Analytical Modeling and Computer Simulation of the Transformation of Ellipsoids Nucleated on Random Parallel Planes

A considerable number of engineering materials is polycrystalline. Cahn proposed analytical expressions for transformations nucleated at the grain faces, triple junctions, and quadruple junctions. Those places are usually the places in which a new phase takes place. Cahn assumed that the new grain boundary nucleated phase grew as spheres. Nonetheless, the austenite grain boundary nucleated ferrite does not always grow as spheres. Bradley et al. demonstrated in a series of papers that a grain boundary nucleated ferrite allotriomorph is best described by an oblate ellipsoid. The reason for ellipsoidal growth is that the growth along the grain boundary plane is faster than the thickening into the austenite. Because of this, it is of interest to have analytical solutions and computer simulations of grain boundary nucleated transformations not only for spherical growth but also for ellipsoidal growth. In this work, we present a computer simulation of grain boundary nucleated transformations that grow as ellipsoids. The computer simulation results were compared with a new exact analytical expression obtained by Villa and Rios.