This article describes the historical background, uncertainties in structural parameters, classifications, and application areas of probabilistic analysis. It provides a discussion on the basic definition of random variables, some common distribution functions used in engineering, selection of a probability distribution, the failure model definition, and a definition of the probability of failure. The article also explains the solution techniques for special cases and general solution techniques, such as first-second-order reliability methods, the advanced mean value method, the response surface method, and Monte Carlo sampling. A brief introduction to importance sampling, time-variant reliability, system reliability, and risk analysis and target reliabilities is also provided. The article examines the various application problems for which probabilistic analysis is an essential element. Examples of the use of probabilistic analysis are presented. The article concludes with an overview of some of the commercially available software programs for performing probabilistic analysis.

This article presents an approach to manage the uncertainty present in materials design. It describes inductive and deductive approaches to deal with uncertainty. The article focuses on providing an understanding of the opportunities for managing uncertainty and the decisions that influence the accuracy of the results. A design of experiments (DOE) represents a sequence of experiments to be performed, expressed in terms of factors set at specified levels. The article discusses the two types of DOEs: the full factorial design and the fractional factorial design. It explains the factors to be considered when selecting a procedure for propagating uncertainty. The article lists the categories of the popular types of uncertainty propagation methods, including simulation-based methods, local expansion methods, and numerical integration-based methods.

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.

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 describes the results obtained by Volmer, Weber, Farkas, Becker, and Doring, which constitute the classical nucleation theory. These results are the predictions of the precipitate size distribution, steady-state nucleation rate, and incubation time. The article reviews a nucleating system as a homogeneous phase using the classical nucleation theory, along with heterophase fluctuations that led to the formation of precipitates. It discusses the gas cluster dynamics using the kinetic approach to describe nucleation. The article presents key parameters, such as cluster condensation and evaporation rates, to describe the time evolution of the system. The predictions and extensions of the classical nucleation theory are discussed. The article also provides the limitations of classical nucleation theories in cluster dynamics.

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.

There are two parts to deal with uncertainty in fatigue design: determining the distributions of possible values for all uncertain inputs and calculating the probability of failure due to all the uncertain inputs. This article discusses the sources of uncertainty in a fatigue analysis, such as the material properties, distribution of applied stress levels within a given environment, environments or loading intensities, and modeling or prediction. It presents a probabilistic approach for analyzing the uncertainties and determining the level of reliability (probability of failure).

X-ray spectroscopy is generally accepted as the most useful ancillary technique that can be added to any scanning electron microscope (SEM), even to the point of being considered a necessity by most operators. While “stand-alone” x-ray detection systems are used less frequently in failure analysis than the more exact instrumentation employed in SEMs, the technology is advancing and is worthy of note due to its capability for nondestructive analysis and application in the field. This article begins with information on the basis of the x-ray signal. This is followed by information on the operating principles and applications of detectors for x-ray spectroscopy, namely energy-dispersive spectrometers, wavelength-dispersive spectrometers, and handheld x-ray fluorescence systems. The processes involved in x-ray analysis in the SEM and handheld x-ray fluorescence analysis are then covered. The article ends with a discussion on the applications of x-ray spectroscopy in failure 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.

The process of optimization involves choosing the best solution from a pool of potential candidate solutions. This article provides a description of some classes of problems and the optimization methods that solve them. These problems include the deterministic single-objective problem, the deterministic multiobjective problem, and the nondeterministic, stochastic optimization problem. The article presents several complementary approaches to solve a wide variety of single-objective and multiobjective mechanical engineering applications. Multiobjective optimization study and stochastic optimization studies are also discussed.

This article provides a detailed account of the basic concepts of Rutherford backscattering spectrometry (RBS). It begins with a description of the principles of RBS, as well as the effect of channeling in conjunction with backscattering measurements and the effect of energy loss under this condition. This is followed by a section on equipment used in RBS analysis. Channel-energy conversion, energy-depth conversion, and separation of the dechanneling background are then discussed as the main steps of RBS data analysis. The article also discusses the applications of RBS—including composition of bulk samples, thin-film composition and layer thickness, impurity profiles, damage depth profile, and surface peak—as well as the various codes developed to simulate it.

This article focuses on transport phenomena and modeling approaches that are specific to vapor-phase processes (VPP). It discusses the VPP for the synthesis of materials. The article reviews the basic notions of molecular collisions and gas flows, and presents transport equations. It describes the modeling of vapor-surface interactions and kinetics of hetereogeneous processes as well as the modeling and kinetics of homogenous reactions in chemical vapor deposition (CVD). The article provides information on the various stages of developing models for numerical simulation of the transport phenomena in continuous media and transition regime flows of VPP. It explains the methods used for molecular modeling in computational materials science. The article also presents examples that illustrate multiscale simulations of CVD or PVD processes and examples that focus on sputtering deposition and reactive or ion beam etching.

This article provides detailed information on the instrumentation and principles of the scanning electron microscope (SEM). It begins with a description of the primary components of a conventional SEM instrument. This is followed by a discussion on the advantages and disadvantages of the SEM compared with other common microscopy and microanalysis techniques. The following sections cover the critical issues regarding sample preparation, the physical principles regarding electron beam-sample interaction, and the mechanisms for many types of image contrast. The article also presents the details of SEM-based techniques and specialized SEM instruments. It ends with example applications of various SEM modes.

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 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 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 provides an overview of the structural design process and discusses the life-limiting factors, including material defects, fabrication practices, and stress. It details the role of a failure investigator in performing nondestructive inspection. The article provides information on fatigue life assessment, elevated-temperature life assessment, and fitness-for-service life assessment.

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.

This article is a detailed account of the principles of electron-excited X-ray microanalysis. It begins by discussing the physical basis of electron-excited X-ray microanalysis and the advantages and limitations of energy dispersive spectrometry (EDS) and wavelength dispersive spectrometry for electron probe microanalysis. Key concepts for performing qualitative analysis and quantitative analysis by electron-excited X-ray spectrometry are then presented. Several sources that lead to measurement uncertainties in the k-ratio/matrix corrections protocol are provided, along with the significance of the raw analytical total. Sections on accuracy of the standards-based k-ratio/matrix corrections protocol with EDS and processes of analysis when severe peak overlap occurs are also included. The article provides information on low-atomic-number elements, iterative qualitative-quantitative analysis for complex compositions, and significance of standardless analysis in the EDS software. It ends with a section on the processes involved in elemental mapping for major and minor constituents.