The growth of protrusions at the boundary of a recrystallized grain

The growth of mesoscopic protrusions at originally straight and circular boundaries of two-dimensional recrystallized grains is simulated by numerical integration of a modified form of the classic kinetic equation for boundary migration. The modified equation relates the boundary velocity in a fixed direction to the boundary curvature and to a non-uniform excess strain energy density in the matrix due to dislocation walls. Calculations are made for an array of equispaced dislocation walls perpendicular to the original boundaries, which migrate, changing their shape, while absorbing the dislocation walls. The strain field of the walls is represented by a sinusoidal function. The time evolution of the boundary shape is calculated for unbounded dislocation walls and for a simplified network of staggered rows of dislocation walls. Steady and scaled regimes of the boundary shape may be reached, which are characterized in detail.