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.

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 article discusses the material and engineering issues associated with plastic components subjected to impact. The first part covers the effects of loading rate, temperature, and state of stress on both deformation and mode of failure. It discusses standard impact tests, along with their associated results. A brief discussion on the linear elastic fracture mechanics method is presented, along with an example of its effectiveness as a predictive tool for impact performance. Various issues with a bearing on impact performance, such as processing, chemical attack, and aging, are also described. The second part describes the engineering calculations used to predict the performance of thin plastic beams, plates, and shells. The issue of assuming small displacements for the calculation of plastic structure performance is discussed and its limitations described. An example of the consequence of the very low modulus of elasticity associated with plastics and some plastic design solutions are offered.

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.

Large-scale yielding at the crack tip and time-dependent crack growth mechanisms, such as stress relaxation due to creep, are nonlinear behaviors requiring nonlinear analysis methods. This chapter presents two such methods, one based on elastic-plastic fracture mechanics, the other on time-dependent fracture mechanics. It also introduces two new fracture indices, the J-integral for handling large-scale yielding and the C*-integral for creep crack growth, providing close-form and handbook solutions for each.

Fracture mechanics is a well-developed quantitative approach to the study of failures. This chapter discusses fracture toughness and fracture mechanics, linear-elastic fracture mechanics, and modes of loading. The discussion also covers plane strain and stress and crack growth kinetics. The chapter presents a case history that illustrates the use of fracture mechanics in failure analysis. An appendix provides a more detailed discussion of fracture mechanics concepts.

This chapter provides a quantitative treatment of the cracking mechanisms associated with fatigue, drawing on the principles of fracture mechanics. It explains that although fracture mechanics originated with the aim of understanding sudden and catastrophic crack extension, the main premise of a stress field in the vicinity of the crack also applies to the study of cycle-by-cycle stable crack growth. A detailed review is given of the many developments and discoveries that helped shape the theory and methods collectively defined as crack mechanics, which the authors then employ to analyze the crack growth behavior of various materials, including steels and nonferrous alloys, under constant-amplitude loading. The authors then deal with the effects of complex loading using crack retardation and crack closure models to show how load fluctuations can slow crack growth rates and even cause total crack arrest. They also present the results of a study on crack initiation, propagation, and fracture in circular (rather than rectangular) specimens and a fatigue study on ductile and quasi-brittle materials.

This chapter discusses the failure mechanisms associated with fiber-reinforced composites. It begins with a review of fiber-matrix systems and the stress-strain response of unidirectional lamina and both notched and unnotched composite laminate specimens. It then explains how cyclic loading can lead to delamination, the primary failure mode of most composites, and describes some of the methods that have been developed to improve delamination resistance, assess damage tolerance, determine residual strength, and predict failure modes.

This appendix provides supplemental information on the metallurgical aspects of atomic structure, the use of dislocation theory, heat treatment processes and procedures, important engineering materials and strengthening mechanisms, and the nature of elastic, plastic, and creep strain components. It also provides information on mechanical property and fatigue testing, the use of hysteresis energy to analyze fatigue, a procedure for inverting equations to solve for dependent variables, and a method for dealing with the statistical nature of failure.

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.

This chapter reviews the theories that have emerged from the widespread study of multiaxial fatigue and assesses their validity using data from different sources. It begins by providing background on the studies that the chapter draws on, pointing out differences in methodology and explaining how they influence test results and data. It then discusses the concept of critical planes and how they are used to correlate the effects of uniaxial loading with multiaxial fatigue behaviors. The section that follows covers the various methods used to analyze multiaxial fatigue and identifies one that best treats the general case. The chapter also defines two important factors, the triaxiality factor and the multiaxiality factor, and presents the results of an extensive study to determine how the two factors are related. One of the more interesting findings is that the atomic structure of a material has a significant effect on which theory best describes its fatigue behavior.

In order to understand how various types of single-load fractures are caused, one must understand the forces acting on the metals and also the characteristics of the metals themselves. All fractures are caused by stresses. Stress systems are best studied by examining free-body diagrams, which are simplified models of complex stress systems. Free-body diagrams of shafts in the pure types of loading (tension, torsion, and compression) are the simplest; they then can be related to more complex types of loading. This chapter discusses the principles of these simplest loading systems in ductile and brittle metals.

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 focuses on the processes and mechanisms involved in fatigue. It begins with a review of some of the early theories of fatigue and the tools subsequently used to obtain a better understanding of the fatigue process. It then explains how plasticity plays a major role in creating dislocations, breaking up grains into subgrains, and causing microscopic imperfections to coalesce into larger flaws. It also discusses the factors that contribute to the development and propagation of fatigue cracks, including surface deterioration, volumetric and environmental effects, foreign particles, and stresses generated by rolling contact.

This chapter examines the phenomena of deformation and fracture in metals, providing readers with an understanding of why it occurs and how it can be prevented. It begins with a detailed review of tension and compression stress-strain curves, explaining how they are produced and what they reveal about the load-carrying characteristics of engineering materials. It then discusses the use of failure criteria and the determination of yielding and fracture limits. It goes on to describe the mechanisms and appearances of brittle and ductile fractures and stress rupture, providing detailed images, diagrams, and explanations. It discusses the various factors that influence strength and ductility, including grain size, loading rate, and temperature. It also provides information on the origin of residual stresses, the concept of toughness, and the damage mechanisms associated with creep and stress rupture, stress corrosion, and hydrogen embrittlement.

This chapter discusses the use of modeling and simulation technology in the development of sheet metal forming processes. It describes the five major steps involved in finite-element analysis and the various ways functions of interest can be approximated at each point or node in a finite-element mesh. It explains how to obtain input data, what to expect in terms of output data, and how to predict specific types of defects. In addition, it presents several case studies demonstrating the use of finite elements in blanking and piercing, deep drawing of round and rectangular cups, progressive die sequencing, blank holder force optimization, sheet hydroforming, hot stamping, and springback and bending of advanced high-strength steels. It also discusses the factors that affect the accuracy of finite element simulations such as springback, thickness variations, and nonisothermal effects.

This chapter concentrates on very low-temperature martensitic transformations, which are of great concern for cryogenic applications and research. The principal transformation characteristics are reviewed and then elaborated. The material classes or alloy systems that exhibit martensitic transformations at very low temperatures are discussed. In particular, the martensitic transformations and their effects in austenitic stainless steels, iron-nickel alloys, practical superconductors, alkali metals, solidified gases, and polymers are discussed.

This chapter discusses the effect of fatigue on polymers, ceramics, composites, and bone. It begins with a general comparison of polymers and metals, noting important differences in microstructure and cyclic loading response. It then presents the results of several studies that shed light on the fatigue behavior and crack growth mechanisms of common structural polymers and moves on from there to discuss the fatigue behavior of bone and how it compares to stable and cyclically softening metals. It also discusses the fatigue characteristics of engineered and composited ceramics and ceramic fiber-reinforced metal-matrix composites.

This chapter provides a detailed review of creep-fatigue analysis techniques, including the 10% rule, strain-range partitioning, several variants of the frequency-modified life equation, damage assessment based on tensile hysteresis energy, the OCTF (oxidation, creep, and thermomechanical fatigue) damage model, and numerous methods that make use of creep-rupture, crack-growth, and void-growth data. It also discusses the use of continuum damage mechanics and includes examples demonstrating the accuracy of each method as well as the procedures involved.