Modeling of structure formation in casting of alloys involves several length scales, ranging from the atomic level to macroscopic scale. Intermediate length scales are used to define the microstructure of the growing phases and the grain structure. This article discusses the principles and applications of phase field method and cellular automaton method for modeling the direct evolution of structure at the intermediate length scales, where transport phenomena govern the spatial and temporal evolution of the structure that involves nucleation and growth.

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.

The electron backscatter diffraction (EBSD) technique has proven to be very useful in the measurement of crystallographic textures, orientation relationships between phases, and both plastic and elastic strains. This article focuses on backscatter diffraction in a scanning electron microscope and describes transmission Kikuchi diffraction. It begins with a discussion on the origins of EBSD and the collection of EBSD patterns. This is followed by sections providing information on EBSD spatial resolution and system operation of EBSD. Various factors pertinent to perform an EBSD experiment are then covered. The article further describes the processes involved in sample preparation that are critical to the success or usefulness of an EBSD experiment. It also discusses the applications of EBSD to bulk samples and the development of EBSD indexing methods.

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.

Computed tomography (CT) is an imaging technique that generates a three-dimensional (3-D) volumetric image of a test piece. This article illustrates the basic principles of CT and provides information on the types, applications, and capabilities of CT systems. A comparison of performance characteristics for film radiography, real-time radiography, and X-ray computed tomography is presented in a table. A functional block diagram of a typical computed tomography system is provided. The article discusses CT scanning geometry that is used to acquire the necessary transmission data. It also provides information on digital radiography, image processing and analysis, dual-energy imaging, and partial angle imaging, of a CT system.

Electronic structure methods based on the density functional theory (DFT) are used as a powerful tool for assessing the mechanical thermodynamic and defect properties of metal alloys. This article presents the origins of the electronic structure methods and their strengths and limitations. It describes the basic procedures for calculating essential structural properties in metal alloys. The article reviews the approximations and computational details of the pseudopotential plane wave methods used in metal systems. It provides information on the applications of DFT methods in metal alloy systems. The article discusses the calculations of a variety of structural, thermodynamic, and defect properties, with particular emphasis on structural metal alloys and their derivatives.

The principal objective of quantitative fractography is to express the characteristics of features in the fracture surface in quantitative terms, such as the true area, length, size, spacing, orientation, and location. This article provides a detailed account of the development of more quantitative geometrical methods for characterizing nonplanar fracture surfaces. Prominent techniques for studying fracture surfaces are based on the projected images, stereoscopic viewing, and sectioning. The article provides information on various roughness and materials-related parameters for profiles and surfaces. The applications of quantitative fractography for striation spacings, precision matching, and crack path tortuosity are also discussed.

Thermoelastic stress analysis (TSA) an increasingly popular infrared (IR)-based technique for measuring stress on the surface of a part subjected to time-varying loads. This article begins by providing a theoretical and historical background of thermoelastic stress analysis. It then describes infrared detectors, such as quantum detectors and thermal/nonquantum detectors, for thermoelastic stress analysis. The article discusses the theoretical aspects for producing thermoelastic stress analysis data and the applications amenable to thermoelastic stress analysis. It concludes with information on the qualitative applications of thermoelastic stress analysis.

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.

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.

Computational fluid dynamics (CFD) is a computationally intensive three-dimensional simulation of thermal fluids systems where non-linear momentum transport plays an important role. This article presents the governing equations of fluid dynamics and an introduction to the CFD techniques. It introduces some common techniques for discretizing the fluid-flow equations and methods for solving the discrete equations. These include finite-difference methods, finite-element methods, spectral methods, and computational particle methods. The article describes the approaches for grid generation with complex geometries. It discusses the four-step procedures used in the CFD process for engineering design: geometry acquisition, grid generation and problem specification, flow solution, and post-processing and synthesis. The article also provides information on the engineering applications of the CFD. It concludes with a discussion on issues and directions for engineering CFD.

Ultrasound is an ideal modality for nondestructive evaluation (NDE) because it enables the interior of objects to be assessed without the safety and access issues associated with radiography. This article summarizes the history of array usage in NDE and its relationship to medical applications. It discusses the mathematics behind classical beamforming, full matrix capture, and total focusing methods of imaging. The article shows how ultrasonic array data can be simulated by direct numerical methods (most commonly using finite-element methods), analytical methods, or hybrid methods. It also considers various methods of comparing the performance of arrays and imaging algorithms. The article provides a comparison of various advanced and nonlinear imaging algorithm and looks at some practical industrial applications of arrays. It concludes with some future perspectives for arrays in NDE.

This article focuses on the modes of operation, physical basis, sample requirements, properties characterized, advantages, and limitations of common characterization methods that are used to evaluate the physical morphology and chemical properties of component surfaces for medical devices. The methods include light microscopy, scanning electron microscopy, atomic force microscopy, energy-dispersive x-ray spectroscopy, Auger electron spectroscopy, secondary ion mass spectrometry, x-ray photoelectron spectroscopy, Fourier transform infrared spectroscopy, and Raman spectroscopy.

This article presents a general description of pulsed-laser deposition. It describes the components of pulsed-laser deposition equipment. The article also discusses the effects of angular distribution of materials. Finally, the article reviews the characteristics of high-temperature superconductors and ferroelectric materials.

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 discusses various concepts of micro x-ray diffraction (XRD) used for the examination of materials in situ. The discussion covers the principles, equipment used, sample preparation procedure, considerations for calibrating a detector, steps for performing data analysis, and applications and interpretation of micro-XRD.

Scanning electron microscopy (SEM) has unique capabilities for analyzing fracture surfaces. This article discusses the basic principles and practice of SEM, with an emphasis on its applications in fractography. The topics include an introduction to SEM instrumentation, imaging and analytical capabilities, specimen preparation, and the interpretation of fracture features. SEM can be subdivided into four systems, namely, illuminating/imaging, information, display, and vacuum systems. The article also describes the major criteria and techniques of SEM specimen preparation, and the general features of ductile and brittle fracture modes.

Additive manufacturing (AM) is the process of joining materials to make parts from three-dimensional (3D) model data, usually layer upon layer, as opposed to subtractive manufacturing and formative manufacturing methodologies. This article discusses various defects in AM components, such as porosity, inclusions, cracking, and residual stress, that can be avoided by using vendor recommended process parameters and approved materials. It describes the development of process-structure-property-performance modeling. The article explains the practical considerations in nondestructive evaluation for additively manufactured metallic parts. It also examines nondestructive testing (NDT) inspection and characterization methods for each of the manufacturing stages in their natural order. The article provides information on various inspection techniques for completed AM manufactured parts. The various electromagnetic and eddy current techniques that can be used to detect changes to nearsurface geometric anomalies or other defects are also discussed. These include ultrasonic techniques, radiographic techniques, and neutron imaging.

This article begins with balance equations for mass, momentum, energy, and solute and the necessary boundary conditions for solving problems of interest in casting and solidification. The transport phenomena cover a vast range of length and time scales, from atomic dimensions up to macroscopic casting size and from nanoseconds for interface attachment kinetics to hours for casting solidification. The article describes how to determine which phenomena are most important at the particular length and time scale for the problem. It concludes with several examples of the application of transport phenomena in solidification, focusing in particular on microstructure formation.

This article presents the governing equations for moving a solidification front, based on the balance of mass, momentum, energy, and solute. It reviews how material properties and geometry can be analyzed in the context of the governing equations. The article provides several example problems that illustrate how the hierarchy of time and length scales associated with transport leads to the important features of cast microstructures. It includes equations for estimating microsegregation in cast alloys.