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.

Of the various thermal processing methods for steel, heat treating has the greatest overall impact on control of residual stress and on dimensional control. This article provides an overview of the effects of material- and process-related parameters on the various types of failures observed during and after heat treating of quenched and tempered steels. It describes phase transformations of steels during heating, cooling of steel with and without metallurgical transformation, and the formation of high-temperature transformation products on the surface of a carburized part. The article illustrates the use of carbon restoration on decarburized spring steels. Different geometric models for carbide formation are shown schematically. The article also describes the different microstructural features such as grain size, microcracks, microsegregation, and banding.

In secondary ion mass spectroscopy (SIMS), an energetic beam of focused ions is directed at the sample surface in a high or ultrahigh vacuum (UHV) environment. The transfer of momentum from the impinging primary ions to the sample surface causes sputtering of surface atoms and molecules. This article focuses on the principles and applications of high sputter rate dynamic SIMS for depth profiling and bulk impurity analysis. It provides information on broad-beam instruments, ion microprobes, and ion microscopes, detailing their system components with illustrations. The article graphically illustrates the SIMS spectra and depth profiles of various materials. The quantitative analysis of ion-implantation profiles, instrumental features required for secondary ion imaging, the analysis of nonmetallic samples, detection sensitivity, and the applications of SIMS are also discussed.

Computational modeling assists in addressing the issues of solid/liquid interface dynamics at the microlevel. It also helps to visualize the grain length scale, fraction of phases, or even microstructure transitions through microstructure maps. This article provides a detailed account of the general capabilities of the various models that can generate microstructure maps and thus transform the computer into a dynamic microscope. These include standard transport models, phase-field models, Monte Carlo models, and cellular automaton models.

This article provides an outline of the issues to consider in performing a probabilistic life assessment. It begins with an historical background and introduces the most common methods. The article then describes those methods covering subjects such as the required random variable definitions, how uncertainty is quantified, and input for the associated random variables, as well as the characterization of the response uncertainty. Next, it focuses on specific and generic uncertainty propagation techniques: first- and second-order reliability methods, the response surface method, and the most frequently used simulation methods, standard Monte Carlo sampling, Latin hypercube sampling, and discrete probability distribution sampling. Further, the article discusses methods developed to analyze the results of probabilistic methods and covers the use of epistemic and aleatory sampling as well as several statistical techniques. Finally, it illustrates some of the techniques with application problems for which probabilistic analysis is an essential element.

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.