Multiphase particle-size-grouping model of precipitation and its application to thermal processing of microalloyed steel

The formation and presence of second phase precipitates greatly influence the properties of metal alloys, and varies with alloy composition and temperature history. In microalloyed steel, for example, precipitates may lead to beneficial grain refinement or detrimental transverse surface cracks. A comprehensive set of models has been developed to determine precipitate formation during metal processing. They include an equilibrium precipitation model and kinetic models for single-phase and multiphase precipitation, and are applied together with heat transfer, grain growth, and other models to predict precipitation and related microstructural parameters and properties during thermal processing of microalloyed steel. First, the equilibrium precipitation model predicts the equilibrium concentrations of dissolved elements and precipitated phases as a function of the steel composition and temperature, which is used to provide the supersaturation or driving force for the kinetic model.Next, a kinetic growth model based on population balance and Particle-Size-Grouping (PSG) method gives the volume fraction and size distribution of precipitates evolving with time. The method features geometrically-based thresholds between each size group, reasonable estimates of border values in order to accurately include intra-group and inter-group diffusion, and an efficient implicit solution method to integrate the equations. The kinetic model is generalized to predict multiphase precipitation to incorporate more realistic heterogeneous complex/mixed precipitates. The corresponding population balance and PSG equations are developed, including mutually-exclusive precipitates and mutually-soluble precipitates. From the results, an austenite grain growth model is applied to predict austenite size evolution under the influence of pinning precipitates. The three models are each extensively validated, including the equilibrium model matching with analytical solutions, the commercial package JMatPro, and experimental measurements of precipitate amounts, types and compositions. The kinetic models are validated by matching with exact solutions of the population balance equations, with each other for special cases, and with experimental measurements of precipitated fraction and size evolution, and a Precipitation-Temperature-Time diagram. By taking advantage of the temperature, phase-fractions, and segregated-composition histories from previous models, the models developed in this work are finally applied together to predict precipitate formation and grain growth at different locations during continuous casting of steel slabs for realistic steel grades and casting conditions. The models track the evolution of the amount, composition, and size distribution of precipitates. In addition, austenite grain size, ductility and estimated susceptibility to transverse cracks, are expected to be explained by the microstructure of particle-containing materials in processes. The results are important to control steel grades and cooling practice to assure product quality, and present new insights into precipitate formation and transverse cracks during continuous casting. In this work, the nucleation, growth and coarsening are modeled as a continuous competing process, and all of the model parameters have physical significance and no fitting parameters are introduced. Although the current work focuses on precipitation in microalloyed steels, if the necessary database is available, the current models can be applied to simulate diffusion-driven precipitation in any materials and processes