GENERALIZED EQUATION OF MESOSCALE DISTRIBUTION OF SECONDARY DENDRITE ARM SPACINGS FOR STEEL CASTING

The need to predict the dendritic structure of castings to ensure their quality by modeling of casting processes remains relevant due to the complexity of the morphology of the mesoscale array of individual branches and trunks, an adequate description of the evolution of which, despite numerous attempts, has not been implemented. The paper considers and successfully solves the problem of a generalized quantitative representation of the kinetics of joint competitive crystallization of a significant array of dendritic branches on the basis of a metallographic analysis of the sizes of dendrite arm spacings by means of a statistical analysis of the samples microstructure. Some of the samples were obtained by quenching the solidifying melt. It is shown that the use of the mathematical apparatus of the lognormal distribution of random variables for a series of representative arrays of secondary dendrite arm spacings of steel castings provides an effective convolution of experimental information, the generalized parameters of which make it possible to obtain a description of the dendritic evolution. The use of the mathematical apparatus of the lognormal distribution of random variables makes it possible to carry out a computational assessment of the heterogeneity of the mesoscale dendritic structure, as well as to calculate previously inaccessible values and structure-dependent characteristics of the continuous skeleton of the solid phase and its filtration permeability when modeling the resulting shrinkage voids.