The objective of quantitative metallography/stereology is to describe the geometric characteristics of the features. This article discusses the geometric attributes of microstructural features that can be divided into: the numerical extents and the number density of microstructural features; derived microstructural properties; feature specific size, shape, and orientation distributions; and descriptors of microstructural spatial clustering and correlations. It emphasizes on the practical aspects of the measurement techniques and applications. The article also provides information on the quantitative metallographic methods for estimation of volume fraction, total surface area per unit volume, and total length of per unit volume.

This article presents the experimental and theoretical aspects of small-angle scattering, and discusses specific applications used in the characterization of metals, glasses, polymers, and ceramics. The basic methods of collimating x-rays, the cause of smearing from a line source, desmearing parameters, and the types of scattering curves are illustrated.

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.

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.

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.

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.

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.

Three types of energy are used primarily as direct heat sources for fusion welding: electric arcs, laser beams, and electron beams. This article reviews the physical phenomena that influence the input-energy distribution of the heat source for fusion welding. It also discusses several simplified and detailed heat-source models that have been used in the modeling of arc welding, high-energy-density welding, and resistance welding.

This article provides an overview of the fundamentals, mechanisms, process physics, advantages, and limitations of laser beam welding. It describes the independent and dependent process variables in view of their role in procedure development and process selection. The article includes information on independent process variables such as incident laser beam power and diameter, laser beam spatial distribution, traverse speed, shielding gas, depth of focus and focal position, weld design, and gap size. Dependent variables, including depth of penetration, microstructure and mechanical properties of laser-welded joints, and weld pool geometry, are discussed. The article also reviews the various injuries and electrical and chemical hazards associated with laser beam welding.

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.

Computational fluid dynamics (CFD) is reserved for computationally intensive three-dimensional simulations of thermal fluids systems where nonlinear momentum transport plays an important role. This article presents the governing equations of fluid dynamics and an introduction to the CFD techniques for their solution. It introduces discretization techniques that are used by finite-difference, finite-volume, finite-element, spectral, and some particle methods. Associated concepts of numerical stability and accuracy are also reviewed. The article describes two approaches for grid generation with complex geometries: the use of unstructured grids and the use of special differencing methods on structured grids. The article describes the four-step procedures of the CFD process: geometry acquisition, grid generation and problem specification, flow solution, and post-processing and synthesis. It provides information on the applications of the engineering CFD. Issues and directions for the engineering CFD are also described.

This article briefly reviews the physical phenomena that influence the input-energy distribution. It discusses the several simplified and detailed heat source models used in the modeling of arc welding, high-energy-density welding, and resistance welding processes.

Laser-beam welding (LBW) is a joining process that produces coalescence of material with the heat obtained from the application of a concentrated coherent light beam impinging upon the surface to be welded. This article describes the steps that must be considered when selecting the LBW process. It reviews the individual process variables that influence procedure development of the LBW process. Joint design and special practices related to LBW are discussed. The article concludes with a discussion on the use of consumables and special welding practices.

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.

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 provides an overview of integrated weld modeling and presents strategic goals for the welding industry. It discusses the fundamentals of the underlying physics and the methodologies to solve the same. The article presents the pioneering work done to predict the heat-affected zone and weld metal microstructure in the early 1980s and 1990s. Applications of computational thermodynamics and kinetics tools to weld metal microstructure prediction for liquid-gas reactions and liquid-slag reactions that happen as a function of high-to-low temperature during fusion welding are discussed. The article also includes a brief discussion on weldability prediction, residual stress prediction, and distortion prediction. It concludes with information on the use of optimization methodologies.

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.

Multiple-layer alloy electrodeposition involves the formation of an inhomogeneous alloy consisting of lamellae of different composition. This article reviews the process description, engineering parameters, characterization, and applications of multiple-layer alloys. Pulsed-current plating and pulsed-potential plating are also discussed.

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.

Field ion microscopy (FIM) can be used to study the three-dimensional structure of materials, such as metals and semiconductors, because successive atom layers can be ionized and removed from the surface by field evaporation. The ions removed from the surface by field evaporation can be analyzed chemically by coupling to the microscope a time-of-flight mass spectrometer of single-particle sensitivity, known as the atom probe (AP). This article describes the principles, sample preparation, and quantitative analysis of FIM. It also provides information on the principles, instrument design and operation, mass spectra and their interpretation, and applications of AP microanalysis.