Formation of grain boundaries in ductile single crystals at finite plastic deformations

• The theory of formation of grain boundaries in ductile single crystals is proposed.
• Governing equations and jump conditions are derived for the energy minimizers admitting grain boundaries as surfaces of discontinuity.
• Energy minimizing sequences having piecewise constant plastic and elastic deformation in two examples of ductile single crystals deforming in plane strain simple shear or uniaxial compression are found.
• The number of lamellae is estimated by minimizing the energy of grain boundaries plus the energy of boundary layers.

The theory of formation of grain boundaries in ductile single crystals is proposed within the nonlinear continuum dislocation theory (CDT), where grain boundaries are interpreted as surfaces of weak discontinuity in placement but strong discontinuity in plastic slip. The set of governing equations and jump conditions are derived for the energy minimizers admitting such surfaces of discontinuity from the variational principle. By constructing energy minimizing sequences having piecewise constant plastic and elastic deformation in two examples of ductile single crystals deforming in plane strain simple shear or uniaxial compression, it is shown that the formation of lamellae structure with grain boundaries is energetically preferable. The number of lamellae is estimated by minimizing the energy of grain boundaries plus the energy of boundary layers.