Protrusions and retrusions typically form on recrystallizing boundaries and thus the boundaries often appear rough. Characterization of the boundary roughness is necessary in order to evaluate the effects of protrusions and retrusions on boundary migration. In the current work, a variable termed area integral invariant is employed to provide quantitative information of individual protrusions/retrusions on boundaries surrounding two selected recrystallizing grains in partly recrystallized copper as well as of the overall roughness of the boundaries.
IntroductionDuring the past few years, in-situ 3-dimensional X-ray diffraction (3DXRD) experiments have been used to observe the growth of recrystallizing grains in the bulk of deformed metals [1,2]. It has been revealed that the nuclei do not grow in a homogeneous manner with constant moving speed as described in classic models, but occur with variations at the local scale: most boundary segment move in a jerky stop-go mode, with locally large protrusions and retrusions forming and disappearing as the boundary migrates [1, 2]. Exsitu electron backscattered diffraction (EBSD) and electron channeling contrast (ECC) studies of local boundary migration have also revealed similar migration behavior [3][4][5]. Quantitative characterizations of local protrusions and retrusions have shown the importance of these local structural variations [4,5]. Results from phase field simulations of boundary migration during recrystallization have shown that the protrusions and retrusions forming on the migrating boundaries may contribute an additional driving force resulting from the boundary curvature and change the migration kinetics at both the local and global scale [6]. Protrusions and retrusions have been observed in both high-purity metals and alloys, also under different thermal-mechanical processing conditions [7][8][9]. For analysis of the effects of protrusions/retrusions on the local boundary migration kinetic or for better knowledge of the effects of macro parameters such as purity of the metal, annealing temperature, deformation strain etc. on the formation of protrusions/retrusions, statistical quantification of protrusions/retrusions on many recrystallization boundaries in partly