This article reviews many commonly used stereological counting measurements and the relationships based on these parameters. The discussion covers the processes involved in sampling and specimen preparation. Quantitative microstructural measurements are described including volume fraction, number per unit area, intersections and intercepts per unit length, grain size, and inclusion content.

Quantifying microstructural parameters has received considerable attention and success in developing procedures and using such data to develop structure/property relationships has been achieved. This article reviews many of the simple stereological counting measurements of volume fraction, grain structure (two-phase grain structures, and nonequiaxed grain structures), grain size, and inclusion content. It also reviews simple relationships between number of grains per unit area, number of intersections of a line of known length with particle or grain, and number of interceptions of particles or grains by a line of known length.

The characterization, testing, and nondestructive evaluation of ceramics and glasses are vital to manufacturing control, property improvement, failure prevention, and quality assurance. This article provides a broad overview of characterization methods and their relationship to property control, both in the production and use of ceramics and glasses. Important aspects covered include the means for characterizing ceramics and glasses, the corresponding rationale behind them, and relationship of chemistry, phases, and microconstituents to engineering properties. The article also describes the effects that the structure of raw ceramic materials and green products and processing parameters have on the ultimate structure and properties of the processed piece. The effects that trace chemistry and processing parameters have on glass properties are discussed. The article describes mechanical tests and failure analysis techniques used for ceramics.

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 discusses the fractal characteristics of fracture surfaces as a means for describing and quantifying irregular, complex curves and surfaces of fractured materials. It describes the important relationship between the profile and surface roughness parameters that yield the surface area of irregular fracture surfaces. The article reviews the experimental procedures required to obtain profiles and measurements that are made. In addition, fractal equations that linearize all the experimental data and provide constant fractal dimensions are presented in the article. Modified fractal dimensions that result from these analyses appear to possess some generality for natural irregular nonplanar surfaces and their profiles.

Quantitative image analysis has expanded the capabilities of surface analysis significantly with the use of computer technology. This article provides an overview of the quantitative image analysis and optical microscopy. It describes the various steps involved in surface preparation of samples prone to abrasion damage and artifacts for quantitative image analysis.

Recrystallization is to a large extent responsible for their final mechanical properties. This article commences with a discussion on static recrystallization (SRX) and dynamic recrystallization (DRX). The DRX includes continuous dynamic recrystallization (CDRX) and discontinuous dynamic recrystallization (DDRX). The article discusses the assumptions and simplifications for the Avrami analysis. It describes the effects of nucleation and growth rates on recrystallization kinetics and recrystallized grain size based on the Johnson-Mehl-Avrami-Kolmogorov model for static recrystallization. The article reviews the kinetics of DRX with the aid of the Avrami relations. It considers the basic framework of the mesoscale approach for DDRX, including the three basic equations for grain size changes, strain hardening and dynamic recovery, and nucleation. The article explains the mesoscale approach for CDRX to predict microstructural evolutions occurring during hot deformation, along with an illustration of the main features of the CDRX mesoscale model.

This article assesses the evolution of martensite modeling in the changing materials engineering environment. It describes the physics of displacive transformations using Ginzburg-Landau theory, microstructure representation, dynamics and simulations, density functional theory, and shuffle transitions. The article reviews the application of the Ginzburg-Landau approach to rigorous solutions for issues in the structure of a martensitic nucleus based on the martensitic nucleation theory. The three basic behavior modes of martensitic growth, such as elastic, elastic/plastic, and fully plastic are discussed. The article also reviews the overall kinetics of martensitic transformations.

Ceramic-matrix composites (CMCs) are being developed for a number of high-temperature and high-performance applications in industrial, aerospace, and energy conservation sectors. This article focuses on processing, fabrication, testing, and characterization methods of CMCs, namely, discontinuously reinforced composites and continuous-fiber-reinforced composites. Processing methods include cold pressing, sintering, hot pressing, reaction bonding, melt infiltration, directed metal oxidation, sol-gel and polymer pyrolysis, self-propagating high-temperature synthesis and joining. A table summarizes the properties of various ceramic reinforcements and industrial applications of these composites.

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.

Alloy phase diagrams are useful for the development, fabrication, design and control of heat treatment procedures that will produce the required mechanical, physical, and chemical properties of new alloys. They are also useful in solving problems that arise in their performance in commercial applications, thus improving product predictability. This article describes different equilibrium phase diagrams (unary, binary, and ternary) and microstructures, description terms, and general principles of reading alloy phase diagrams. Further, the article discusses plotting schemes; areas in a phase diagram; and the position and shapes of the points, lines, surfaces, and intersections, which are controlled by thermodynamic principles and properties of all phases that comprise the system. It also illustrates the application of the stated principles with suitable phase diagrams.