The microstructure that develops during the solidification stage of cast iron largely influences the subsequent solid-state transformations and mechanical properties of the cast components. This article provides a brief introduction of methods that can be used for simulating the solidification microstructure of cast iron. Analytical as well as numerical models describing solidification phenomena at both macroscopic and microscopic scales are presented. The article introduces macroscopic transport equations and presents analytical microscopic models for solidification. These models include the dendrite growth models and the cooperative eutectic growth models. The article provides some solutions using numerical models to simulate the kinetics of microstructure formation in cast iron. It concludes with a discussion on cellular automaton (CA) technique that can handle complex topology changes and reproduce most of the solidification microstructure features observed experimentally.

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.

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 provides an overview of integrated weld modeling and discusses the fundamentals of the underlying physics and methodologies involved in process modeling. It presents approaches for microstructure modeling that help to predict phase fractions as well as grain size in the heat-affected zone and weld metal region as a function of alloy composition and thermal cycles. The article discusses the uses of computational thermodynamic and kinetic tools. It describes the concept of performance modeling, whose goal relates to the prediction of weldability, geometrical distortion, and/or locked-in residual stress as a function of material, restraint, process, and process parameters as well as service temperature. Finally, the article presents a case study, evaluating the use of X-65 steels using the E-WeldPredictor tool.

This article presents the background to the CALculation of PHAse Diagrams (CALPHAD) method, explaining how it works, and how it can be applied in industrial practice. The extension of CALPHAD methods as a core basis for the modeling of generalized material properties is explored. It informs that one of the aims of CALPHAD methods has been to calculate phase equilibria in the complex, multicomponent alloys that are used regularly by industry. The article discusses the application of CALPHAD calculations to industrial alloys. Modeling of general material properties, such as thermophysical and physical properties, temperature- and strain-rate-dependent mechanical properties, properties for use in the modeling of quench distortion, and properties for use in solidification modeling, is also reviewed. The article also describes the linking of thermodynamic, kinetic, and material property models.

This article focuses on the industrial applications of phase diagrams. It presents examples to illustrate how a multicomponent phase diagram calculation can be readily useful for industrial applications. The article demonstrates how the integration of a phase diagram calculation with kinetic and microstructural evolution models greatly enhances the power of the CALPHAD approach in materials design and processing development. It also discusses the limitations of the CALPHAD approach.

This article reviews the characterization methods for producing 3-D microstructural data sets. The methods include serial sectioning by mechanical material removal method and focused ion beam tomography method. The article describes how these data sets are used in realistic 3-D simulations of microstructural evolution during materials processing and materials response. It also explains how the 3-D experimental data are actually input and used in the simulations using phase-field modeling and finite-element modeling.

This article provides a summary of the overall development of the finite element method (FEM) and its contribution to the materials forming industry. It focuses on the overall philosophy and evolution of the FEM for solving bulk forming issues. A number of applications of FEM are presented in the order they would be used in a typical manufacturing process sequence: primary materials processing, hot forging and cold forming, and product assembly. The article discusses four FEM modules: the deformation model, the heat-transfer model, the microstructural model, and the carbon diffusion model. The article also covers material fracture and die stress analysis and reviews optimization of the design of forming processes.

Self-consistent models are a particular class of models in continuum micromechanics, that is, the field concerned with making predictions of the properties and evolution of aggregates whose single-crystal deformation behavior is known. This article provides information on the measurement and representation of textures as well as prediction of texture evolution in single-phase materials and two-phase aggregates.

This article presents the Schmid's law that describes the response of crystal structures to loading. It describes the Taylor model to calculate the uniaxial yield stress of an isotropic face-centered cubic aggregate in terms of critical resolved shear stress. The article discusses the stress-based approach of the Bishop and Hill procedure to directly find stress states that could simultaneously operate at least five independent slip systems. It presents ways to find isostress or lower-bound yield loci for sheets having single-crystal orientation.

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 provides an explanation on how crystal plasticity is implemented within finite element formulations by the use of physical length scales: crystal scale and continuum scale. It provides theoretical formulations for kinematic framework for deforming crystals and polycrystals, elastic and plastic behaviors of single crystals, refinements to the single-crystal constitutive, and crystal-scale finite-element. The article also presents examples that illustrate the capabilities of the formulations at the length scales.

This article focuses on the analyzing and modeling of stress-strain behavior of polycrystals of pure face-centered cubic (fcc) metals in the range of temperatures and strain rates where diffusion is not important. It presents a phenomenological description of stress-strain behavior and provides information on the physical background, alternative interpretations, and directions of research. The quantitative description of strain hardening of fcc polycrystals is provided. The article also discusses the modeling of stress-strain behavior in body-centered cubic metals, hexagonal metals, stage IV work hardening, and the various classes of single-phase alloys.

The modeling and simulation of texture evolution for titanium alloys is often tightly coupled to microstructure evolution. This article focuses on a number of problems for titanium alloys in which such coupling is critical in the development of quantitative models. It discusses the phase equilibria, crystallography, and deformation behavior of titanium and titanium alloys. The article describes the modeling and simulation of recrystallization and grain growth of single-phase beta and single-phase alpha titanium. The deformation- and transformation-texture evolution of two-phase (alpha/beta) titanium alloys are also discussed.

This article explores the potential of through-process simulations of the development of microstructure, texture, and resulting properties during the thermomechanical processing of Al-Mn-Mg alloys, starting from the as-cast ingot to final-gage sheet. It provides an introduction of the thermomechanical production of aluminum sheet and, in particular, highlights the main effects governing the evolution of microstructure and texture. The simulation tools used to model the evolution of microchemistry, microstructure, and texture upon deformation and recrystallization of aluminum alloys are described. The article discusses the recrystallization behavior of alloy AA 3104 during the interstand times in between two consecutive hot rolling passes with the help of combined microstructure models.

This article examines how cellular automaton (CA) can be applied to the simulation of static and dynamic recrystallization. It describes the steps involved in the CA simulation of recrystallization. These include defining the CA framework, generating the initial microstructure, distributing nuclei of recrystallized grains, growing the recrystallized grains, and updating the dislocation density. The article concludes with information on the developments in CA simulations.

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.

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.

Recrystallization is to a large extent responsible for their final mechanical properties. This article commences with a discussion on static recrystallization (SRX) and dynamic recrystallization (DRX). The DRX includes continuous dynamic recrystallization (CDRX) and discontinuous dynamic recrystallization (DDRX). The article discusses the assumptions and simplifications for the Avrami analysis. It describes the effects of nucleation and growth rates on recrystallization kinetics and recrystallized grain size based on the Johnson-Mehl-Avrami-Kolmogorov model for static recrystallization. The article reviews the kinetics of DRX with the aid of the Avrami relations. It considers the basic framework of the mesoscale approach for DDRX, including the three basic equations for grain size changes, strain hardening and dynamic recovery, and nucleation. The article explains the mesoscale approach for CDRX to predict microstructural evolutions occurring during hot deformation, along with an illustration of the main features of the CDRX mesoscale model.

This article, to develop an understanding of the underlying mechanisms governing deformation at elevated temperatures, discusses the phenomenological effects resulting from temperature-induced thermodynamic and kinetic changes. It describes the deformation behavior of engineering materials using expressions known as constitutive equations that relate the dependence of stress, temperature, and microstructure on deformation. The article reviews the characteristics of creep deformation and mechanisms of creep, such as power-law creep, low temperature creep, power-law breakdown, diffusional creep, twinning during creep deformation, and deformation mechanism maps. It discusses the creep-strengthening mechanisms for most structural engineering components. The article provides a description of the microstructural modeling of creep in engineering alloys.