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.

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 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 various types of material fracture toughness and the methods by which they are determined. It begins with a review of the basic principles of linear elastic fracture mechanics, covering the Griffith-Irwin theory of fracture, the concept of strain energy release rate, the use of fracture indices and failure criteria, and the ramifications of crack-tip plasticity in ductile and brittle fractures. It goes on to describe the different types of plain-strain and plane-stress fracture toughness, explaining how they are measured and how they are influenced by metallurgical and environmental variables and loading conditions. It also examines the crack growth resistance curves of several aluminum alloys and describes the characteristics of fracture when all or some of the applied load is in the plane of the crack.

This chapter presents a fracture-mechanics-based approach to damage tolerance, accounting for mechanical, metallurgical, and environmental factors that drive crack development and growth. It begins with a review of stress-intensity factors corresponding to a wide range of crack geometries, specimen configurations, and loading conditions. The discussion covers two- and three-dimensional cracks as well as the use of correction factors and problem-simplification techniques for dealing with nonstandard configurations. The chapter goes on to describe how fatigue loading affects crack growth rates in each of the three stages of progression. Using images, diagrams, and data plots, it reveals how cracks advance in step with successive stress cycles and explains how fatigue crack growth rates can be determined by examining striations on fracture specimens and correlating their widths with stress profiles. It also describes how material-related factors, load history, corrosion, and temperature affect crack growth rates, and discusses the steps involved in life assessment.

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.

Structural and fracture mechanics-based tools for metals are believed to be applicable to nonmetals, as long as they are homogeneous and isotropic. This chapter discusses the essential aspects of the fatigue and fracture behaviors of nonmetallic materials with an emphasis on how they compare with metals. It begins by describing the fracture characteristics of ceramics and glasses along with typical properties and subcritical crack growth mechanisms. It then discusses the properties of engineering plastics and the factors affecting crack formation and growth, fracture toughness, fatigue life, and stress rupture failures.

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.

Deformation within a crystal lattice is governed principally by the presence of dislocations, which are two-dimensional defects in the lattice structure. Slip from shear stress is the most common deformation mechanism within crystalline lattices of metallic materials, although deformation of crystal lattices can also occur by other processes such as twinning and, in special circumstances, by the migration of vacant lattice sites. This appendix describes the notation used to specify lattice planes and directions and discusses the mechanisms of slip and twinning as well as the effect of stacking faults.

This appendix presents a close-form solution to determine the stress distribution around a hole of any shape or size in a strip of any material of any width. It also compares the close-form equation to classical solutions and the results of finite element analysis, demonstrating near perfect matches in each case.

This appendix presents an analytical model that estimates damage rates for both crack initiation and propagation mechanisms. The model provides a nonarbitrary definition of fatigue crack initiation length, which serves as an analytical link between initiation and propagation analyses and appears to have considerable merit in estimating the total fatigue life of notched and cracked structures.

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.

Stress severity factors are used in design and analysis to account for stress concentrations, variations in material properties and fabrication quality, and other analytical uncertainties. They indicate the severity of stress in areas that are prone to crack development. This appendix discusses stress severity factors associated with fastener holes in attachment joints.

This appendix contains figures that illustrate specimen orientation and crack plane codes for rolled plate, drawn bars, and hollow cylinders.

This appendix provides fracture toughness and tensile property data for aluminum alloys in the 2000, 6000, 7000, and 8000 series as well as B201 and D357 aluminum castings and powder metal alloys.

This appendix provides tensile property data for titanium alloys and castings and plane-strain fracture toughness data for Ti-6Al-4V castings.

This appendix provides tensile property and fracture toughness data for titanium aluminides developed for aerospace applications.

This appendix provides tensile property and fracture toughness data for various low-alloy and stainless steels.

This appendix is a conversion table for various units of measure.

This appendix is a compilation of terms, definitions, abbreviations, and symbols associated with the mechanics and mechanisms of fracture.