This article provides an overview of the finite-element-based analyses (FEA) of advanced composite structures and highlights key aspects such as the homogenization of materials properties and post-processing of numerical results. It discusses the analysis of composite structures based on micromechanics and macromechanics. The article describes the FEA of 3-D solid elements, 2-D cylindrical shell elements, and 1-D beam elements. It contains a table that lists the commercially available finite element codes related to the analysis of fibrous composite materials. The article presents classical examples of the mechanics of composite materials to illustrate the aspects of multilayered composite structures.

In order to model macrosegregation, one must consider convection and the partitioning of segregating elements at the dendritic length scale. This article describes microsegregation with diffusion in the solid. It presents a continuum model of macrosegregation and illustrates the simulation of macrosegregation and microsegregation.

The crystal structure of a material is an important aspect of corrosion and oxidation processes. This article provides a general introduction to the crystal structure of materials, providing information on the crystal systems, lattice dimensions, nomenclature, and solid-solution mechanisms used to characterize structures. It illustrates the unit cells and ion positions for some simple metal crystals, arranged alphabetically according to the Pearson symbol. The space lattice and crystal system, space-group notation, and prototype for each crystal are also illustrated.

Aluminum mill products are those that have been subjected to plastic deformation by hot- and cold-working mill processes such as rolling, extruding, and drawing, either singly or in combination. Microstructural changes associated with the working and with any accompanying thermal treatments are used to control certain properties and characteristics of the worked, or wrought, product or alloy. This article discusses the designation system, classification, product forms, corrosion and fabrication characteristics, and applications of wrought aluminum alloys. Commercial wrought aluminum products are divided into flat-rolled products (sheet, plate, and foil); rod, bar, and wire; tubular products; shapes; and forgings. The article discusses factors affecting the strengthening mechanisms, fracture toughness, and physical properties of aluminum alloys, in addition to the effects of alloying on the physical and mechanical properties. Important alloying elements and impurities are listed alphabetically as a concise review of major effects.

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.

Homogenization heat treatment can be useful for improving the performance and life of an alloy while in service or for improving the processability during fabrication and hot working. This article describes the identification of incipient melt point, slowest-diffusing elements, and microstructural scale for homogenization of metal alloys. It also discusses the CALPHAD software to optimize the homogenization heat treatment and the Scheil module of the commercial thermodynamic modeling software.

This article describes the viscoelastic behavior of plastics in their solid state only, from the standpoint of the material deforming without fracturing. The consequences of viscoelasticity on the mechanical properties of plastics are described, especially in terms of time-dependencies, as well as the dependence of the viscoelastic character of a plastic on chemical, physical, and compositional variables. By examining the viscoelastic behavior of plastics, the information obtained are then applied in situations in which it may be important to anticipate the long-term properties of a material. This includes assessing the extent of stress decay in materials that are pre-stressed, the noise and vibration transmission characteristics of a material, the amount of heat build-up in a material subjected to cyclic deformation, and the extent a material can recover from any prior deformation. Several qualitative graphs are presented, which highlights the possible differences in the viscoelastic behavior that can exist among plastics.

Fusion welding induces residual stresses and distortion, which may result in loss of dimensional control, costly rework, and production delays. In thermal analysis, conductive heat transfer is considered through the use of thermal transport, heat-input, and material models that provide values for the applied welding heat input. This article describes how the solid-phase transformations that occur during the thermal cycle produced by welding lead to irreversible plastic deformation known as transformation plasticity. Residual stress and welding distortion are also discussed.

Coatings and thin films can be studied with surface analysis methods because their inherently small depth allows characterization of the surface composition, interface composition, and in-depth distribution of composition. This article describes principles and examples of common surface analysis methods, namely, Auger electron spectroscopy, X-ray photoelectron spectroscopy, ion scattering spectroscopy, secondary ion mass spectroscopy, and Rutherford backscattering spectroscopy. It also provides useful information on the applications of surface analysis.

One impressive example of plane front solidification (PFS) is the industrial production of large silicon single crystals, used mainly as substrates for integrated circuits. This article explores the PFS of a single phase, without taking convection into account. It discusses the solute build-up at the solid-liquid interface forming transients and steady state, the morphological stability/instability and perturbation theory, and rapid solidification effects, including solute trapping and oscillatory instabilities. The article presents a microstructural selection map that presents an overview of interface stability as a function of composition for a given alloy.

This article introduces various analytical techniques commonly used in the characterization of organic solids and liquids and discusses the challenges in performing the analysis, with examples. Some general advice in approaching a material analysis is also provided.

This article reviews the fundamental solidification concepts for understanding microstructural evolution in fusion welds. The common concepts, namely, nucleation, competitive grain growth, constitutional supercooling, solute redistribution, and rapid solidification, depend on the solidification parameters during welding, are discussed. The article discusses important solidification parameters, including temperature gradient, solid/liquid interface growth rate, and cooling rate.

The electronic microcircuit industry has placed severe demands on metal suppliers to provide metals of the highest reproducible purity attainable as a result of the constant quest for the true values of physical and chemical properties of metals. This article describes the commonly used methods for ultrapurification of metals produced by electrolytic processes, including fractional crystallization, zone refining, vacuum melting, distillation, chemical vapor deposition, and solid state refining techniques. In addition, it describes the trace element analysis and resistance-ratio test methods used to characterize purity. Tables list the values for resistance ratios of zone-refined metals and their corresponding chemical compositions, and provide an example of the detection of impurities to concentrations in the parts per billion range, utilizing a combination of the glow discharge mass spectroscopy method and Leco combustion methods.

Several methods are developed for the numerical solution of partial differential equations, namely, meshed-solution methods such as the finite-element method (FEM), finite-difference method, and boundary-element method; and numerical algorithms consisting of so-called meshed-solution methods. This article introduces the methods of so-called meshed solutions, with an emphasis on the FEM. It presents some basic differential equations that are used to model the responses of structures, components, processes, or systems with emphasis on continuum mechanics. The article provides an outline on the mathematical principles of solving differential equations. It also reviews linear structural problems to illustrate the concept of the FEMs.

Thermal analysis is used to analyze solidification processes by recording the temperature as a function of time during cooling or heating of a metal or alloy to or from a temperature above its melting point. This article describes the use of cooling curves for analyzing a solidification process, such as the solidification temperature, structure analysis, fraction of phases and heat of fusion with focus on solidification of cast iron, and the use of cooling curves to control and adjust the casting conditions. It discusses deviations from equilibrium that occur due to kinetic effects during solidification. The article also illustrates the evaluation of fraction of solid formed during the precipitation of austenite from heat balance.

This article discusses the three different modeling approaches for grain structures formed during solidification of metallic alloys: direct modeling of dendritic structure, direct modeling of grain structure, and indirect modeling of grain structure. The main construction bases, the scale at which it applies, and the mathematical background are presented for each modeling approach. The article concludes with a table that presents a comparison of the main inputs/outputs, approximations, numerical methods, kinetics laws, and applications for the three approaches to modeling of dendritic grain solidification.

Rare earth metals belong to Group IIIA of the periodic table that includes scandium, yttrium, and the lanthanide elements which are lanthanum, cerium, praseodymium, neodymium, promethium, samarium, europium, gadolinium, terbium, dysprosium, holmium, erbium, thulium, ytterbium, and lutetium. This article classifies the rare earth metals based on their purity level, which are designated as research grades (>99.8% pure) and commercial grades (95% - 98% pure), and describes the preparation and purification, including solid-state electrolysis. It further discusses physical, mechanical, and chemical properties; electronic configurations; crystal structures, and explains the alloy forming characteristics of rare earth elements. The article concludes by describing the various applications of commercial-grade rare earth elements and commercial alloys, which incorporates rare earth elements as additives.

This article describes the three solidification mechanisms of peritectic structures, namely, peritectic reaction, peritectic transformation, and direct precipitation. It discusses the theoretical analysis, which shows that the rate of the peritectic transformation is influenced by the diffusion rate and the extension of the beta-phase region in the phase diagram. The article also provides information on the peritectic transformations in multicomponent systems.