This article presents effective stress equations that are based on the von Mises criterion, the Tresca criterion, and the Huddleston criterion. It describes the calculation of effective stresses for different cases: elastic stresses, steady-state creep stresses, stresses in a fully plastic case, and thermal stresses in a tube. The article illustrates the comparison of life predictions by the stress criteria and presents a simple mean diameter hoop stress equation, which is used for designing components. It also provides information on the multiaxial creep ductility of tubular components and multiaxial testing methods.

This article provides the definitions of stress and strain, and describes the relationship between stress and strain by stress-strain curves and true-stress/true-strain curves. The emphasis is on understanding the factors that determine the extent of deformation a metal can withstand before cracking or fracture occurs. The article reviews the process variables that influence the degree of workability and summarizes the mathematical relationships that describe the occurrence of room-temperature ductile fracture under workability conditions. It discusses the most common situations encountered in multiaxial stress states. The construction of a processing map based on deformation mechanisms is also discussed.

This article provides the theoretical background for understanding many of the physical processes relevant to mechanical testing methods, experimental results, and analytical approaches described in this volume.

This article focuses on the modeling and simulation of cavitation phenomena. It summarizes the experimental observations of cavitation and reviews the modeling of cavity nucleation and growth. The article discusses the modeling of the cavity growth based on mesoscale and microscale under uniaxial versus multiaxial tensile-stress conditions. Mesoscale models incorporate the influence of local microstructure and texture on cavitation. The article outlines the descriptions of cavity coalescence and shrinkage. It also describes the simulation of the tension test to predict tensile ductility and to construct failure-mechanism maps.

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 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.

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 discusses the mechanical properties of soft-interlayer solid-state welds and the implications of these behaviors to service stress states and environments. It illustrates the microstructure of as-deposited coatings and solid-state-welded interlayers. The article reviews factors that affect the tensile loading of strength of soft-interlayer welds: the interlayer thickness, the interlayer strain, and the interlayer fabrication method. It also provides information on stress-corrosion cracking of interlayers and stress behavior of these interlayers during shear and multiaxial loading.

Soft-interlayer solid-state welds that join stronger base metals have unique mechanical properties that are of fundamental interest and may be of critical importance to designers. This article discusses the mechanical properties of soft-interlayer solid-state welds and the implications of these behaviors to service stress states and environments. It describes the tensile loading of soft-Interlayer welds in terms of the effect of interlayer thickness on stress, interlayer strain, time-dependent failure, effect of base-metal properties, and effect of interlayer fabrication method. The article concludes with a discussion on multiaxial loading.

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.

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.

This article summarizes many approaches that are used to simulate relaxation of bulk residual stresses in components. It presents analytical examples to highlight the complexity of residual stress and strain distributions observed in simple geometries, with ideal material behavior and trivial loading and boundary conditions. The article discusses approximate and advanced solution techniques that can be employed in practice for simulation of residual stress relief: finite-difference method and finite-element method. It also describes advanced techniques applicable to transient creep, advanced constitutive models, and complicated stress and temperature loading histories.

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.

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.