Dimensional analysis of the transition from columnar to equiaxial structure in aluminium-copper and lead-tin alloys

The importance of directional solidification studies is well known from systematic scientific research undertaken to understand the characteristics of the solidification of alloys. Such studies offer much information about the morphology of the interphase and the distribution of solute during solidification. Most alloys grow while attaining dendritic interphases. So considerable effort has been expended to understand the dendritic growth characteristics under controlled solidification conditions. A treatment that can quantitatively explain all the available test data and that correctly includes the physics of the problem is not yet available. This work carries out a theoretical analysis of columnar and equiaxial growth and of dendritic spacing under different conditions of solidification of the test pieces. The basic parameters that are used characterize a given alloy system. Next, we define non-dimensional parameters, that are used to formulate the final result of our problem regardless of the specific alloy being studied. We present the important functional relationships of our study, including the physical interpretation of the results obtained in the first work (CW)