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 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.

Metalworking is one of the three major technologies used to fabricate metal products. This article tabulates the classification of metal forming processes. It discusses different types of metalworking equipment, including rolling mills, ring-rolling machines, and thread-rolling and surface-rolling machines. The article outlines the significant characteristics of pressing-type machines: load and energy characteristics, time-related characteristics, and accuracy characteristics. It summarizes different specialized processes such as advanced roll-forming methods, equal-channel angular extrusion, incremental forging, and microforming. The article describes the thermomechanical processing of nickel- and titanium-base alloys and concludes with information on the advancements in process simulation.

This article describes the mechanisms involved in creating texture for various metal-fabrication processes, namely, solidification, deformation, recrystallization and grain growth, thin-film deposition, and imposition of external magnetic fields. It discusses two experimental and analytical approaches for experimental determination of texture: one using classical diffraction and pole figure measurement techniques and the other using individual orientation measurements. The article also provides information on microtexture, grain-boundary character, and texture gradients. It concludes with information on texture evolution through modeling.

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 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.

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 outlines several polycrystal formulations commonly applied for the simulation of plastic deformation and the prediction of deformation texture. It discusses the crystals of cubic and hexagonal symmetry that constitute the majority of the metallic aggregates used in technological applications. The article defines the basic kinematic tensors, reports their relations, and presents expressions for calculating the change in crystallographic orientation associated with plastic deformation. It surveys some of the polycrystal models in terms of the relative strength of the homogeneous effective medium (HEM). The article analyzes the anisotropy predictions of rolled face-centered-cubic and body centered-cubic sheets and presents simulations of the axial deformation of hexagonal-close-packed zirconium. The applications of polycrystal constitutive models to the simulation of complex forming operations, through the use of the finite element method, are also presented.

This article provides a brief historical perspective, a classification of metallurgical processes, basic model development efforts, and an overview of the potential future directions for the modeling of metals processing. It describes the classification of material behavior models, which can be grouped broadly into three classes: statistical, phenomenological, and mechanistic models. The article also presents an overview of the potential directions for the modeling of metals processing.

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.

The processing of steel involves five distinct sets of texture development mechanisms, namely, austenite deformation, austenite recrystallization, gamma-to-alpha transformation, ferrite deformation, and static recrystallization during annealing after cold rolling. This article provides an introduction on crystallographic textures. It discusses the effects of austenite rolling and recrystallization on the texture and transformation behavior of recrystallized austenite and deformed austenite. The article illustrates the overall summary of the rolling and transformation behavior. It details cold-rolling textures, annealing textures, and recrystallization textures of steel samples. The article concludes with a summary of texture development during cold rolling and annealing.

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 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.

The thermomechanical processing (TMP) of conventional and advanced nickel and titanium-base alloys is aimed at altering or enhancing one or more metallurgical features within the material and component. This article presents a number of examples of the TMP of nickel-base superalloys and titanium alloys. The TMP techniques include retained-strain processing, dual-microstructure processing, and dual-alloy processing. The article also describes the TMP of alpha-beta titanium alloys, including fine-grain processing, hybrid-structure processing, dual-microstructure processing, and dual-alloy processing. It concludes with a discussion on computer simulation of advanced TMP processes.

Additive manufacturing (AM) process modalities offer access to rich sets of structures for metallic materials that are otherwise difficult to obtain through a single conventional manufacturing process for bulk-scale materials. This article presents the primary aim of understanding the linkage between the process and structure in AM, which is typically focused on the correlation of machine process settings to defects such as material porosity and cracking. It also presents the development of scan strategies for site-specific microstructure control and discusses factors influencing process-structure relationships in fusion metals AM.

This article reviews network models and their applications for the simulation of various physical phenomena related to grain-boundary migration. It discusses the steps involved in the implementation of two and three-dimensional network models, namely, acquisition and discretization of the microstructure, formulation of the equation of motion, and implementation of the topological transformations. The article presents examples that illustrate the simulation of physical phenomena to demonstrate the predictive power and flexibility of network models.

The misorientation of a boundary of a growing grain is defined not only by its crystallography but also by the crystallography of the grain into which it is growing. This article focuses on the Monte Carlo Potts model that is typically used to model grain growth, Zener-Smith pinning, abnormal grain growth, and recrystallization. It introduces the basics of the model, providing details of the dynamics, simulation variables, boundary energy, boundary mobility, pinning systems, and stored energy. The article explains how to incorporate experimental parameters and how to validate the model by comparing the observed behavior quantitatively with theory. The industrial applications of the model are also discussed. The article also provides a wide selection of the algorithms for implementing the Potts model, such as boundary-site models, n -fold way models, and parallel models, which are needed to simulate large-scale industrial applications.

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 discusses the central aspect of anisotropy modeling, namely, texture measurement and analysis. It provides an overview of the methods available for characterizing crystallographic preferred orientation, or texture, in polycrystalline materials. These methods include pole figure measurement and electron backscatter diffraction (EBSD). The article describes the process considerations for pole figure measurement, including X-ray diffraction, neutron diffraction, stereographic projection, equal area projection, graphing pole figures, typical textures, and orientation distribution. It also deals with the limitations and challenges associated with the EBSD, and applications of the diffraction.

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.