The main objective for the study of combined-stress fatigue is to obtain fatigue data for axles and to find the criterion for fatigue limit under combined stress. This article begins with a description of the stress states of combined stress and stress fields near crack tips. It provides an account of the various biaxial and multiaxial fatigue testing methods, specimen geometries, and stress intensity factors important in the study multiaxial fatigue. Widely used test methods are the torsion-rotating bending fatigue test and biaxial and triaxial fatigue tests. Common specimen geometries include rectangular plate specimens, cruciform specimens, compact tension shear specimens, compact shear specimens, mode II crack growth specimen, circumferentially notched cylindrical specimens, tubular specimens containing a slit, and solid cylindrical specimens containing a small hole or initial crack.

The design of components against fatigue failure may involve several considerations of irregular loading, variable temperature, and environment. This article focuses on design considerations against fatigue related to material performance under mechanical loading at constant temperature. It reviews the traditional methods of fatigue design on smooth and notched components. The article discusses high-cycle fatigue in terms of fatigue strength and tensile strength, mean stress effects, stress concentration, and multiaxial fatigue. It describes low-cycle fatigue in terms of deformation behavior and concludes with a discussion on lifetime analysis based on a strain approach.

Failure of structural polymeric materials under cyclic application of stress or strain is a subject of industrial importance. The understanding of fatigue mechanisms (damage) and the development of constitutive equations for damage evolution, leading to crack initiation and propagation as a function of loading or displacement history, represent a fundamental problem for scientists and engineers. This article describes the approaches to predict fatigue life and discusses the difference between thermal and mechanical fatigue failure of polymers.

This article provides information on the typical experimental observations of formation and propagation of small fatigue cracks under various stress states and explores the relation to long crack fracture mixed-mode fracture mechanics. It discusses state I crystallographic and stage II normal stress-dominated growth, along with some observations regarding the influence of combined stress state on the propagation of small cracks. The article discusses the differences between low-cycle fatigue and high-cycle fatigue (HCF) behaviors. Several other features of multiaxial fatigue are also explained, including mean stress effects, sequences of stress/strain amplitude or stress state, nonproportional loading and cycle counting, and HCF fatigue limits. In addition, the article covers the formation and propagation of cracks on the order of several grain sizes in diameter in initially isotropic and ductile structural alloys.

This article reviews the common methods of shear and multiaxial testing for the evaluation of engineering components such as fasteners and mill products. It discusses shear test methods, including through-thickness tests, in-plane shear tests, and double-notched shear test. The article provides information on torsional (rotational shear) tests as well as the basic equipment and setup of torsion testing. Motors, twist and torque transducers, torque sensors, and heating systems as well as the specimen preparation procedure are also discussed.

The purposes and methods of fatigue modeling and simulation in high-cycle fatigue (HCF) regime are to design either failsafe components or components with a finite life and to quantify remaining life of components with pre-existing cracks using fracture mechanics, with the intent of monitoring via an inspection scheme. This article begins with a discussion on the stages of the fatigue damage process. It describes hierarchical multistage fatigue modeling and several key points regarding the physics of crack nucleation and microstructurally small crack propagation in the HCF regime. The article provides a description of the microstructure-sensitive modeling to model fatigue of several classes of advanced engineering alloys. It describes the various modeling and design processes designed against fatigue crack initiation. The article concludes with a discussion on the challenges in microstructure-sensitive fatigue modeling.

This article offers an overview of fatigue fundamentals, common fatigue terminology, and examples of damage morphology. It presents a summary of relevant engineering mechanics, cyclic plasticity principles, and perspective on the modern design by analysis (DBA) techniques. The article reviews fatigue assessment methods incorporated in international design and post construction codes and standards, with special emphasis on evaluating welds. Specifically, the stress-life approach, the strain-life approach, and the fracture mechanics (crack growth) approach are described. An overview of high-cycle welded fatigue methods, cycle-counting techniques, and a discussion on ratcheting are also offered. A historical synopsis of fatigue technology advancements and commentary on component design and fabrication strategies to mitigate fatigue damage and improve damage tolerance are provided. Finally, the article presents practical fatigue assessment case studies of in-service equipment (pressure vessels) that employ DBA methods.

This article describes the phenomena of crack initiation and early growth. It examines specimen design and preparation as well as the apparatus used in crack initiation testing. The article provides descriptions of the various commercially available fatigue testing machines: axial fatigue testing machines and bending fatigue machines. Load cells, grips and alignment devices, extensometry and strain measuring devices, environmental chambers, graphic recorders, furnaces, and heating systems of ancillary equipment are discussed. The article presents technologies available to accomplish closed loop control of materials testing systems in performing standard materials tests and for the development of custom testing applications. It explores the advanced software tools for materials testing. The article includes a description of baseline isothermal fatigue testing, creep-fatigue interaction, and thermomechanical fatigue. The effects of various variables on fatigue resistance and guidelines for fatigue testing are also presented.

Brittle materials, such as ceramics, intermetallics, and graphites, are increasingly being used in the fabrication of lightweight components. This article focuses on the design methodologies and characterization of certain material properties. It describes the fundamental concepts and models associated with performing time-independent and time-dependent reliability analyses for brittle materials exhibiting scatter in ultimate strength. The article discusses the two-parameter and three-parameter Weibull distribution for representing the underlying probability density function for tensile strength. It reviews life prediction reliability models used for predicting the life of a component with complex geometry and loading. The article outlines reliability algorithms and presents several applications to illustrate the utilization of these reliability algorithms in structural applications.

An integral aspect of designing and material selection is the use of mechanical properties derived from various mechanical testing. This article introduces the basic concepts of mechanical design and its relation with the properties derived from various mechanical testings, namely, tensile, compressive, hardness, torsion and bend, shear load, shock, and fatigue and creep testings. It describes the design criteria for combined properties derived from each of the mechanical testing. The article concludes with a discussion on the effect of environment on the mechanical properties.

Fatigue properties are an integral part of materials comparison activities and offer information for structural life estimation in many engineering applications. This article presents three general approaches to fatigue design, with a discussion on their respective attributes. These include infinite-life criterion, finite-life criterion, and damage tolerant criterion. The article describes the individual property requirements of these approaches. It also presents selected examples of properties that reflect some detail of these approaches.

Fatigue failures may occur in components subjected to fluctuating (time-dependent) loading as a result of progressive localized permanent damage described by the stages of crack initiation, cyclic crack propagation, and subsequent final fracture after a given number of load fluctuations. This article begins with an overview of fatigue properties and design life. This is followed by a description of the two approaches to fatigue, namely infinite-life criterion and finite-life criterion, along with information on damage tolerance criterion. The article then discusses the characteristics of fatigue fractures followed by a discussion on the effects of loading and stress distribution, and material condition on the microstructure of the material. In addition, general prevention and characteristics of corrosion fatigue, contact fatigue, and thermal fatigue are also presented.

The goal of micromechanics and analysis is to use the predictive methodology to develop tailored composites and also to make accurate predictions of their performance in service. This article reviews results derived from micromechanics analyses, based on finite-element method of unidirectional fiber reinforced metal matrix composites (MMCs). It discusses the elastic deformation and elastic-plastic deformation analysis of discontinuously reinforced MMCs. The article provides an overview of analysis of strength, fatigue, and fracture toughness for macromechanics fiber-reinforced and discontinuous reinforced composites.

In the design of composite structures for durability and damage tolerance, the primary concerns are out-of-plane failures, such as delamination, material degradation associated with environment, stability under compression loading, large degree of scatter in fatigue life, and bearing failure of joints. This article presents an introductory discussion on the fatigue damage process, methodologies assessing fatigue behavior, and life prediction models. It describes the damage mechanisms introduced for a quasi-isotropic laminate under tension-compression fatigue loading. Delamination is a critical issue in fatigue and generally results from high interlaminar normal and shear stresses. The article schematically illustrates the structural elements in which high interlaminar stresses are common. It concludes with a discussion on the classification of fatigue models such as mechanistic or phenomenological, for composite materials under cyclic loading.

Open molding is the method used in the polymer-matrix composites industry to make thermoset composite products. This article discusses the advantages, disadvantages, and applications of the open molding. It describes the various process of the open molding, such as hand lay-up process and spray-up process. Workmanship for hand lay-up and spray-up processes is reviewed. The article provides information on the matrix-resin materials used for open molding, including unsaturated polyester resins, epoxy vinyl ester resins, and reinforcements. It explains the component design and short- and long-term properties of a fiber reinforced composite laminate depending on material selection and workmanship. The article also presents the basic design guidelines for open molding.

Understanding fatigue crack growth is critical for the safe operation of many structural components. This article reviews the standard fracture mechanics and methods to determine the crack growth rate for a material and loading condition experimentally. It also addresses the two most important aspects of crack-growth modeling: loading environment and crack geometry.

Structure-property relationships for metal additive manufacturing (AM) using solidification-based AM processes (e.g., powder-bed fusion and directed-energy deposition) are the focus of this article. Static strength and ductility properties in AM materials are impacted heavily by the microstructure but are also affected by porosity and surface roughness. Fatigue failure in AM materials is also influenced by porosity, surface roughness, microstructure, and residual stress due to applied manufacturing processing parameters. Post-processing treatments can further influence fatigue failure in AM materials.

This article discusses two major approaches in estimating fatigue life from the viewpoint of their use as engineering methods. These include the stress-based (S-N curve) approach and strain-based approach. The stress-based and strain-based approaches are compared, with some comments on their manner of use and limitations. The use of the Palmgren-Miner rule for life prediction for variable amplitude loading is also discussed.

This article provides some new developments in elevated-temperature and life assessments. It is aimed at providing an overview of the damage mechanisms of concern, with a focus on creep, and the methodologies for design and in-service assessment of components operating at elevated temperatures. The article describes the stages of the creep curve, discusses processes involved in the extrapolation of creep data, and summarizes notable creep constitutive models and continuum damage mechanics models. It demonstrates the effects of stress relaxation and redistribution on the remaining life and discusses the Monkman-Grant relationship and multiaxiality. The article further provides information on high-temperature metallurgical changes and high-temperature hydrogen attack and the steps involved in the remaining-life prediction of high-temperature components. It presents case studies on heater tube creep testing and remaining-life assessment, and pressure vessel time-dependent stress analysis showing the effect of stress relaxation at hot spots.

This article describes three design-life methods or philosophies of fatigue, namely, infinite-life, finite-life, and damage tolerant. It outlines the three stages in the process of fatigue fracture: the initial fatigue damage leading to crack initiation, progressive cyclic growth of crack, and the sudden fracture of the remaining cross section. The article discusses the effects of loading and stress distribution on fatigue cracks, and reviews the fatigue behavior of materials when subjected to different loading conditions such as bending and loading. The article examines the effects of load frequency and temperature, material condition, and manufacturing practices on fatigue strength. It provides information on subsurface discontinuities, including gas porosity, inclusions, and internal bursts as well as on corrosion fatigue testing to measure rates of fatigue-crack propagation in different environments. The article concludes with a discussion on rolling-contact fatigue, macropitting, micropitting, and subcase fatigue.