Search Results for elastic-plastic bending

The mechanical behavior of a material, in the most practical sense, is how it deforms or breaks under load; in other words, how it responds when stressed. This chapter provides a brief review of the properties associated with mechanical behavior, including stress, strain, elasticity, plastic deformation, ductility, hardness, creep, fatigue, and fracture. It also describes the primary components of a Charpy impact tester and the role they serve.

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.

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.

Sheet metal forming operations consist of a large family of processes, ranging from simple bending to stamping and deep drawing of complex shapes. Because sheet forming operations are so diverse in type, extent, and rate, no single test provides an accurate indication of the formability of a material in all situations. However, as discussed in this chapter, the uniaxial tensile test is one of the most widely used tests for determining sheet metal formability. This chapter describes the effect of material properties and temperature on sheet metal formability. Information on the types of formability tests is also provided. The chapter discusses the processes involved in uniaxial and plane-strain tensile testing. Examples include the uniaxial tensile test and the plane-strain tensile test which are subsequently described.

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.

Fracture mechanics is the science of predicting the load-carrying capabilities of cracked structures based on a mathematical description of the stress field surrounding the crack. The fundamental ideas stem from the work of Griffith, who demonstrated that the strain energy released upon crack extension is the driving force for fracture in a cracked material under load. This chapter provides a summary of Griffith’s work and the subsequent development of linear elastic and elastic-plastic fracture mechanics. It includes detailed illustrations and examples, familiarizing readers with the steps involved in determining strain energy release rates, stress intensity factors, J-integrals, R-curves, and crack tip opening displacement parameters. It also covers fracture toughness testing methods and the effect of measurement variables.

Tensile tests are performed for several reasons related to materials development, comparison, selection, and quality control. The properties derived from tensile tests are used in selecting materials for engineering applications. Tensile properties often are used to predict or estimate the behavior of a material under forms of loading other than uniaxial tension. This chapter provides a brief overview of tensile specimens and test machines, stress-strain curves, true stress and strain, and test methodology and data analysis.

This chapter discusses the factors that influence the load-deformation relationship at the heart of most metal forming operations. It describes the changes that occur in tensile test samples and the various ways test data can be plotted and analyzed, particularly for design purposes. It discusses the effect of normal and planar anisotropy, the development and use of flow stress curves, and how formability is usually measured and expressed. It explains how formability measurements serve as a guide for process and tool design engineers as well as others. It also discusses the development and use of forming limit curves and the extensive amount of information they provide.

This chapter provides an introduction to metal forming processes and where they fit among the five general areas of manufacturing. It also discusses the basic differences between bulk deformation and sheet-metal forming processes and how they relate to hybrid forming processes such as drawing, bending, and coining.

This chapter is a compilation of terms and definitions related to tensile testing.

The relationship of stress and strength gradients must be considered simultaneously in analysis of a particular type of fracture. This chapter discusses the principal elastic stress distribution in members of various shapes under different types of pure loads. A basic understanding of both the stress and strength gradients of metal parts with and without stress concentrations and under different types of loading is provided. The chapter also describes the effect of service conditions on applied stresses.

This chapter provides an overview of factors that must be considered in the design of structural components for satisfactory service performance in terms of mechanical behavior of steel castings. The chapter discusses designing against yielding, excessive deflection, and creep and stress rupture. The chapter describes the three main approaches to evaluating and designing structures relative to fatigue resistance: the S-N curve approach for high cycle fatigue, the strain range approach for low cycle fatigue, and the fracture mechanics approach. Two approaches to design against brittle fracture are described, the ductile to brittle transition concept and the fracture mechanics approach. The chapter also discusses several types of corrosion behavior and emphasizes the need to interact with corrosion specialists in the design process. It illustrates the unique advantages that designers may gain by designing components as castings to achieve low stress concentrations economically.

Distortion failures are readily identified by the inherent change in size and/or shape. They are serious because they can lead to other types of failure or may even cause complete collapse of structures, such as bridges, ladders, beams, and columns. Distortion failures may be classified in different ways. One way is to consider them either as dimensional distortion (growth or shrinkage) or as shape distortion (such as bending, twisting, or buckling). They may also be classified as being either temporary or permanent in nature. This chapter discusses the nature, causes, and effects of all of these types of failures as well as the methods to manage them.

This chapter describes the nature of the problems arising from using advanced high-strength steels, including limited formability, reduced weldability, increased springback, elevated press tonnage, and accelerated die wear, and discusses potential remedies to minimize the adverse effects that may limit the adoption of AHSS in the automotive industry.

This chapter discusses the factors that play a role in fatigue failures and how they affect the service life of metals and structures. It describes the stresses associated with high-cycle and low-cycle fatigue and how they differ from the loading profiles typically used to generate fatigue data. It compares the Gerber, Goodman, and Soderberg methods for predicting the effect of mean stress from bending data, describes the statistical nature of fatigue measurements, and explains how plastic strain causes cyclic hardening and softening. It discusses the work of Wohler, Basquin, and others and how it led to the development of a strain-based approach to fatigue and the use of fatigue strength and ductility coefficients. It reviews the three stages of fatigue, beginning with crack initiation followed by crack growth and final fracture. It explains how fracture mechanics can be applied to crack propagation and how stress concentrations affect fatigue life. It also discusses fatigue life improvement methods and design approaches.