Misorientation and crystal lattice distortions as the source of driving force for grain boundary movement

A thermodynamic theory of the movement of misorientation surface is considered. This theory is based on the tensorial measures of elastic-plastic distortions and curvatures (contortions). The crystal plasticity is described by vector constitutive equations stated for dislocation movement and for grain boundary migration. The compatibility equations across the discontinuity surface together with the well-known balance laws have been used to find the driving forces acting on the surface. Using the derived relations the constitutive modelling of the movement of defects is considered. The constitutive equations presented take into account the elastic strain, dislocation density and temperature. Special attention is given to the dependency of free energy on the misorientation vector on the grain boundary.