Crystal plasticity model of shear and kink bands–energetic approach

Abstract

We present a continuum crystal plasticity model of a lamellar deformation substructure of shear and kink bands. An evolutionary problem for the development of a spontaneous structural inhomogeneity is formulated in the framework of energetic solutions. Conti and Theil proved that in the case of an isothermal single-slip crystal, rigid plasticity with no hardening lamellaea form an optimal microstructure. Moreover, their model predicts the existence of a boundary layer which accommodates the lamellar substructure to displacement boundary conditions. It is suggested that the width of the shear and kink bands is a compromise: the minimization of bulk energy tends to decrease their size, while the energy of the band interfaces or the inner structure of the bands opposes this tendency.

Keywords:

• crystal plasticity
• energetic approach
• plastic deformation
• plasticity of crystals

Acknowledgements

This work was supported by the grants VZ6840770021 (MŠMT ČR) and A100750802 (GAAV ČR).

Notes

†Currently with AREVA NP, Erlangen, Germany

Note

1. In detail: , where is the rate of plastic distortion in the reference lattice, is the rate of plastic distortion rotated with the lattice into the current configuration, and is the lattice spin.

Additional information

Notes on contributors

Radan Sedláček†

†Currently with AREVA NP, Erlangen, Germany