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 is a comprehensive collection of the thermodynamic equations and property relations of the first and second laws of thermodynamics that are applicable to closed-system consisting of several homogeneous and heterogeneous phases.

This article is a comprehensive collection of fluid dynamic equations for properties of fluids, fluid statics, fluid motion, dimensional analysis, and boundary layer flow. It presents equations for analyzing problems in fluid mechanics, continuity equation, momentum equation, and energy equation for solving various problems related to fluid dynamics.

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 focuses on approximate closed-form analytical methods, such as slab and upper bound methods, used for forward and inverse design of metal forming problems. Selected examples of application of these methods to metal forming processes are also discussed.

This article discusses the conditions for collapse in center-cracked panels and describes the energy criterion for fracture. Measurement of toughness of any material by means of tensile and crack test is discussed. The procedures to be followed for linear elastic fracture mechanics cases are reviewed, along with elastic-plastic fracture mechanics and plastic fracture mechanics procedures with the aid of residual strength diagram. The article also explains the geometry factors needed to determine the toughness of materials.

Computational fluid dynamics (CFD) provides an efficient, alternate, virtual approach for simulating and analyzing quenching processes with an impact on component design, manufacturing process, and quality. This article provides domain insights for quenching researchers and CFD practitioners for the modeling of the industrial quenching process and for supporting the diverse multifunctional needs in an industry, ranging from primary metallurgical companies (steel, aluminum, and other alloys), original equipment manufacturers, engineering companies, captive and commercial heat treating facilities, quench system manufacturers, and quench fluid suppliers. It describes the governing differential equations for the fluid flow and heat-transfer phenomena during quenching. The article also discusses different modeling categories to determine a CFD methodology for quenching.

This article presents a mechanical description of superplasticity and discusses constitutive equations that are essential for simulating superplastic forming processes, applicable to structural superplasticity. It presents the phenomenological constitutive equations of superplasticity and classical physical constitutive equations. The article also reviews the accommodation mechanisms that are divided into two major groups, namely, diffusional accommodation and accommodation by dislocations.

Work or strain hardening is a natural consequence of most working and forming operations on aluminum and its alloys. This article describes the annealing practices of strain-hardened alloys. It lists the temper designations for strain-hardened alloys. The article discusses the annealing of worked structures in terms of recovery, recrystallization, and grain coarsening. It summarizes some of the annealing treatments used in conjunction with fabrication by metal working, including preheating, interannealing, self-annealing, stabilization, and stoving. The article concludes with information on the key process parameters affecting the final properties of aluminum alloys.

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.

Controlled-potential coulometry is a highly precise and accurate method primarily used for major constituent analysis of analyte substances such as alloys, compounds, nonmetallic materials and organic compounds. This article illustrates the apparatus required for controlled-potential coulometry, and provides information on its techniques and applications. It contains a table that lists the metals for which accurate methods have been developed and the basic electrochemistry of the procedures. The article explains that gold and uranium are the elements that are determined frequently in various sample types.

This article describes friction force as a function of normal force in dry forming. It focuses on metal forming operations usually classified as cold working and hot working based on metallurgical considerations. The article discusses surface flattening and roughening of workpiece asperities in metal forming. It presents advanced tribology models and results for friction in isothermal forging operations in which the tooling is maintained at a temperature close to that of the workpiece. The article provides information on heat transfer models. It discusses the effect of wear in manufacturing processes. The article concludes with information on the main categories of tool and die materials used for a variety of manufacturing application.

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 four subsystems of the electrochemical machining (ECM) system: power source, electrolyte cleaning and supply system, tool and tool-feed system, and workpiece and workpiece-holding system. It describes the theory of ECM and provides information on the electrolytes used in ECM. The article reviews the methods associated with workpiece shape prediction. The procedures and integrated approach for the tool design in ECM are discussed. The article also explains the process control, capabilities, and the limitations of ECM. It concludes with information on the applications of ECM.

This article describes the use of compression tests, namely, cylindrical compression, ring compression, and plane-strain compression tests at elevated temperatures. It discusses the effects of the temperature, strain rate, and deformation heating on metals during the cylindrical compression test, with the help of flow curves. The article illustrates the testing apparatus used in the cylindrical compression test. It describes the issues regarding friction and temperature, and strain-rate control with proper test equipment and experimental planning during the ring compression test and plane-strain compression test. The article also reviews the testing conditions, procedures, and advantages of hot plane-strain compression test.

This article focuses on the analyzing and modeling of stress-strain behavior of polycrystals of pure face-centered cubic (fcc) metals in the range of temperatures and strain rates where diffusion is not important. It presents a phenomenological description of stress-strain behavior and provides information on the physical background, alternative interpretations, and directions of research. The quantitative description of strain hardening of fcc polycrystals is provided. The article also discusses the modeling of stress-strain behavior in body-centered cubic metals, hexagonal metals, stage IV work hardening, and the various classes of single-phase alloys.

This article focuses on the general internal state variable method, and its simplification, for single-parameter models, in which the microstructure evolution may be treated as an isokinetic reaction. It explains that isokinetic microstructure models are applied to diffusional transformations in fusion welding, covering particle dissolution, growth, and coarsening of precipitates in the heat-affected zone. The article discusses the versatility of the internal state variable approach in modeling of nonisothermal transformations for various materials and processes. It describes the process models applied to predict the microstructure evolution in Al-Mg-Si alloys during multistage thermal processing involving heat treatment and welding. The article also provides information on the microstructure models exploited in engineering design to optimize the load-bearing capacity of welded aluminum components.

Hardness testing is perhaps the simplest and the least expensive method of mechanically characterizing a material. This article provides an overview of the principles of hardness testing. It compares Brinell with Meyer hardness testing and hardness testing of fully cold worked metals with fully annealed metals. The article discusses the plastic deformation of ideal plastic metals under an indenter, by a flat punch, and by spherical indenters. The classification of the hardness tests using various criteria, including type of measurement, magnitude of indentation load, and nature of the test, is also provided.

Coextrusion is defined as the simultaneous extrusion of two or more metals to form an integral product that can be carried out using conventional extrusion or drawing equipment at a temperature appropriate to the metal system being formed. This article discusses the applications, billet configurations, and metal flow modes of coextrusion. It presents the analytical studies of coextrusion: deformation energy methods, lower-bound (slab) analyses, upper-bound analyses, and finite-element analyses. These studies are used to identify the regime of material properties and process variables for which sound extrusions can be obtained. The article concludes with a discussion on the state-of-the-art of coextrusion that assists in developing process models, which accurately describe both the macroscopic and microscopic aspects of a process.

Modern, solids-based computer-aided design/computer-aided manufacturing (CAD/CAM) systems provide a good share of what is needed for companies to develop products using modern methods. This article provides a brief history and an overview of CAD technology. Form features combined with constraint parameters have greatly simplified how designers work with solid modelers to design parts and assemblies. The article describes four types of constraints: numeric, geometric, algebraic, and attributes. It presents a discussion on data associativity and assembly design used in CAD system. The article provides information on the applications of CAD systems, including integrated product development, drafting and product documentation, product visualization, mechanical analysis, and numerical control programming.