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.

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 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 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 focuses on mechanical behavior under conditions of uniaxial tension during tensile testing. It begins with a discussion of properties determined from the stress-strain curve of a metal, namely, tensile strength, yield strength, measures of ductility, modulus of elasticity, and resilience. 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. The chapter reviews the effect of strain rate and temperature on the stress-strain curve and 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.

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 used 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 and covers expanding ring tests, flat plate impact tests, split-Hopkinson pressure bar tests, and rotating wheel tests.