Introduction

Elasticity deals with elastic stresses and strains, their relationship, and the external forces that cause them. An elastic strain is defined as a strain that disappears instantaneously once the forces that cause it are removed. The theory of elasticity for Hookean solids – in which stress is proportional to strain – is rather complex in its more rigorous treatment. However, it is essential to the understanding of micro- and macromechanical problems. Examples of the former are stress fields around dislocations, incompatibilities of stresses at the interface between grains, and dislocation interactions in work hardening; examples of the latter are the stresses developed in drawing, and rolling wire, and the analysis of specimen–machine interactions in testing for tensile strength. This chapter is structured in such a way as to satisfy the needs of both the undergraduate and the graduate student. A simplified treatment of elasticity is presented, in a manner so as to treat problems in an undergraduate course. Stresses and strains are calculated for a few simplified cases; the tridimensional treatment is kept at a minimum. A graphical method for the solution of two-dimensional stress problems (the Mohr circle) is described. On the other hand, the graduate student needs more powerful tools to handle problems that are somewhat more involved. In most cases, the stress and strain systems in tridimensional bodies can be better treated as tensors, with the indicial notation.

Introduction

The relaxation times for the molecular processes in gases and in a majority of liquids are so short, that molecules/atoms are almost always in a well-defined state of complete equilibrium. Consequently, the structure of a gas or liquid does not depend on its past history. In contrast, the relaxation times for some of the significant atomic processes in crystals are so long, that a state of equilibrium is rarely, if ever, achieved. It is for this reason that metals in general (and ceramics and polymers, under special conditions) show the usually desirable characteristic of work-hardening with straining, or strain-hardening. In other words, plastic deformation distorts the atoms from their equilibrium positions, and this manifests itself subsequently in hardening.

In fact, hardening by plastic deformation (rolling, drawing, etc.) is one of the most important methods of strengthening metals, in general. Figure 6.1 shows a few deformation-processing techniques in which metals are work-hardened. These industrial processes are used in the fabrication of parts and enable the shape of metals to be changed. The figure is self-explanatory. Rolling is used to produce flat products such as plates, sheets, and also more complicated shapes (with special rolling cylinders). In forging, the top hammer comes down, and the part is pushed into a die (closed-die forging) or is simply compressed. Extrusion uses a principle similar to that in the use of a tube of toothpaste. The material is squeezed through a die, and its diameter is reduced.

Introduction

The technological developments wrought since the early twentieth century have required materials that resist higher and higher temperatures. Applications of these developments lie mainly in the following areas:

1. Gas turbines (stationary and on aircraft), whose blades operate at temperatures of 800–950 K. The burner and afterburner sections operate at even higher temperatures, viz. 1,300–1,400 K.

2. Nuclear reactors, where pressure vessels and piping operate at 650–750 K. Reactor skirts operate at 850–950 K.

3. Chemical and petrochemical industries.

All of these temperatures are in the range (0.4–0.65) Tm, where Tm is the melting point of the material in kelvin.

The degradation undergone by materials in these extreme conditions can be classified into two groups:

1. Mechanical degradation. In spite of initially resisting the applied loads, the material undergoes anelastic deformation; its dimensions change with time.

2. Chemical degradation. This is due to the reaction of the material with the chemical environment and to the diffusion of external elements into the materials. Chlorination (which affects the properties of superalloys used in jet turbines) and internal oxidation are examples of chemical degradation.

This chapter deals exclusively with mechanical degradation. The time-dependent deformation of a material is known as creep. A great number of high-temperature failures can be attributed either to creep or to a combination of creep and fatigue. Creep is characterized by a slow flow of the material, which behaves as if it were viscous.

Introduction

Upon being mechanically stressed, a material will, in general, exhibit the following sequence of responses: elastic deformation, plastic deformation, and fracture. This chapter addresses the second response: plastic deformation. A sound knowledge of plasticity is of great importance for the following reasons.

• Many projects are executed in which small plastic deformations of the structure are accepted. The “theory of limit design” is used in applications where the weight factor is critical, such as space vehicles and rockets. The rationale for accepting a limited plastic deformation is that the material will work-harden at that region, and plastic deformation will cease once the flow stress (due to work-hardening) reaches the applied stress.

• It is very important to know the stresses and strains involved in deformation processing, such as rolling, forging, extrusion, drawing, and so on. All these processes involve substantial plastic deformation, and the response of the material will depend on its plastic behavior during the processes. The application of plasticity theory to such processes is presented later in this chapter.

• The mechanism of fracture can involve plastic deformation at the tip of a crack. The way in which the high stresses that develop at the crack can be accommodated by the surrounding material is of utmost importance in the propagation of the crack. A material in which plastic deformation can take place at the crack is “tough,” while one in which there is no such deformation is “brittle.”

• […]

Introduction

The separation or fragmentation of a solid body into two or more parts, under the action of stresses, is called fracture. The subject of fracture is vast and involves disciplines as diverse as solid-state physics, materials science, and continuum mechanics. Fracture of a material by cracking can occur in many ways, principally the following:

1. Slow application of external loads.

2. Rapid application of external loads (impact).

3. Cyclic or repeated loading (fatigue).

4. Time-dependent deformation (creep).

5. Internal stresses, such as thermal stresses caused by anistropy of the thermal expansion coefficient or temperature differences in a body.

6. Environmental effects (stress corrosion cracking, hydrogen embrittlement, liquid metal embrittlement, etc.)

The process of fracture can, in most cases, be subdivided into the following categories:

1. Damage accumulation.

2. Nucleation of one or more cracks or voids.

3. Growth of cracks or voids. (This may involve a coalescence of the cracks or voids.)

Damage accumulation is associated with the properties of a material, such as its atomic structure, crystal lattice, grain boundaries, and prior loading history. When the local strength or ductility is exceeded, a crack (two free surfaces) is formed. On continued loading, the crack propagates through the section until complete rupture occurs. Linear elastic fracture mechanics (LEFM) applies the theory of linear elasticity to the phenomenon of fracture – mainly, the propagation of cracks. If we define the fracture toughness of a material as its resistance to crack propagation, then we can use LEFM to provide us with a quantitative measure of fracture toughness.

Introduction

Environment by its omnipresence, except perhaps in space, affects the behavior of all materials. Such effects can range from swelling in polymers to surface oxidation of metals and nonoxide ceramics to catastrophic failure of some materials under a combined action of stress and environment. Environmental degradation of materials is often referred to as corrosion. Such damage is generally time-dependent, i.e., one is able to predict it. Over time, however, envir-onmental damage can become critical. There is, however, a more insidious corrosion problem which is time-independent. Examples of time-independent corrosion include stress corrosion cracking (SCC), environment induced embrittlement, etc. Such damage can occur at anytime, without much warning. There are many examples of such failures resulting in human and economic loss. Corrosion of structural components in aging aircraft is a serious problem. Just to cite one such example, a Boeing 737 belonging to Aloha Airlines, which flew inter island in Hawaii, lost a large portion of its upper fuselage at 7,500 m (24,000 feet) in the air. It turned out that the fuselage panels joined by rivets had corroded, which resulted in the mid-flight failure due to corrosion fatigue.

All materials (metals, ceramics, and polymers) show phenomena of premature failure or mechanical property degradation under certain combinations of stress and environment. We describe below the salient points in regard to environmental effects in different materials. We emphasize the role that the microstructure of a given mater-ial plays in this phenomenon, especially in environmentally assisted fracture.

Courses in the mechanical behavior of materials are standard in both mechanical engineering and materials science/engineering curricula. These courses are taught, usually, at the junior or senior level. This book provides an introductory treatment of the mechanical behavior of materials with a balanced mechanics–materials approach, which makes it suitable for both mechanical and materials engineering students. The book covers metals, polymers, ceramics, and composites and contains more than sufficient information for a one-semester course. It therefore enables the instructor to choose the path most appropriate to the class level (junior- or senior-level undergraduate) and background (mechanical or materials engineering). The book is organized into 15 chapters, each corresponding, approximately, to one week of lectures. It is often the case that several theories have been developed to explain specific effects; this book presents only the principal ideas. At the undergraduate level the simple aspects should be emphasized, whereas graduate courses should introduce the different viewpoints to the students. Thus, we have often ignored active and important areas of research. Chapter 1 contains introductory information on materials that students with a previous course in the properties of materials should be familiar with. In addition, it enables those students unfamiliar with materials to “get up to speed.” The section on the theoretical strength of a crystal should be covered by all students. Chapter 2, on elasticity and viscoelasticity, contains an elementary treatment, tailored to the needs of undergraduate students.

Introduction

In Chapter 7, we described the macroscopic aspects of the fracture behavior of materials. As with other characteristics, the microstructure of a material has a great influence on its fracture behavior. In what follows, we present a brief description of the microstructural aspects of crack nucleation and propagation, as well as the effect of the environment on the fracture behavior of different materials. Figure 8.1 shows, schematically, some important fracture modes in a variety of materials. These different modes will be analyzed in some detail in this chapter. Metals fail by two broad classes of mechanisms: ductile and brittle failure.

Ductile failure occurs by (a) the nucleation, growth, and coalescence of voids, (b) continuous reduction in the metal's cross-sectional area until it is equal to zero, or (c) shearing along a plane of maximum shear. Ductile failure by void nucleation and growth usually starts at second-phase particles. If these particles are spread throughout the interiors of the grains, the fracture will be transgranular (or transcrystalline). If these voids are located preferentially at grain boundaries, fracture will occur in an intergranular (or intercrystalline) mode. The appearance of a ductile fracture, at high magnification (500× or higher) is of a surface with indentations, as if marked by an ice-cream scooper. This surface morphology is appropriately called dimpled. Rupture by total necking is very rare, because most metals contain second-phase particles that act as initiation sites for voids.

The second edition of Mechanical Behavior of Materials has revised and updated material in every chapter to reflect the changes occurring in the field. In view of the increasing importance of bioengineering, a special emphasis is given to the mechanical behavior of biologi-cal materials and biomaterials throughout this second edition. A new chapter on environmental effects has been added. Professors Fine and Voorhees make a cogent case for integrating biological materials into materials science and engineering curricula. This trend is already in progress at many US and European universities. Our second edition takes due recognition of this important trend. We have resisted the temptation to make a separate chapter on biological and biomaterials. Instead, we treat these materials together with traditional materials, viz., metals, ceramics, polymers, etc. In addition, taking due cognizance of the importance of electronic materials, we have emphasized the distinctive features of these materials from a mechanical behavior point of view.

The underlying theme in the second edition is the same as in the first edition. The text connects the fundamental mechanisms to the wide range of mechanical properties of different materials under a variety of environments. This book is unique in that it presents, in a unified manner, important principles involved in the mechanical behavior of different materials: metals, polymers, ceramics, composites, electronic materials, and biomaterials. The unifying thread running throughout is that the nano/microstructure of a material controls its mechanical behavior. A wealth of micrographs and line diagrams are provided to clarify the concepts.

Introduction

In this chapter, we discuss one important means of altering the mechanical response of metals and ceramics: martensitic transformation. Martensitic transformation is a highly effective means of increasing the strength of steel. An annealed medium-carbon steel (such as AISI 1040) has a strength of approximately 100 MPa. By quenching (and producing martensite), the strength may be made to reach about 1 GPa, a tenfold increase. The ductility of the steel is, alas, decreased.

A quite different effect is observed in ceramics. Martensitic transformation can be exploited to enhance the toughness of some ceramics. If a ceramic undergoes a martensitic transformation during the application of a mechanical load, the propagation of cracks is inhibited. For example, partially stabilized zirconia has a fracture toughness of approximately 7 MPa m1/2. An equivalent ceramic not undergoing martensitic transformation would have a toughness less than or equal to 3 MPa m1/2.

An additional, and very important, effect associated with martensitic transformations is the “shape-memory effect.” Alloys undergoing this effect “remember” their shape prior to deformation. The three effects just described have important technological applications.

Structures and Morphologies of Martensite

Quenching has been known for over 3,000 years and is, up to this day, the single most effective mechanism known for strengthening steel. However, it is only fairly recently that the underlying mechanism has been studied in a scientific manner and understood.

Introduction

There is some confusion in the literature about the terminology pertaining to fatigue. We define fatigue as a degradation of mechanical properties leading to failure of a material or a component under cyclic loading. This definition excludes the so-called phenomenon of static fatigue, which is sometimes used to describe stress corrosion cracking in glasses and ceramics in the presence of moisture. Brittle solids (glasses and crystalline ceramics) undergo subcritical crack growth in an aggressive environment under static loads. Silica-based glasses are especially susceptible to this kind of crack growth in the presence of moisture. If a glassy phase exists at grain boundaries and interfaces, it will be susceptible to such an attack. Thus, static fatigue is more appropriately a stress corrosion phenomenon, rather than a cyclic stress-related phenomenon.

In general, fatigue is a problem that affects any structural component or part that moves. Automobiles on roads, aircraft (principally the wings) in the air, ships on the high sea constantly battered by waves, nuclear reactors and turbines under cyclic temperature conditions (i.e., cyclic thermal stresses), and many other components in motion are examples in which the fatigue behavior of a material assumes a singular importance. It is estimated that 90% of service failures of metallic components that undergo movement of one form or another can be attributed to fatigue. Often, a fatigue fracture surface will show some easily identifiable macroscopic features, such as beach markings.

These lecture notes were made after Professor Koiter's last official course at Delft's University of Technology, in the academic year 1978–79. Although these notes were prepared in close collaboration with Professor Koiter, they are written in the author's style. The author is therefore fully responsible for possible errors.

This course covers the entire field of elastic stability, although recent developments in the field of stiffened plates and shells are not included. Hopefully, these lecture notes reflect some of the atmosphere of Dr. Koiter's unique lectures.