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.

THE SOPHISTS, PROTAGORAS AND THE PROTAGORAS

These days, the term ‘sophist’ is used solely as a term of disdain, for those who hope to get away with shoddy reasoning. It was not always thus. Our term ‘sophist’ derives from a Greek term σοφιστής; and in the fifth century bc, when that term was first used, σοφισταί were men to be reckoned with.

The first σοφισταί were so called because of some expertise or σοφία. In principle, any expert might be given the name σοφιστής. We hear, for example, of those who were given the name because they were experts in poetry, statecraft or ritual (311e4n.). In practice, the main bearers of the name were men like three of the characters in the Protagoras: Protagoras of Abdera himself, Hippias of Elis and Prodicus of Ceos. Among the better documented of the others like them were Gorgias of Leontini, Thrasymachus of Chalcedon and Antiphon of Athens. These men did not all make claim to exactly the same expertise (312d9–e1n.): for example, Prodicus had a special flair for distinguishing between words of very similar meaning (337a1–c4); Hippias cultivated a special mnemonic technique that enabled him to repeat a list of fifty names after hearing it just once (Hp. Ma. 285e; cf. 318e3n.); and Protagoras won so special a reputation for his understanding of how institutions can be managed (318e4–319a6) that he was commissioned to devise the constitution for a new Panhellenic settlement at Thurii (DK 80 A 1.50).

SOCRATES MEETS SOME FRIENDS

The Introduction to this book contains general remarks that could not conveniently be digested into the piecemeal format of the commentary. In spite of its name ‘Introduction’, and its position before the text, there is no need to have read the Introduction before starting to read the rest of the book. If some preliminary orientation to the Protagoras is required, it will be found in the italicised paragraphs of summary that are scattered throughout the commentary.

I have incurred many intellectual debts in writing this book: to the Editors of this series; to the unfailingly efficient and helpful staff of that marvellous resource, the Thesaurus Linguae Graecae; to those who took part in the Mayweek 2004 seminars on the Protagoras; to Bernard Dod, an exact and scrupulous copy-editor; and to Adam Beresford, Lynne Broughton, Myles Burnyeat, Andrea Capra, Giovanni di Pasquale, David Konstan, Geoffrey Lloyd, Catherine Osborne, Philomen Probert, Christopher Rowe, Catherine Steel, Liba Taub, Christopher Taylor, James Warren, Roslyn Weiss, and Jo Willmott.

More important than any intellectual debt is my debt to my father, Ronald Denyer. He died while I was writing this book. I dedicate it to his memory.

COMBINING BETWEEN- AND WITHIN-SUBJECTS FACTORS

As discussed in Chapter 13, a mixed design is one that contains at least one between-subjects independent variable and at least one within-subjects independent variable. Simple mixed designs have only two independent variables and so, by definition, must have one of each type of variable. Complex mixed designs contain at least three independent variables. The three-way complex mixed designs presented in this chapter and in Chapter 15 must (by definition) have two of one type and one of the other type of factor. In this chapter, we will focus on the design with two between-subjects factors and one within-subjects factor; Chapter 15 will present the design with one between-subjects factor and two within-subjects factors.

A NUMERICAL EXAMPLE OF A COMPLEX MIXED DESIGN

College students who signed up for a research study read vignettes in which their romantic partner was described as being attracted to another person; this attraction was depicted as being either emotional attraction with no physical component or physical attraction with no emotional component. Because this type-of-attraction variable was intended to be a within-subjects variable, students read both vignettes. After reading each vignette, the students completed a short inventory evaluating their feelings of jealousy; the response to this inventory served as the dependent variable. For the purposes of this hypothetical example, assume that no effects concerning the order of reading these vignettes was obtained; thus, we will present the results without considering the vignette ordering factor.

OVERVIEW

Once we have determined that an independent variable has yielded a significant effect, we must next turn our attention to the differences between the means of the conditions in the study. If there are only two means, then we automatically know that they are significantly different. With three or more means a significant F ratio reveals only that there is a difference between at least one pair of means in the design; in this case we must perform an additional, post-ANOVA multiple comparison procedure to determine which of the three or more means differ from which others.

There are a variety of multiple comparison procedures that are available to researchers. Before presenting them, we will first describe some dimensions along which they differ; this will help us, as we go through this chapter, to discuss the differences among them.

PLANNED VERSUS UNPLANNED COMPARISONS

In an idealized world of research, hypotheses regarding differences between certain of the groups in a design are formulated in advance of the data collection on the basis of the theoretical context out of which the research was generated. Once the study is completed and a statistically significant F ratio is obtained in the omnibus ANOVA (although in this idealized world a statistically significant F ratio may not even be necessary if there are a very few hypothesized mean differences), the researchers then carry out the mean comparisons that they have already specified.

COMBINING BETWEEN-SUBJECTS AND WITHIN-SUBJECTS FACTORS

A mixed design is one that contains at least one between-subjects independent variable and at least one within-subjects independent variable. In a simple mixed design, there are only two independent variables, one a between-subjects factor and the other a within-subjects factor; these variables are combined factorially. The number of levels of each independent variable is not constrained by the design. Thus, we could have a 2 × 2, a 4 × 3, or even a 3 × 7 factorial design. Chapters 14 and 15 will address two complex mixed designs that contain three independent variables.

Because there are two independent variables, there are three effects of interest: the main effect of the between-subjects variable (A), the main effect of the within-subjects variable (B), and the two-way interaction (A × B). Note that this is analogous to what we have seen in the two-way between-subjects and two-way within-subjects designs. Furthermore, the conceptual understanding of main effects and interactions in those designs carries forward to the simple mixed design. Main effects focus on the mean differences of the levels of each independent variable (e.g., a1 vs. a2) and interactions focus on whether or not the patterns of differences are parallel (e.g., a1 vs. a2 under b1 compared to a1 vs. a2 under b2).

The primary difference between a simple mixed design and the between-subjects and within-subjects designs is in the way that the total variance of the dependent variable is partitioned.

COMBINING TWO INDEPENDENT VARIABLES FACTORIALLY

NAMING THE DESIGN

In Chapter 6, we discussed a between-subjects design that contained a single independent variable (preparation time for the SAT). However, we are not limited to studying the effects of just one independent variable in a research design. In this chapter, we will deal with the inclusion of a second independent variable (note that we still have only one dependent variable). A design containing more than one independent variable is known as a factorial design when the variables are combined in a manner described in Section 8.1.2. When those independent variables are between-subjects variables, the design is called a between-subjects design or a between-subjects factorial design. Designs containing two between-subjects independent variables that are simultaneously varied are two-way between-subjects (factorial) designs. These designs are also sometimes referred to as two-way completely randomized designs because subjects are assumed to be randomly assigned to the various treatments.

COMBINING INDEPENDENT VARIABLES IN A SINGLE DESIGN

Intertwining two independent variables within the same design is done by combining them in a factorial fashion in which each level of one independent variable is combined with each level of the other independent variable. If our independent variables were, for example, gender (female and male) and size of city in which participants resided (large and small), then one combination of the levels of the independent variables might be females living in large cities. This would then be one condition or group in the factorial design.