Stochastic Characterization of Cast Metal Microstructure

Abstract

The major goal of this work is to provide a means to characterize the final structure of a metal that has solidified from a melt. The thermally controlled solidification of a binary alloy, nucleated at isolated sites, is described by the evolution of a probability distribution function (PDF). The relevant equation required for propagating the PDF is developed with variables for grain size and distance to nearest neighbor. The phenomena of nucleation, growth, and impingement of the grains are discussed, and used as the basis for developing rate equations that evolve the PDF. The complementary equations describing global heat and solute transfer are discussed, and coupled with the microstructure evolution equations for grain growth and PDF evolution. The full set of equations is solved numerically and results are compared with experimental data for the plutonium 1 weight percent gallium system. The three principal results of this work are: (1) The formulation of transient evolution equations for the PDF description of nucleation, growth, and impingement of a distribution of grain sizes and locations; (2) Solution of the equations to give a correlation for final average grain size as a function of material parameters, nucleation site density, and cooling rate; and (3) Solution of the equations for final distribution of grain size as a result of the initial random spatial distribution of nucleation sites.