Abstract One typically characterizes the transformation kinetics of a parent phase, α, into a single phase, β, by measuring the volume fraction transformed, V V β, against time. Sometimes one also reports the interfacial area density between the new and the parent phase, S V α β, against the volume fraction transformed. S V α β is a dynamic interface. It migrates as the growth of the new phase takes place. Interfaces between transformed phases might be called static interfaces. These may be present before transformation starts, for example, grain boundaries of a polycrystalline parent phase. Alternatively, static interfaces, S V β β , may appear during the transformation because of impingement. Therefore, one may better understand the microstructural evolution following the behavior of the volume fraction, dynamic and static interfaces. A more complicated situation occurs if the parent phase transforms into two or more product phases, for example, α→β,γ. In this work, we apply parameters to describe the transformation of a parent phase into a single phase, the contiguity and the dispersion, to the situation in which the parent phase transforms into two or more phases. We tested these parameters against computer simulations and concluded that they combine a good description of the behavior of the simulated transformations and simplicity.

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.

This paper generalizes previous work of Rios and Villa on spherical growth. The generalized equation applies to nucleation of ellipsoids according to an inhomogeneous Poisson point process. Microstructural evolution in three dimensions of nucleation and growth transformations of ellipsoids is simulated using the causal cone method. In the simulation, nuclei are located in space according to an inhomogeneous Poisson point process. The transformed regions grow with prolate and oblate ellipsoidal shapes. The ellipsoids have their corresponding axes parallel. The simulation and the exact analytical solution are in excellent agreement. Microstructures generated by the computer simulation are displayed. From these generated microstructures one can obtain the contiguity. In the contiguity against volume fraction plot, data from the sphere and all ellipsoids fall on the same curve. The contiguity curve for nucleation according to an inhomogeneous Poisson point process falls above the contiguity curve for nucleation according to a homogeneous Poisson point process. This behavior indicates that nucleation according to an inhomogeneous Poisson point process introduced a nucleus clustering effect.

Computer simulation of simultaneous evolution of individual texture components during recrystallization of an IF steel is carried out. A new methodology has been developed that takes as its starting point experimental data of each texture component evolving during recrystallization. In particular, Magnusson et al. data on IF steel was analyzed in a previous work with the help of the exact analytical tools developed by Rios and Villa for simultaneous transformations. From this analysis parameters such as number of nuclei of each texture component per unit of volume could be obtained and were employed as input for the present computer simulation. From this input 3-d microstructures could then be generated. The methodology proposed here combines experimental data, exact analytical methods and computer simulation and may be employed to extract the maximum information from the experimental data.

Microstructural evolution in three dimensions of nucleation and growth transformations is simulated by means of cellular automata (CA). In the simulation, nuclei are located in space according to a heterogeneous Poisson point processes. The simulation is compared with exact analytical solution recently obtained by Rios and Villa supposing that the intensity is a harmonic function of the spatial coordinate. The simulated data gives very good agreement with the analytical solution provided that the correct shape factor for the growing CA grains is used. This good agreement is auspicious because the analytical expressions were derived and thus are exact only if the shape of the growing regions is spherical.

Recrystallization of an iron single crystal was reported in detail by Vandermeer and Rath (V&R). We present predictions of recrystallization based on cellular automata (CA) simulations, and compare them with the data and analysis from V&R's study. Agreement is found between our CA simulations and V&R's results, provided that the CA simulations were carried out using a sufficient dynamic range for time, precision spatial dimensionalization, and accommodation of grain shape effects inherent in CA techniques.

Cellular automata simulation in three dimensions is carried out to simulate microstrutural evolution for nuclei distribution ranging from a periodic arrangement to clusters of nuclei. The effect of clustering in three dimensions is found to be much more difficult to detect using conventional microstructural path analysis than in two dimensions. Microstructural path equations fit simulated data well, even when the nuclei are non-randomly located. However, the parameters obtained by means of this fitting lead to erroneous time dependent velocities. Therefore, measuring a descriptor that is sensitive to non-randomness such as the contiguity is even more important in three than in two dimensions.