This article describes the integration of thermodynamic modeling, mobility database, and phase-transformation crystallography into phase-field modeling and its combination with transformation texture modeling to predict phase equilibrium, phase transformation, microstructure evolution, and transformation texture development during heat treatment of multicomponent alpha/beta and beta titanium alloys. It includes quantitative description of Burgers orientation relationship and path, discussion of lattice correspondence between the alpha and beta phases, and determination of the total number of Burgers correspondence variants and orientation variants. The article also includes calculation of the transformation strain with contributions from defect structures developed at alpha/beta interfaces as a precipitates grow in size. In the CALculation of PHAse Diagram (CALPHAD) framework, the Gibbs free energies and atomic mobilities are established as functions of temperature, pressure, and composition and serve directly as key inputs of any microstructure modeling. The article presents examples of the integrated computation tool set in simulating microstructural evolution.

Metal transparency and interaction with X-rays have been recognized as obvious candidate principles from which methods for in situ monitoring of solidification processes could be developed. This article describes the use of X-ray imaging-based techniques to investigate interface morphology evolution, solute transport, and various process phenomena at spatiotemporal resolutions. It discusses the three viable imaging techniques made available by synchrotron radiation for the real-time investigation of solidification microstructures in alloys. These include two-dimensional X-ray topography, two-dimensional X-ray radiography, and ultra-fast three-dimensional X-ray tomography.

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.

The solidification of hypoeutectic cast iron starts with the nucleation and growth of austenite dendrites, while that of hypereutectic iron starts with the crystallization of primary graphite in the stable system or cementite in the metastable system. This article begins with a discussion on the nucleation and growth of austenite dendrites. It describes the nucleation of lamellar graphite, spheroidal graphite, and austenite-iron carbide eutectic. The article reviews three main graphite morphologies crystallizing from the iron melts during solidification: lamellar (LG), compacted or vermicular (CG), and spheroidal. It discusses the metastable solidification of austenite-iron carbide eutectic and concludes with information on gray-to-white structural transition of cast iron.

This article focuses on the intermediate length scales, where transport phenomena govern the spatial and temporal evolution of a structure. It presents the cellular automaton (CA) and phase field (PF) methods that represent the state of the art for modeling macrostructure and microstructure. The article describes the principles of the PF method and provides information on the applications of the PF method. The CA model is introduced as a computationally efficient method to predict grain structures in castings using the mesoscopic scale of individual grains. The article discusses the coupling of the CA to macroscopic calculation of heat, flow, and mass transfers in castings and applications to realistic casting conditions.

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.

This article summarizes the general features of microstructure evolution during the thermomechanical processing (TMP) of nickel-base superalloys and the challenges posed by the modeling of such phenomena. It describes the fundamentals and implementations of various modeling methodologies. These include JMAK (Avrami) models, topological models, and mesoscale physics-based models.

This article reviews the general aspects of microstructure evolution during thermomechanical processing. The effect of thermomechanical processing on microstructure evolution is summarized to provide insight into the aspect of process design. The article provides information on hot working and key processes that control microstructure evolution: dynamic recovery, static recovery, recrystallization, and grain growth. Some of the key phenomenological descriptions of plastic flow and microstructure evolution are also summarized. The article concludes with a discussion on the modeling of microstructure evolution.

The systematic study of microstructural evolution during deformation under hot working conditions is important in controlling processing variables to achieve dimensional accuracy. This article explains the microstructural features that need to be modeled and provides an outline of the principles and achievements of each of the various microstructural models, including black-box modeling, gray-box modeling, white-box modeling, and hybrid modeling.

Computer simulation of microstructural evolution during hot rolling of steels is a major topic of research and development in academia and industry. This article describes the methodology and procedures commonly employed to develop microstructural evolution models to simulate microstructural evolution in steels. It presents an example of the integration of finite element modeling and microstructural evolution models for the simulation of metal flow and microstructural evolution in a hot rolling process.