Dislocation pile-ups in bicrystals within continuum dislocation theory

Within continuum dislocation theory the plastic deformation of bicrystals under a mixed deformation of plane constrained uniaxial extension and shear is investigated with regard to the nucleation of dislocations and the dislocation pile-up near the phase boundaries of a model bicrystal with one acti...

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Bibliographic Details
Published in:International journal of plasticity 2008-11, Vol.24 (11), p.2125-2147
Main Authors: Kochmann, D.M., Le, K.C.
Format: Article
Language:English
Subjects:
A. Dislocations
A. Microstructures
A. Twinning
B. Crystal plasticity
Bicrystal
Bicrystals
Condensed matter: structure, mechanical and thermal properties
Continuums
Defects and impurities in crystals
microstructure
Dislocations
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Inelasticity (thermoplasticity, viscoplasticity...)
Linear defects: dislocations, disclinations
Mathematical analysis
Mathematical models
Nucleation
Phase boundaries
Physics
Shear
Solid mechanics
Structural and continuum mechanics
Structure of solids and liquids
crystallography
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Summary:Within continuum dislocation theory the plastic deformation of bicrystals under a mixed deformation of plane constrained uniaxial extension and shear is investigated with regard to the nucleation of dislocations and the dislocation pile-up near the phase boundaries of a model bicrystal with one active slip system within each single crystal. For plane uniaxial extension, we present a closed-form analytical solution for the evolution of the plastic distortion and of the dislocation network in the case of symmetric slip planes (i.e. for twins), which exhibits an energetic as well as a dissipative threshold for the dislocation nucleation. The general solution for non-symmetric slip systems is obtained numerically. For a combined deformation of extension and shear, we analyze the possibility of linearly superposing results obtained for both loading cases independently. All solutions presented in this paper also display the Bauschinger effect of translational work hardening and a size effect typical to problems of crystal plasticity.
ISSN:0749-6419
1879-2154
DOI:10.1016/j.ijplas.2008.03.007