A time-dependent Ginzburg-Landau model of plastic deformation in
two-dimensional solids is presented. The fundamental dynamic variables are the
displacement field \bi u and the lattice velocity {\bi v}=\p {\bi u}/\p t.
Damping is assumed to arise from the shear viscosity in the momentum equation.
The elastic energy density is a periodic function of the shear and tetragonal
strains, which enables formation of slips at large strains. In this work we
neglect defects such as vacancies, interstitials, or grain boundaries. The
simplest slip consists of two edge dislocations with opposite Burgers vectors.
The formation energy of a slip is minimized if its orientation is parallel or
perpendicular to the flow in simple shear deformation and if it makes angles of
±π/4 with respect to the stretched direction in uniaxial stretching.
High-density dislocations produced in plastic flow do not disappear even if
the flow is stopped. Thus large applied strains give rise to metastable,
structurally disordered states. We divide the elastic energy into an elastic
part due to affine deformation and a defect part. The latter represents degree
of disorder and is nearly constant in plastic flow under cyclic straining.Comment: 16pages, Figures can be obtained at
http://stat.scphys.kyoto-u.ac.jp/index-e.htm
