Product design requires an understanding of the mechanical properties of materials, much of which is based on tensile testing. This chapter describes how tensile tests are conducted and how to extract useful information from measurement data. It begins with a review of the different types of test equipment used and how they compare in terms of loading force, displacement rate, accuracy, and allowable sample sizes. It then discusses the various ways tensile measurements are plotted and presents examples of each method. It examines a typical load-displacement curve as well as engineering and true stress-strain curves, calling attention to certain points and features and what they reveal about the test sample and, in some cases, the cause of the behavior observed. It explains, for example, why some materials exhibit discontinuous yielding while others do not, and in such cases, how to determine when yielding begins. It also explains how to determine other properties via tensile tests, including ductility, toughness, and modulus of resilience.

This appendix provides readers with worked solutions to 25 problems involving calculations associated with tensile testing and the determination of mechanical properties and variables. The problems deal with engineering factors and considerations such as stress and strain, loading force, sample lengthening, and machine stiffness, and with mechanical properties and parameters such as elastic modulus, Young’s modulus, strength coefficient, strain-hardening exponent, and modulus of resilience. They also cover a wide range of materials including various grades of aluminum and steel as well as iron, titanium, brass, and copper alloys.

This chapter provides a brief review of industry’s battle with fatigue and fracture and what has been learned about the underlying failure mechanisms and their effect on product lifetime and service. It recounts some of the tragic events that led to the discovery of fatigue and brittle fracture and explains how they reshaped design philosophies, procedures, and tools. It also discusses the influence of material and manufacturing defects, operating conditions, stress concentration and intensity, temperature and pressure, and cyclic loading, all of which play a role in the onset of fatigue cracking and thus should be considered when predicting useful product life.

Fracture is the separation of a solid body into two or more pieces under the action of stress. Fracture can be classified into two broad categories: ductile fracture and brittle fracture. Beginning with a comparison of these two categories, this chapter discusses the nature and causes of these failure modes. Some body-centered cubic and hexagonal close-packed metals, and steels in particular, exhibit a ductile-to-brittle transition when loaded under impact and the chapter describes the use of notched bar impact testing to determine the temperature at which a normally ductile failure transitions to a brittle failure. The discussion then covers the Griffith theory of brittle fracture and the formulation of fracture mechanics. Procedures for determination of the plane-strain fracture toughness are subsequently covered. Finally, the chapter describes the effects of microstructural variables on fracture toughness of steels, aluminum alloys, and titanium alloys.

This chapter gives a brief overview of the role of fatigue in component failures. It presents examples of fatigue failures along with statistics on the causes and costs of fatigue damage in various industries. It also includes a chapter-by-chapter summary of the content in the book, noting that the book deals primarily with fatigue at temperatures below the creep range with high-temperature fatigue being treated in a companion publication.

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.

This chapter familiarizes readers with the methods used to quantify the effects of fatigue on component lifetime and failure. It discusses the development and use of S-N (stress amplitude vs. cycles to failure) curves, the emergence of strain-based approaches to fatigue analysis, and important refinements and modifications. It demonstrates the use of approximate equations, including the method of universal slopes and the four-point correlation technique, which provides reasonable estimates of elastic and plastic lines from information obtained in standard tensile tests. It also discusses high-cycle, low-cycle, and ultra-high cycle fatigue and presents several models that are useful for fatigue life predictions.

This chapter discusses the concept of mean stress and explains how it is used in fatigue analysis and design. It begins by examining the stress-strain response of test samples subjected to cyclic forces and strains, noting important features and what they reveal about materials and their fatigue behaviors. It then discusses the challenge of developing hysteresis loops for complex loading patterns and accounting for effects such as ratcheting and stress relaxation. The sections that follow provide a summary of the various ways mean stress is described in the literature and the methods used to calculate or predict its effect on the fatigue life of machine components. The discussion also sheds light on why tensile mean stress is detrimental to both fatigue life and ductility, while compressive mean stress is highly beneficial.

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.

This chapter addresses the cumulative effects of fatigue and how to determine its impact on component lifetime and performance. It begins by defining a loading history and its corresponding hysteresis loops that exposes the deficiencies of some of the theories discussed. It then proceeds to demonstrate the methods commonly used to analyze cumulative fatigue damage and its effect on component life starting with the classical linear damage rule. After pointing out the inherent limitations of the model, it presents a method that incorporates two linear damage rules, one applying prior to crack initiation and the other after the crack has started. Although the method accounts somewhat better for loading-order effects, the transition in behavior that the rules presume to model occurs prior to any signs of cracking. Two modified versions of the double linear damage rule method, neither of which are related to a physical crack initiation event, are subsequently presented along with several applications showing how the different methods compare. The examples provided include two-level and multilevel tests, a gas-turbine engine compressor disk, and the cumulative damage associated with the irreversible hardening of type 304 stainless steel.

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 describes how notches affect the load-carrying capacity and fatigue life of materials under cyclic loads. It explains that stresses and strains can be three to four times higher in the vicinity of a notch, greatly accelerating fatigue damage. It discusses the use of stress concentration factors and how they are determined for the general case and for specific geometries, materials, and surface conditions. The chapter covers both elastic and plastic fatigue behaviors as well as a wide range of methods. It also explains how small nuances in loading can introduce tensile or compressive stress in the hysteresis loops causing variations in fatigue life as large as 50:1 depending on where the transition in fatigue behavior occurs.

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 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 is largely a compendium of best practices and procedures for minimizing the effects of fatigue. It explains how to make products more resistant to fatigue by choosing the right materials and manufacturing processes, avoiding geometries and features that concentrate strains, preventing or removing surface damage, and by inducing compressive mean stresses that prolong fatigue life. It also discusses the use of property conditioning and restoration treatments, the benefits of interference fits and processes such as coaxing, the effects of assembly damage and operating overload, the importance of surface cleanliness and finish, and the role of inspection, testing, replacement, and repair in safe-life and fail-safe designs. Examples highlighting the benefits and potential pitfalls of proof loading tests are included as well.

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 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.

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.