cu and Nb crystals during rolling.
This results in a reduction of the rotation of the crystal, leading to partial preservation of the interface relation.
Boundaries as Sources of Mobile Dislocations
The challenge is to predict the response of the fine grained material, especially the appearance of the plateau just beyond yielding.
The importance of the annealing twins in controlling the initial mechanical response was revealed by the in-situ TEM experiments.
Annealing twins serve as a source for both glissile dislocations and nucleation of deformation twins.
Effects of annealing twins were taken into account in constructing the composite grain VPSC plasticity model.
Each composite grain consists of matrixtwin lamellar structure.
Stress-Strain Response of High Purity Ag with Two Grain Sizes
As-Received Sample
Annealing twin that contains a high density of dislocations.
Deformed to e = 0.001, just beyond the proportional limit
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Conclusions:
Consideration of the evolution of mobile and immobile 'forest' dislocation density improves the model prediction of system hardening.
Excellent agreement between model predictions and experimental stressstrain curves, including the region of the plateau.
Future Work:
Details of the dislocationtwin and twintwin interactions have still to be evaluated and included in the model.
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