This chapter discusses the role of plastic deformation in forging and the effect of strain and strain rate on metal flow. It demonstrates the use of stress tensors and shows how metal flow can be represented qualitatively by the displacement of volume elements and quantitatively by the distribution of velocity components and strain rates. It describes the conditions associated with homogeneous deformation in a frictionless upset forging and explains how they can also be obtained using engineering and true stress-strain curves.

This chapter discusses the fundamentals of plastic deformation and the role of strain and strain rate in sheet metal forming processes. It describes the conditions associated with uniform deformation, the significance of engineering and true strain, the effect of volume constancy on the tensile response of isotropic and anisotropic materials, and how infinitesimal strains or strain rates are used to express and analyze instantaneous deformation and local stain. It also discusses the concept of principal strain and strain paths and explains how to determine, and when to use, equivalent strain and strain rate.

This chapter demonstrates the versatility of the strain-range partitioning method and its application to creep-fatigue problems involving complex loading histories. It begins with a derivation showing that it is possible to assess the damage of hysteresis loops combining two or more strain ranges using generic loops based on fundamental data. It then explains how to treat problems involving sequential loading with both healing and damage cycles and presents a general solution for combining two loops with arbitrary amounts of the four strain-range components. The chapter also derives closed-form equations that account for interactions among any number of adjacent loops and can be used, through successive application, to analyze any loading history.

This chapter explains why it is sometimes necessary to separate inelastic from elastic strains and how to do it using one of two methods. It first discusses the direct calculation of strain-range components from experimental data associated with large strains. It then explains how the method can be extended to the treatment of very low inelastic strains by adjusting tensile and compressive hold periods and continuous cycling frequencies. The chapter then begins the presentation of the second approach, called the total strain-range method, so named because it combines elastic and inelastic strain into a total strain range. The discussion covers important features, procedures, and correlations as well as the use of models and the steps involved in predicting thermomechanical fatigue (TMF) life. It also includes information on isothermal fatigue, bithermal creep-fatigue testing, and the predictability of the method for TMF cycling.

The stress-strain curves in this data set are representative examples of the behavior of several cast alloys under tensile or compressive loads. The curves are arranged by alloy designation. Each figure cites the original source of the curve and provides pertinent background information as available. Compressive tangent modulus curves are presented for certain alloys. The effects of cyclic loading are given on several curves.

This chapter provides a detailed analysis of the cyclic stress-strain behavior of materials under uniaxial stress and strain cycling. It first considers the case of a stable material under constant-amplitude strain cycling then broadens the discussion to materials that harden or soften with continued strain reversals. It compares and contrasts the response patterns of such materials, explaining how the movement of dispersed particles and dislocations influences their behavior. It then examines the behavior of materials under uniaxial strain reversals of varying amplitude and explains how to construct double-amplitude stress-strain curves that account for complex straining histories. For special cases, those involving complex materials such as gray cast iron or highly complex straining patterns, the chapter presents other methods of analysis, including the rainflow cycle counting method, mechanical modeling based on displacement-limited elements, Wetzel’s method, and deformation modeling. It also explains the difference between force cycling and stress cycling and presents alternate techniques for predicting whether a material will become harder or softer in response to strain cycling.

Strain-range partitioning is a method for assessing the effects of creep fatigue based on inelastic strain paths or strain reversals. The first part of the chapter defines four distinct strain paths that can be used to model any cyclic loading pattern and describes the microstructural damages associated with each of the four basic loading cycles. The discussion then turns to fatigue life prediction for different types of materials and more realistic loading conditions, particularly those in which hysteresis loops have more than one strain-range component. To that end, the chapter considers two cases. In one, the relationship between strain range and cyclic life is established from test data. In the other, a rule is required to determine the damage of each concurrent strain and the total damage of the cycle is used to predict creep-fatigue life. The chapter presents several such damage rules and discusses their applicability in different situations.

This chapter reviews the current technology and examines force application systems, force measurement, strain measurement, important instrument considerations, gripping of test specimens, test diagnostics, and the use of computers for gathering and reducing data. The influence of the machine stiffness on the test results is also described, along with a general assessment of test accuracy, precision, and repeatability of modern equipment. The chapter discusses various types of testing machines and their operations. Emphasis is placed on strain-sensing equipment. The chapter briefly describes load condition factors, such as strain rate, machine rigidity, and various testing modes by load control, speed control, strain control, and strain-rate control. It provides a description of environmental chambers for testing and discusses the processes involved in the force verification of universal testing machines. Specimen geometries and standard tensile tests are also described.

High strain rate tensile testing is necessary to understand the response of materials to dynamic loading. The behavior of materials under high strain rate tensile loads may differ considerably from that observed in conventional tensile tests. This chapter discusses the processes involved in determining strain rate effects in tension by conventional tensile tests, expanding ring test, flat plate impact tests, split-Hopkinson pressure bar test, and rotating wheel test, along with their applications, advantages, and disadvantages.

This appendix lists etch compositions and procedures that reveal strain patterns in aluminum and nickel-base superalloys.

This chapter discusses three measurements parameters: temperature, strain, and magnetic field strength. It stresses the measurement of temperature because it is the primary variable in nearly all low-temperature material properties. The chapter contains information on methods and auxiliary materials. Areas of frequent concern, such as thermal contact, heat leak, thermal anchoring, thermal conductivity of greases, insulators, lead wires, ground loops, and feedthroughs are also reviewed. The chapter provides an overview and historical development of temperature scales because the practical use of all thermometers is associated with some approximation of the thermodynamic temperature scale. A short section is devoted to types of temperature measuring devices. The characteristics of commercially available resistance-type strain gauges at low temperatures are stressed.

This chapter reviews the fundamentals of stress, strain, and deformation and demonstrates some of the tools and techniques used to analyze how materials and structures respond to tension, compression, bending, and shear. It begins with an overview of the behavior of perfectly elastic and plastic materials and viscous substances. It then describes the stress-strain response of two- and three-dimensional solids, explaining how to determine principle stresses and strains using Mohr’s circle and how to derive equivalent stress and strain using the von Mises relationship. It then goes on to analyze the stress state of load-bearing members, pressurized tubes, and pin-loaded lugs, accounting for the effect of geometric discontinuities, such as cutouts, fillets, and holes, as well as cracks. It also explains how finite element methods are used to solve problems involving complex geometric and loading conditions.

This chapter focuses on mechanical behavior under conditions of uniaxial tension during tensile testing. It begins with a discussion on the parameters that are used to describe the engineering stress-strain curve of a metal, namely, tensile strength, yield strength or yield point, percent elongation, and reduction in area. This is followed by a section describing the parameters determined from the true stress-true strain curve. The chapter then presents the mathematical expressions for the flow curve. Next, it reviews the effect of strain rate and temperature on the stress-strain curve. The chapter then describes the instability in tensile deformation and stress distribution at the neck in the tensile specimen. It discusses the processes involved in ductility measurement and notch tensile test in tensile specimens. The parameter that is commonly used to characterize the anisotropy of sheet metal is covered. Finally, the chapter covers the characterization of fractures in tensile test specimens.

This chapter discusses the methodology of the tensile test and the effect of some of the variables on the tensile properties. The methodology and variables discussed are shape of the item being tested, method of gripping the item, method of applying the force, determination of strength properties other than the maximum force required to fracture the test item, ductility properties to be determined, speed of force application or speed of elongation, and test temperature. The chapter presents the definitions of the basic terms and their units, along with discussions of basic stress-strain behavior and the differences between related terms, such as stress and force and strain and elongation. It considers the parts of a tensile test, namely, test-piece preparation, geometry, and material condition; test setup and equipment; and test procedures. The chapter provides information on post-test measurements and describes the effect of strain concentrations and strain rate on tensile properties.

The design and optimization of sheet metal forming operations is aided by tools and techniques that have been developed and refined over several decades. This chapter covers many of these methods and practices and explains where and how they are used. It begins by showing how the stress state at any point in a material can be expressed in different ways for different purposes. It then compares and contrasts some of the more widely used yield criteria and demonstrates the use of flow rules. It also explains how to calculate power, energy, and effective strain and strain rate and how hardening laws are used to predict strain-hardening behaviors.

This chapter deals with the effects of fatigue in rotating shafts subjected to elastic and plastic strains associated with bending stresses. It begins with a review of the basic approach to treating low-cycle fatigue in bending, explaining that the assumption that stress is proportional to strain is incorrect due to plastic flow, causing considerable discrepancy between measured and calculated stresses. Data plots of the axial and bending fatigue characteristics of a 4130 steel help illustrate the problem. A closed-form solution is then presented and used to analyze the effects of flexural bending on solid as well as hollow rectangular and round bars. The chapter also discusses the difference in the treatment of a rotating shaft in which all surface elements undergo the same stress and strain and a nonrotating shaft in which a few surface elements carry most of the load. The difference, as explained, is due to the volumetric effect of stress in fatigue.

This chapter addresses the challenge of selecting an appropriate stress-corrosion cracking (SCC) test to evaluate the serviceability of a material for a given application. It begins by establishing a generic model in which SCC is depicted in two stages, initiation and propagation, that further subdivide into several zones plus a transition region. It then discusses SCC test standards before describing basic test objectives and selection criteria. The chapter explains how to achieve the required loading conditions for different tests and how to prepare test specimens to determine elastic strain, plastic strain, and residual stress responses. It also describes the difference between smooth and precracked specimens and how they are used, provides information on slow-strain-rate testing and how to assess the results, and discusses various test environments and procedures, including tests for weldments. The chapter concludes with a section on how to interpret time to failure, threshold stress, percent survival, stress intensity, and propagation rate data, and assess the precision of the associated tests.

The tensile test provides a relatively easy, inexpensive technique for developing mechanical property data for the selection, qualification, and utilization of metals and alloys in engineering service. The tensile test may require interpretation, and interpretation requires a knowledge of the factors that influence the test results. This chapter provides a metallurgical perspective for such interpretation. The topics covered include elastic behavior, an elasticity, damping, proportional limit, yield point, ultimate strength, toughness, ductility, strain hardening, yielding, and the onset of plasticity. The chapter describes the effects of grain-size on yielding, effect of cold work on the hardness and strength, and effects of temperature and strain-rate on the properties of metals and alloys. It provides information on true stress-strain relationships and special tests developed to measure the effects of test/specimen conditions. Finally, the chapter covers the characterization of tensile fracture of ductile metals and alloys.

This chapter covers the fundamentals of metal flow and the tools and techniques used to predict and control it. It begins by illustrating the local state of stress in a metal cylinder during upset forging and showing how stress components can be expressed in matrix form. It then explains how to determine the onset of yielding, which corresponds to the start of plastic deformation and the flow of metal within the workpiece. The chapter then goes on to present two important yield criteria, one based on shear stress (Tresca criterion), the other on distortion energy (von Mises criterion). It compares and contrasts the two methods and demonstrates their use as flow rules. It also explains how to calculate effective strain and strain rate and includes a brief discussion on the mechanical energy consumed during deformation.

This chapter begins with a review of the mechanics of bending and the primary elements of a bending system. It examines stress-strain distributions defined by elementary bending theory and explains how to predict stress, strain, bending moment, and springback under various bending conditions. It describes the basic principles of air bending, stretch bending, and U- and V-die bending as well as rotary, roll, and wipe die bending, also known as straight flanging. It also discusses the steps involved in contour (stretch or shrink) flanging, hole flanging, and hemming and describes the design and operation of press brakes and other bending machines.