A thermodynamic theory for dislocation cell formation and misorientation in metals

Expressions for obtaining the dislocation cell size and misorientation angle evolution as functions of strain, strain rate and temperature are presented. The basis of the theory is to express the cell formation energy as a set of dislocation partials, which is equated to the energy of the dislocation forest in the non-cellular material plus the dislocation slip energy to form cellular structures. The latter is expressed in terms of the statistical entropy for dislocation slip. The Young–Laplace equation is applied to obtain the cell misorientation angle at stages III and IV of deformation. This equation is also applied to obtain an expression for the dislocation density evolution at stage IV. The theory is applied to the deformation of Cu, Al and Ni, from low to high temperature conditions and at various strain rates, describing well the cell properties and the corresponding stress–strain curves.