This article briefly describes the historical development of fracture resistance testing of polymers and reviews several test methods developed for determining the fracture toughness of polymeric materials. The discussion covers J-integral testing, the methods for determining linear elastic fracture toughness, testing of thin sheets and films, normalization methods, and hysteresis methods.

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 compares and contrasts empirical approaches for partitioning hysteresis loops and predicting creep-fatigue life. The first part of the chapter presents experimental partitioning methods, explaining how they can be used to partition any loading cycle into its basic strain-range components. The methods covered include rapid cycling between peak stress extremes, half-cycle rapid loading and unloading, and variations of the incremental step-stress approach. The methods are then compared based on their ability to predict creep-fatigue life. The chapter goes on from there to describe how fatigue life can be estimated from ductility measurements when cyclic data are unavailable or are likely to change. It also explains how cyclic life is influenced by the time-dependent nature of creep-plasticity and the physical and metallurgical effects of environmental exposure.

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.

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 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 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.

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 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 addresses the question of how to deal with multiaxial stresses and strains when using the strain-range partitioning method to analyze the effects of creep fatigue. It is divided into three sections: a general discussion on the rationale used in formulating rules for treating multiaxiality, a concise listing of the rules, and an example problem in which axial creep-fatigue data is used to predict the torsional creep-fatigue life of type 304 and 316 stainless steel. The chapter also includes a brief introduction in which the authors outline the challenges presented by multiaxial loading and set practical limits on the problem they intend to treat.

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 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.

This chapter examines the stress-strain characteristics of metals and alloys subjected to cyclic loading and the cumulative effects of fatigue. It begins by explaining how a single load reversal can lower the yield stress of a material and how repeated reversals can cause strain hardening and softening, both of which lead to premature failure. It then discusses the stages of fatigue fracture, using detailed images to show how cracks initiate and grow and how they leave telltale marks on fracture surfaces. It goes on to describe fatigue life assessment methods and demonstrate their use on different metals and alloys. The chapter also discusses design-based approaches for preventing fatigue failures.

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 article discusses the compositions, structures, and properties of the most common grades of soft magnetic metals and permanent magnet alloys. It explains how alloying additions and impurities affect the magnetic properties of these materials, which include commercially pure and phosphorus irons, low-carbon and silicon steels, ferritic stainless steels, and nickel-iron and iron-cobalt alloys.

This chapter discusses the advantages of using powder metallurgy to produce magnetic materials, particularly its ability to control chemistry and near-net shape. It also explains how process parameters and powder characteristics influence the physical and magnetic properties of common stainless steels.

This chapter provides a view of magnetism in materials used at low temperatures. The discussion covers the concepts, definitions, and systems of units that are unique to the study of magnetic properties. The chapter provides a description of some of the techniques and devices used for determining magnetic properties.

This chapter discusses the selection, use, and integration of methods to control process variables in induction heating, including control of workpiece and processing temperature and materials handling systems. The discussion of temperature control includes a review of proportional controllers and heat-regulating devices. Integration of control functions is illustrated with examples related to heating of steel slabs, surface hardening of steel parts, vacuum induction melting for casting operations, and process optimization for electric-demand control. Distributed control within larger manufacturing systems is discussed. The chapter also covers nondestructive techniques for process control and methods for process simulation.

Fatigue life analysis and crack growth life prediction require an accurate interpretation of the load spectrum. This appendix presents two methods for interpreting load spectra and provides several data plots and tables comparing fatigue test data with analytically predicted values.