The term “mechanical behavior” encompasses the response of materials to external forces. This text considers a wide range of topics. These include mechanical testing to determine material properties, plasticity for FEM analyses of automobile crashes, means of altering mechanical properties, and treatment of several modes of failure.

The two principal responses of materials to external forces are deformation and fracture. The deformation may be elastic, viscoelastic (time-dependent elastic deformation), plastic, or creep (time-dependent plastic deformation). Fracture may occur suddenly or after repeated application of loads (fatigue). For some materials, failure is time-dependent. Both deformation and fracture are sensitive to defects, temperature, and rate of loading.

The key to understanding these phenomena is a basic knowledge of the three-dimensional nature of stress and strain and common boundary conditions, which are covered in the first chapter. Chapter 2 covers elasticity, including thermal expansion. Chapters 3 and 4 treat mechanical testing. Chapter 5 is focused on mathematical approximations to stress–strain behavior of metals and how these approximations can be used to understand the effect of defects on strain distribution in the presence of defects. Yield criteria and flow rules are covered in Chapter 6. Their interplay is emphasized in problem solving. Chapter 7 treats temperature and strain-rate effects and uses an Arrhenius approach to relate them. Defect analysis is used to understand superplasticity as well as strain distribution.

Chapter 8 is devoted to the role of slip as a deformation mechanism. The tensor nature of stresses and strains is used to generalize Schmid's law.

Introduction

Most crystals can deform by twinning. Twinning is particularly important in hcp metals because hcp metals do not have enough easily activated slip systems to produce an arbitrary shape change.

Mechanical twinning, like slip, occurs by shear. A twin is a region of a crystal in which the orientation of the lattice is a mirror image of that in the rest of the crystal. Normally the boundary between the twin and the matrix lies in or near to the mirror plane. Twins may form during recrystallization (annealing twins), but the concern here is formation of twins by uniform shearing (mechanical twinning), as illustrated in Figure 11.1. In this figure, plane 1 undergoes shear displacement relative to plane 0 (the mirror plane). Then plane 2 undergoes the same shear relative to plane 1, and plane 3 relative to plane 2, etc. The net effect of the shear between each successive pair of planes is to reproduce the lattice, but with the new (mirror image) orientation.

Both slip and twinning are deformation mechanisms that involve shear displacements on specific crystallographic planes and in specific crystallographic directions. However, there are important differences.

1. With slip, the magnitude of the shear displacement on a plane is variable, but it is always an integral number of interatomic repeat distances nb, where b is the Burgers vector. Slip occurs on only a few of the parallel planes separated by relatively large distances.

2. […]

Introduction

The treatment of fracture in Chapter 13 was descriptive and qualitative. In contrast, fracture mechanics provides a quantitative treatment of fracture. It allows measurements of the toughness of materials and provides a basis for predicting the loads that structures can withstand without failure. Fracture mechanics is useful in evaluating materials, in the design of structures, and in failure analysis.

Early calculations of strength for crystals predicted strengths far in excess of those measured experimentally. The development of modern fracture mechanics started when it was realized that strength calculations based on assuming perfect crystals were far too high because they ignored preexisting flaws. Griffith reasoned that a preexisting crack could propagate under stress only if the release of elastic energy exceeded the work required to form the new fracture surfaces. However, his theory, based on energy release, predicted fracture strengths that were much lower than those measured experimentally. Orowan realized that plastic work should be included in the term for the energy required to form a new fracture surface. With this correction, experiment and theory were finally brought into agreement. Irwin offered a new and entirely equivalent approach by concentrating on the stress states around the tip of a crack.

Theoretical fracture strength

Early estimates of the theoretical fracture strength of a crystal were made by considering the stress required to separate two planes of atoms. Figure 14.1 shows schematically how the stress might vary with separation.

Introduction

The shapes of most metallic products are achieved by mechanical working. The exceptions are those produced by casting and by powder processing. Mechanical shaping processes are conveniently divided into two groups, bulk-forming and sheet-forming. Bulk-forming processes include rolling, extrusion, rod and wire drawing, and forging. In these processes the stresses that deform the material are largely compressive. One engineering concern is to ensure that the forming forces are not excessive. Another is to ensure that the deformation is as uniform as possible, in order to minimize internal and residual stresses. Forming limits of the material are set by the ductility of the work piece and by the imposed stress state.

Products as diverse as cartridge cases, beverage cans, automobile bodies, and canoe hulls are formed from flat sheets by drawing or stamping. In sheet-forming the stresses are usually tensile, and the forming limits usually correspond to local necking of the material. If the stresses become compressive, buckling or wrinkling will limit the process.

Bulk-forming energy balance

An energy balance is a simple way of estimating the forces required in many bulk-forming processes. As a rod or wire is drawn through a die, the total work, Wt, equals the drawing force, Fd, times the length of wire drawn, ΔL; Wt = FdΔL.

Introduction

A separate chapter is devoted to polymers because of their engineering importance and because their mechanical behavior is so different from that of metals and ceramics. The mechanical response of polymers is far more time-dependent than that of crystalline materials. Viscoelastic effects (Chapter 15) are much more important in polymers than in metals or ceramics. The properties of polymers are also much more sensitive to temperature than those of other materials. Changes of molecular orientation with deformation cause large changes in properties and a much greater degree of anisotropy than is observed in metals or ceramics. The phenomena of crazing and rubber elasticity have no analogs in crystalline materials. Some polymers exhibit very large tensile elongations. Although a few alloys exhibit shape-memory behavior, the effect is much greater in polymers, more common, and of greater technological importance.

Elastic behavior

Elastic strains in metals and ceramics occur by stretching of primary metallic, covalent, or ionic bonds. The elastic modulus of most crystals varies with direction by less than a factor of 3. The effects of alloying, and of thermal and mechanical treatments on the elastic moduli of crystals are relatively small. As the temperature is increased from absolute zero to the melting point, Young's modulus usually decreases by a factor of no more than 5. For polymers, however, a temperature change of 30°C may change the elastic modulus by a factor of 1000.

Introduction

In classic elasticity there is no time delay between the application of a force and the deformation that it causes. For many materials, however, there is additional time-dependent deformation that is recoverable. This is called viscoelastic or anelastic deformation. When a load is applied to a material, there is an instantaneous elastic response, but the deformation also increases with time. This viscoelasticity should not be confused with creep (Chapter 16), which is time-dependent plastic deformation. Anelastic strains in metals and ceramics are usually so small that they are ignored. In many polymers, however, viscoelastic strains can be very significant.

Anelasticity is responsible for the damping of vibrations. A high damping capacity is desirable where vibrations might interfere with the precision of instruments or machinery and for controlling unwanted noise. A low damping capacity is desirable in materials used for frequency standards, in bells, and in many musical instruments. Viscoelastic strains are often undesirable. They cause sagging of wooden beams, denting of vinyl flooring by heavy furniture, and loss of dimensional stability in gauging equipment. The energy associated with damping is released as heat, which often causes an unwanted temperature increase. Study of damping peaks and how they are affected by processing has been useful in identifying mechanisms. The mathematical descriptions of viscoelasticity and damping will be developed in the first part of this chapter. Then several damping mechanisms will be described.

Introduction

This book is concerned with the mechanical behavior of materials. The term mechanical behavior refers to the response of materials to forces. Under load, a material may either deform or break. The factors that govern a material's resistance to deformation are very different from those governing its resistance to fracture. The word strength may refer either to the stress required to deform a material or to the stress required to cause fracture; therefore, care must be used with the term strength.

When a material deforms under small stresses, the deformation may be elastic. In this case, when the stress is removed, the material will revert to its original shape. Most of the elastic deformation will recover immediately. There may be, however, some time-dependent shape recovery. This time-dependent elastic behavior is called anelastic or viscoelastic.

Larger stresses may cause plastic deformation. After a material undergoes plastic deformation, it will not revert to its original shape when the stress is removed. Usually, high resistance to deformation is desirable, so that a part will maintain its shape in service when stressed. On the other hand, it is desirable to have materials deform easily when they are being formed by rolling, extrusion, or other methods. Plastic deformation usually occurs as soon as the stress is applied. At high temperatures, however, time-dependent plastic deformation called creep may occur.

Fracture is the breaking of a material into two or more pieces. If fracture occurs before much plastic deformation occurs, we say that the material is brittle.

Introduction

Once the concept of dislocations was accepted, there were three important questions to be answered.

1. When a single crystal is deformed, slip occurs with shear offsets of thousands of atom distances on relatively widely spaced planes, rather than uniformly throughout the crystal. See Figure 10.1. Why doesn't slip occur uniformly at an atomic scale?

2. Cold working increases the dislocation content of crystals even though dislocations must run out of the crystals. See Figures 10.2 and 10.3. Where do the additional dislocations come from?

3. The yield stress increases as the number of dislocations increases even though without any dislocations, the strength would be even higher. See Figure 10.4. Why does the yield stress increase with dislocation density?

Frank–Read sources

The first two of these questions can be answered in terms of the Frank–Read source, which generates dislocations. Suppose that there is a dislocation of finite length, AB, in a slip plane (Figure 10.5). The dislocation leaves the plane at A and B, but the end points are pinned at A and B. A shear stress, τ, acting on the plane will create a force that causes the dislocation to bow. This bowing is resisted by the line tension of the dislocation. As the shear stress is increased the dislocation will bow out until it spirals back on itself. The sections that touch annihilate each other, leaving a dislocation loop that can expand under the stress and a restored dislocation segment between the pinning points.

The stereographic projection is often used to represent the angular relations between directions and planes in a crystal. This projection system can be visualized by imagining a tiny (infinitesimal) crystal at the center of a sphere. All of the planes and directions of interest are extended until they intersect the surface of the sphere. Directions intersect the sphere as points and planes intersect it as great circles, as shown in Figure B.1 These points and great circles are then projected onto a flat surface. See Figure B.2 The problem of plotting these on a flat surface is exactly the same as the mapmaker's problem of plotting the spherical surface of the earth. For crystals, it is necessary to plot only half of the spherical surface, because the opposite hemisphere is identical. Barrett and Cullity describe the details of stereographic projection.

The book entitled Fundamentals of Jet Propulsion with Applications, by Ronald D. Flack, will satisfy the strong need for a comprehensive, modern book on the principles of propulsion – both as a textbook for propulsion courses and as a reference for the practicing engineer.

Professor Flack has written an exciting book for students of aerospace engineering and design. His book offers a combination of theory, practical examples, and analysis utilizing information from actual aerospace databases to motivate students; illustrate, and demonstrate physical phenomena such as the principles behind propulsion cycles, the fundamental thermofluids governing the performance of – and flow mechanisms in – propulsion components, and insight into propulsion-system matching.

The text is directed at upper-level undergraduate students in mechanical and aerospace engineering, although some topics could be taught at the graduate level. A basic understanding of fluid mechanics, gas dynamics, and thermodynamics is presumed, although most principles are thoroughly reviewed early in the book and in the appendixes. Propulsion is the primary thrust, but the material can also be used for the fundamentals of ground- and marine-based gas turbines. Turbomachinery is a secondary target, and the fundamentals and some advanced topics in compressors and turbines are covered. The specific and unique contributions of this book and its strengths are that fundamental mathematics and modern hardware are both covered; moreover, subjects are treated with equal emphasis.

Introduction

The purposes of the diffuser or inlet are first to bring air smoothly into the engine, second to slow the fluid and to increase the pressure, and third to deliver a uniform flow to the compressor. As indicated by studies for cycle analyses in Chapters 2 and 3, engine performance improves with increasing pressure to the burner. The first component the air encounters is the diffuser, and the second component is the compressor. Thus, if the diffuser incurs a large total pressure loss, the total pressure into the burner will be reduced by the compressor total pressure ratio times this loss. For example, if 2 psia are lost in the diffuser, for a large engine this can result in 50 psia less in the burner.

The losses result from several processes and affect engine performance in several ways. First, losses in total pressure occur outside of the diffuser primarily as the result of shock interactions. The flow outside the diffuser can also actually affect the flow around the entire engine and add a drag to the aircraft. Second, ideally the flow inside the diffuser is uniform and the streamlines are smooth. However, because of the unfavorable pressure gradient, the boundary layer on the walls tends to grow and separate. This has three subeffects.

Introduction

As discussed in previous chapters, a fan or compressor is the first rotating component that the fluid encounters. A cross-sectional view of a compressor for a simple, single-shaft turbojet is shown in Figure 6.1. The basic function of a compressor is to impart kinetic energy to the working fluid (air) by means of some rotating blades and then to convert the increase in energy to an increase in total pressure, which is needed by the combustor. The limits of operation of an engine are often dictated by a compressor, as is discussed in this chapter. Furthermore, the design of an efficient axial flow fan or compressor remains such a complex process that the success or failure of an engine often revolves around the design of a compressor. Many fundamental and advanced design details are available in Cumpsty (1988), Hawthorne (1964), Horlock (1958), Howell (1945a, 1945b) and Johnsen and Bullock (1965). Rhie et al. (1998), LeJambre et al. (1998), Adamczyk (2000), and Elmendorf et al. (1998) demonstrate how modern computational fluid dynamic (CFD) tools can effectively be used for the complex three-dimensional analysis and design of compressors.

Compressors were the main stumbling block of the early engines and the primary cause of the delays in the development of jet engines for World War II. Dunham (2000) and Meher-Homji (1996, 1997a, 1999) present interesting historical perspectives and technical information on early compressor development.

Introduction

In the previous seven chapters, much emphasis has been placed on the analysis and design of individual components of gas turbines. On the other hand, in Chapters 2 and 3 cycle analyses are presented for ideal and nonideal engines as a whole in which the different components are integrated into a system. However, in Chapter 3, component efficiencies and some characteristics are assumed or assigned a priori for the overall cycle analyses. In general, however, the previous seven chapters demonstrate, through the use of either theoretical analyses or empirical characteristic curves (or “maps”), that component efficiencies and other operating characteristics change significantly at different conditions–for example, at different flow rates and rotational speeds.

To understand the overall effects of changing operating conditions, one can consider an engine initially at some steady-state operating condition. However, as the fuel injection rate in the burner is changed, the turbine inlet temperature and pressure are changed. Thus, the turbine will change rotational speeds. Because the turbine and compressor are on the same shaft, however, this change in rotational speed in turn changes the ingested mass flow rate and pressure ratio developed by the compressor, which influences the burner inlet pressure and the turbine inlet pressure, and so on. Eventually, the engine will again reach a different steady-state operating condition.