This article provides an in-depth treatment on the deformation and recrystallization of titanium alloys. It provides information on the predominant mode of plastic deformation that occurs in titanium in terms of the most common crystallographic planes. The article explains the relationship of the recovery process to the recrystallization, grain-growth process, and the effects of time and temperature on stress relief. It describes the factors that influence the rate of recrystallization and the conditions required for neocrystallization to occur. The article explains the mechanism of strain hardening and its effects on the mechanical properties of titanium alloys. It also discusses the factors that influence the superplasticity of titanium alloys.

This article contains nine tables that present useful formulas for deformation analysis and workability testing. The tables present formulas for effective stress, strain, and strain rate in arbitrary coordinates, principal, compression and tension testing of isotropic material. The article also provides formulas for flat rolling, conical-die extrusion, wire drawing, deep drawing of cups from sheet metal, and bending, and formulas for anisotropic sheet materials.

Plastic deformation can occur in metals from various mechanisms, such as slip, twinning, diffusion creep, grain-boundary sliding, grain rotation, and deformation-induced phase transformations. This article emphasizes on the mechanism of slip and twinning under cold working conditions. It discusses the factors on which the structures developed during plastic deformation depend. These factors include crystal structure, amount of deformation, composition, deformation mode, and deformation temperature and rate. The article illustrates the microstructural features that appear after substantial deformation when revealed through metallographic investigation.

Engineering component and structure failures manifest through many mechanisms but are most often associated with fracture in one or more forms. This article introduces the subject of fractography and aspects of how it is used in failure analysis. The basic types of fracture processes (ductile, brittle, fatigue, and creep) are described briefly, principally in terms of fracture appearances. A description of the surface, structure, and behavior of each fracture process is also included. The article provides a framework from which a prospective analyst can begin to study the fracture of a component of interest in a failure investigation. Details on the mechanisms of deformation, brittle transgranular fracture, intergranular fracture, fatigue fracture, and environmentally affected fracture are also provided.

This article outlines several polycrystal formulations commonly applied for the simulation of plastic deformation and the prediction of deformation texture. It discusses the crystals of cubic and hexagonal symmetry that constitute the majority of the metallic aggregates used in technological applications. The article defines the basic kinematic tensors, reports their relations, and presents expressions for calculating the change in crystallographic orientation associated with plastic deformation. It surveys some of the polycrystal models in terms of the relative strength of the homogeneous effective medium (HEM). The article analyzes the anisotropy predictions of rolled face-centered-cubic and body centered-cubic sheets and presents simulations of the axial deformation of hexagonal-close-packed zirconium. The applications of polycrystal constitutive models to the simulation of complex forming operations, through the use of the finite element method, are also presented.

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 physical analysis, including slab method and upper-bound method and slip-line field analysis, for calculating stress states in plastic deformation processes. It presents various validation standards and models for evaluating the criterion of fracture for use in finite-element analyses of deformation processing. The article reviews the Cockcroft-Latham criterion of fracture and its reformulated extension for analysing the fracture locus for compression. It concludes with information on fundamental fracture models.

This article discusses the deformation and viscoelastic characteristics of plastics as polymeric materials, focusing on the test methods used for the evaluation of their mechanical properties, methods available for analytically predicting the deformation response of polymers, and the effect of viscoelasticity on the test methods used. Two common ways of evaluating viscoelasticity of plastics are by means of creep experiments and dynamic mechanical experiments. Graphic or tabular analysis of test data, time-temperature superposition, and empirical correlation methods are commonly employed for analytical prediction of deformation characteristics of polymers.

Any model that describes the early stage of cavitation must therefore address experimental observations of continuous nucleation, cracklike interface cavities, cavity growth from nanometer-scale sizes, and debonding at particle interfaces and formation of large-faceted cavities. This article summarizes the microstructural details of the early stages of cavitation in metals for understanding the interface-constrained plasticity cavitation model. It discusses formulation, predictions and implications, involved in analysis of cavitation under constrained conditions.

Distortion often is observed in the analysis of other types of failures, and consideration of the distortion can be an important part of the analysis. This article first considers that true distortion occurs when it was unexpected and in which the distortion is associated with a functional failure. Then, a more general consideration of distortion in failure analysis is introduced. Several common aspects of failure by distortion are discussed and suitable examples of distortion failures are presented for illustration. The article provides information on methods to compute load limits, errors in the specification of the material, and faulty process and their corrective measures to meet specifications. It discusses the general process of material failure analysis and special types of distortion and deformation failure.

This article examines the deformation processes in metal-forming operations and considers the effects introduced by scale factors when microforming. It discusses the process parameters and variables affecting surface interactions, including temperature, speed, reduction, stiffness, and dynamic response of equipment. The article reviews the determination of friction coefficient using laboratory monitoring methods, indirect measurements, and the inverse method. It considers the determination of the interface heat-transfer coefficient by using the ring test and computer simulations. The article describes the behavior of oxide scale on the surface of hot metal undergoing thermomechanical processing. It concludes with information on the effects of process and material parameters on interfacial phenomena.

This article discusses a number of workability tests that are especially applicable to the forging process. The primary tests for workability are those for which the stress state is well known and controlled. The article provides information on the tension test, torsion test, compression test, and bend test. It examines specialized tests including plane-strain compression test, partial-width indentation test, secondary-tension test, and ring compression test. The article explains that workability is determined by two main factors: the ability to deform without fracture and the stress state and friction conditions present in the bulk deformation process. These two factors are described and brought together in an experimental workability analysis.

This article focuses on the factors that determine the extent of deformation a metal can withstand before cracking or fracture occurs. It informs that workability depends on the local conditions of stress, strain, strain rate, and temperature in combination with material factors. The article discusses the common testing techniques and process variables for workability prediction. It illustrates the simple and most widely used fracture criterion proposed by Cockcroft and Latham and provides a workability analysis using the fracture limit line. The article describes various workability tests, such as the tension test, ring compression test, plane-strain compression test, bend test, indentation test, and forgeability test. It concludes with information on the role of the finite-element modeling software used in workability analysis.

This article, to develop an understanding of the underlying mechanisms governing deformation at elevated temperatures, discusses the phenomenological effects resulting from temperature-induced thermodynamic and kinetic changes. It describes the deformation behavior of engineering materials using expressions known as constitutive equations that relate the dependence of stress, temperature, and microstructure on deformation. The article reviews the characteristics of creep deformation and mechanisms of creep, such as power-law creep, low temperature creep, power-law breakdown, diffusional creep, twinning during creep deformation, and deformation mechanism maps. It discusses the creep-strengthening mechanisms for most structural engineering components. The article provides a description of the microstructural modeling of creep in engineering alloys.

The processing of steel involves five distinct sets of texture development mechanisms, namely, austenite deformation, austenite recrystallization, gamma-to-alpha transformation, ferrite deformation, and static recrystallization during annealing after cold rolling. This article provides an introduction on crystallographic textures. It discusses the effects of austenite rolling and recrystallization on the texture and transformation behavior of recrystallized austenite and deformed austenite. The article illustrates the overall summary of the rolling and transformation behavior. It details cold-rolling textures, annealing textures, and recrystallization textures of steel samples. The article concludes with a summary of texture development during cold rolling and annealing.

The presence of macroscopic residual stresses in heat treatable aluminum alloys can give rise to machining distortion, dimensional instability, and increased susceptibility to in-service fatigue and stress-corrosion cracking. This article details the residual-stress magnitudes and distributions introduced into aluminum alloys by thermal operations associated with heat treatment. The available technologies by which residual stresses in aluminum alloys can be relieved are also described. The article shows why thermal stress relief is not a feasible stress-reduction technology for precipitation-hardened alloys. It examines the consequences of aging treatments on the residual stress, namely, annealing, precipitation heat treatment, and cryogenic treatment. The article provides information on uphill quenching, which attempts to reverse thermal gradients encountered during quenching. It examines how quench-induced residual stresses in heat treatable aluminum alloys are reduced when sufficient load is applied to cause plastic deformation. The article also shows how plastic deformation reduces residual stress.

This article provides the definitions of stress and strain, and describes the relationship between stress and strain by stress-strain curves and true-stress/true-strain curves. The emphasis is on understanding the factors that determine the extent of deformation a metal can withstand before cracking or fracture occurs. The article reviews the process variables that influence the degree of workability and summarizes the mathematical relationships that describe the occurrence of room-temperature ductile fracture under workability conditions. It discusses the most common situations encountered in multiaxial stress states. The construction of a processing map based on deformation mechanisms is also discussed.

The constitutive relations for metalworking include elements of behavior at ambient temperature as well as high-temperature response. This article presents equations for strain hardening and strain-rate-sensitive flow, with alternate sections on empirically determined properties, followed by the models of constitutive behavior. It provides a discussion on creep mechanisms involving dislocation and diffusional flow, such as the Nabarro-Herring creep and the Coble creep. The equations for the several creep rates are also presented. Research on the mechanism of the superplastic flow in fine-grain metals has encompassed many ideas, such as the diffusional creep, dislocation creep with diffusional accommodation at grain boundaries, and concepts of grain-mantle deformation. The article concludes with information on the kinetics of superplastic deformation processes, including low stress behavior, concurrent grain growth, and high stress behavior.

Recovery, recrystallization, and grain growth are microstructural changes that occur during annealing after cold plastic deformation and/or during hot working of metals. This article reviews the structure of the deformed state and describes the changes in the properties and microstructures of a cold-worked metal during recovery stage. It discusses the recrystallization that occurs by the nucleation and growth of grains. The article also reviews the growth behavior of the grains, explaining that the grain growth can be classified into two types: normal or continuous grain growth and abnormal or discontinuous grain growth. It also examines the key mechanisms that control microstructure evolution during hot working and subsequent heat treatment. These include dynamic recovery, dynamic recrystallization, metadynamic recrystallization, static recovery, static recrystallization, and grain growth.

The modeling and simulation of texture evolution for titanium alloys is often tightly coupled to microstructure evolution. This article focuses on a number of problems for titanium alloys in which such coupling is critical in the development of quantitative models. It discusses the phase equilibria, crystallography, and deformation behavior of titanium and titanium alloys. The article describes the modeling and simulation of recrystallization and grain growth of single-phase beta and single-phase alpha titanium. The deformation- and transformation-texture evolution of two-phase (alpha/beta) titanium alloys are also discussed.