The control volume X for the analys

The control volume X for the analysis of cracking during solidification, which occurs along the grain boundary, is shown in Fig. 4. X is the space, not the liquid, that is between two neighboring columnar dendritic grains and that is inside the dotted box of width w and thickness Dz, where Dz is the thickness of a thin slice of the grains normal to the growth axis z (see Fig. 1). For the purpose of discussion, the grain on the left is considered stationary while the one on the right moves under tension in the lateral direction at the local speed of Vlocal