Constitutive relations for metal-working include elements of behavior at ambient temperature as well as high-temperature response. This article presents the equations for the strain hardening and strain-rate-sensitive flow, with alternate sections on empirically determined properties, followed by models of constitutive behavior. These models include the isothermal constitutive model and the physical model for superplastic flow. A formal description of the superposition of the operative mechanisms for dynamic recovery at hot-working strain rates is also provided. The article describes creep mechanisms that are useful for illustrating the strong stress dependence of dislocation and diffusional flow.

This article reviews the classical models for the pseudo-steady-state temperature distribution of the thermal field around moving point and line sources. These include thick- and thin-plate models and the medium-thick-plate model. The analytical solutions to the differential heat flow equation under conditions applicable to fusion welding are provided. The article also provides an overview of the factors affecting heat flow in a real welding situation using the analytical modeling approach because this makes it possible to derive relatively simple equations that provide the required background for an understanding of the temperature-time pattern.

This article describes the liquidus plots, isothermal plots, and isopleth plots used for a hypothetical ternary phase space diagram. It discusses the single-phase boundary (SPB) line and zero-phase fraction (ZPF) line for carbon-chromium-iron isopleth. The article illustrates the Gibbs triangle for plotting ternary composition and discusses the ternary three-phase phase diagrams by using tie triangles. It describes the peritectic system with three-phase equilibrium and ternary four-phase equilibrium. The article presents representative binary iron phase diagrams, showing ferrite stabilization (iron-chromium) and austenite stabilization (iron-nickel).

This article discusses continuum modeling, which is the most relevant approach in modeling grain growth, densification, and deformation during sintering. Continuum plasticity models are frequently used to describe the mechanical response of metal powders during compaction. The article illustrates the typical procedure for computer simulation for press and sinter process. It describes the procedure to obtain the material properties based on the generalized Shima-Oyane model. The article presents a wide variety of tests, accounting for data on the grain growth, densification, and distortion where these data help in the development of a constitutive model for sintering simulation. Finally, the article provides information on the simulation approaches used to optimize die compaction and sintering.

This article presents the governing equations and methodologies to model the press and sinter powder metallurgy, including continuum, micromechanical, multiparticle, and molecular dynamics approaches. It describes the constitutive relation for compaction and sintering. The article discusses the experimental determination of material properties and simulation verification for compaction and sintering. It reviews the use of modeling and simulation of press and sinter powder metallurgy, including gravitational distorting in sintering, compaction optimization, sintering optimization, and coupled press and sinter optimization.

Forming processes can be divided into three major categories: bulk forming, sheet-metal forming, and semisolid forming and polymer extrusion. This article introduces each process category with a description of the constitutive models. It outlines the required properties for process modeling and describes the test methods for determining these properties. The article discusses several compression tests used to determine stress-strain curves for bulk forming and tensile tests used to obtain stress-strain curves for sheet-metal forming. The article concludes with information on the measurement of viscosity of semisolid alloy materials by using three types of viscometers: the coaxial cylinder viscometer, the cone-and-plate viscometer, and the capillary viscometer.

Structural alloys are commonly subjected to a variety of thermal and thermomechanical loads. This article provides an overview of the experimental methods in thermal fatigue (TF) and thermomechanical fatigue (TMF) and presents experimental results on the structural materials that have been considered in TF and TMF research. Life prediction models and constitutive equations suited for TF and TMF are covered. The structural materials discussed include carbon steels, low-alloy steels, stainless steels, aluminum alloys, and nickel-base high-temperature alloys. The article explains crack initiation and crack propagation in TF and TMF. It describes thermal ratcheting and thermal shock behavior of structural metallic materials. The article concludes with information on life prediction of structural materials under TF and TMF.

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.

This article provides information on the classification of various composites manufacturing processes based on similar transport processes. The composites manufacturing processes can be grouped into three categories: short-fiber suspension methods, squeeze flow methods, and porous media methods. The article presents an overview of the modeling philosophy and approach that is useful in describing composite manufacturing processes.

This article summarizes some issues and approaches in performing computational analyses of mechanical behavior, distortion, and hot tearing during solidification. It presents the governing equations and describes the methods used to solve them. The article reviews the finite element formulation, multidomain approaches, and arbitrary Lagrangian Eulerian method in solidification modeling. It illustrates the sand casting of braking disks and continuous casting of steel slabs.

High strain rate testing is important for many engineering structural applications and metalworking operations. This article describes various methods for high strain rate testing. Several methods have been developed, starting with the pioneering work of John Hopkinson and his son, Bertram Hopkinson. Based on these contributions and also on an important paper by R.M. Davies, H. Kolsky invented the split-Hopkinson pressure bar, which allows the deformation of a sample of a ductile material at a high strain rate, while maintaining a uniform uniaxial state of stress within the sample.

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.

This article discusses selected highlights of thermodynamic relationships during solidification and nucleation kinetics behavior in connection with the basis of nucleation treatments, such as grain refinement and inoculation, to provide a summary of nucleation phenomena during casting. The article describes nucleation phenomenon such as homogeneous nucleation and heterogeneous nucleation. It examines various grain refinement models, such as the carbide-boride model, the free growth model, and the constitutional undercooling model. The article concludes with information on the thermal analysis techniques for assessing grain-refining characteristics during master alloy processing.

Rapid solidification is a tool for modifying the microstructure of alloys that are obtained by ordinary casting. This article describes the fundamentals of the four microstructural changes, namely, microsegregation, identity of the primary phase, identity of the secondary phase, and the formation of noncrystalline phases. It considers three factors to understand the fundamentals of these changes: heat flow, thermodynamic constraints/conditions at the liquid-solid interfaces, and diffusional kinetics/microsegregation. These factors are described in detail.

The goal of micromechanics and analysis is to use the predictive methodology to develop tailored composites and also to make accurate predictions of their performance in service. This article reviews results derived from micromechanics analyses, based on finite-element method of unidirectional fiber reinforced metal matrix composites (MMCs). It discusses the elastic deformation and elastic-plastic deformation analysis of discontinuously reinforced MMCs. The article provides an overview of analysis of strength, fatigue, and fracture toughness for macromechanics fiber-reinforced and discontinuous reinforced composites.

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.

The design of components against fatigue failure may involve several considerations of irregular loading, variable temperature, and environment. This article focuses on design considerations against fatigue related to material performance under mechanical loading at constant temperature. It reviews the traditional methods of fatigue design on smooth and notched components. The article discusses high-cycle fatigue in terms of fatigue strength and tensile strength, mean stress effects, stress concentration, and multiaxial fatigue. It describes low-cycle fatigue in terms of deformation behavior and concludes with a discussion on lifetime analysis based on a strain approach.

This article focuses on the concepts involved in heat-transfer modeling, thermomechanical modeling, and microsegregation modeling of hot tearing. It discusses the modeling of solidification defects, namely, inclusion entrapment, segregation, shrinkage cavities, gas porosity, mold-wall erosion, and hot-tear cracks.

This article outlines a general approach to develop a coupled electrical-thermal-mechanical analysis for the resistance spot welding process. It provides information on the discretization of sheet-electrode geometry and distribution of contact resistivity along the sheet-sheet and electrode-sheet interfaces. The distribution can be estimated based on the discretized geometry used for the numerical modeling. The article also details the results obtained from this modeling.

Castability of alloys is a measure of their ability to be cast to a given shape with a given process without the formation of casting defects. This article describes the factors that limit fluidity as well as experimental methods for measuring fluidity of various alloys. Various tests designed for measuring the hot tearing tendency in alloys are discussed. The article also discusses the temperature dependence, criteria, and modeling of hot tearing.