This article discusses the fundamental aspects of phase-field microstructure modeling. It describes the evolution of microstructure modeling, including nucleation, growth, and coarsening. The article reviews two approaches used in the modeling nucleation of microstructure: the Langevin force approach and explicit nucleation algorithm. Calculation of activation energy and critical nucleus configuration is discussed. The article presents the deterministic phase-field kinetic equations for modeling growth and coarsening of microstructure. It also describes the material-specific model inputs, chemical free energy and kinetic coefficients, for phase-field microstructure modeling. The article provides four examples that illustrate some aspects of phase-field modeling.

This article focuses on the general internal state variable method, and its simplification, for single-parameter models, in which the microstructure evolution may be treated as an isokinetic reaction. It explains that isokinetic microstructure models are applied to diffusional transformations in fusion welding, covering particle dissolution, growth, and coarsening of precipitates in the heat-affected zone. The article discusses the versatility of the internal state variable approach in modeling of nonisothermal transformations for various materials and processes. It describes the process models applied to predict the microstructure evolution in Al-Mg-Si alloys during multistage thermal processing involving heat treatment and welding. The article also provides information on the microstructure models exploited in engineering design to optimize the load-bearing capacity of welded aluminum components.

This article focuses on the modeling of microstructure evolution during thermomechanical processing in the two-phase field for alpha/beta and beta titanium alloys. It also discusses the mechanisms of spheroidization, the coarsening, particle growth, and phase decomposition in titanium alloys, with their corresponding equations.

Spray casting, also known as spray forming, is a niche casting process for the manufacture of preforms. This article lists commercial examples of alloys manufactured by spray casting and provides sequential steps of the spray casting process. Gas atomization is a chaotic, stochastic process that always produces a wide range of droplet diameters. The article schematically illustrates a typical log-normal droplet diameter probability density distribution on a mass or volume basis obtained by gas atomization. It also explains the changes in solid fraction during the spray casting process as a function of axial distance from the point of droplet atomization. The article concludes with information on the occurrence of macrosegregation and coarsening in spray cast preforms.

Recovery, recrystallization, and grain growth are the stages that a cold worked metal undergoes when it is annealed. This article describes the changes in the structure and properties that occur on annealing a cold-worked metal. It summarizes the experimental recrystallization studies by Burke and Turnbull with six laws of recrystallization. Applications of these laws of recrystallization are discussed in detail with examples. The article reviews the classification of grain growth according to the growth behavior of grains, namely, normal or continuous grain growth and abnormal or discontinuous grain growth. The latter has also been termed exaggerated grain growth, coarsening, or secondary recrystallization.