Theory of Thermal Stresses

Bruno A. Boley, Jerome H. Weiner

• Publisher: Dover Publications
• Year: 2012
• ISBN:
  9780486143866
• Topic: Technik & Maschinenbau
• Subtopic: Bauingenieurwesen

Elevated temperatures and extreme temperature gradients arise in a large variety of engineering problems, and often produced thermal stresses and thermal deformations that crucially affect the life of the materials and the systems involved. Early examples arose with the advent of high-speed rocket-powered flight and the development of nuclear energy sources. More recent applications can be found in fields ranging from reentry heating and ablation in space flight to the localized heat generation in computer chips, produced by high temperature during fabrication and by high current density during service.
This highly regarded text, aimed both at the researcher and the practicing engineer, as well as the student, presents a detailed discussion of fundamental aspects of the theory, accompanied by detailed solutions of typical and illustrative problems. The book is divided into four parts: Part I develops the fundamentals of thermoelasticity, starting with a presentation of the thermodynamic foundations of the subject and leading to various alternate formulations and methods of solutions of thermoelastic problems. Part II discusses the physical basis of heat transfer theory and methods of solution of heat conduction boundary-value problems. Part III covers more practical aspects of thermal stress analysis, mainly from the strength-of-materials viewpoint. Finally, Part IV presents the manner in which temperature effects can be included in inelasticity theory.
The result is an extremely useful resource which presents the salient features of the subject in a single volume from a unified and basic theoretical point of view.

P A R T I

BASIC THEORY

CHAPTER

1

MECHANICAL AND THERMODYNAMICAL FOUNDATIONS

1.1 Introduction

The mathematical formulations describing the behavior of solid media under the combined action of heat and external loads are examined in this chapter. This examination makes use of the basic concepts which underlie all investigations regarding continuous media, concepts which arise from two different disciplines, namely mechanics and thermodynamics. Since the mechanical concepts enter, as well, into the consideration of constant- temperature problems and are discussed thoroughly in many works on elasticity theory, they are treated here only briefly with frequent references to the existing literature. It is, however, essential to consider the thermodynamic aspects of the problem only when nonconstant temperature problems are under consideration; for this reason, this subject is treated in only a cursory fashion in most elasticity textbooks. It is therefore necessary to devote a major portion of this chapter to an exposition of the principles of thermodynamics, starting first with the classical theory as relating to uniform systems and using it as a basis for the subsequent choice of postulates suitable for the nonuniform systems with which this book is concerned.

Thus the theory presented in this chapter forms the basis of all the subsequent developments in linear thermoelasticity in this book, and leads to a general formulation (summarized in Article 1.14) of the coupled thermoelastic boundary-value problem; simplifications and alternative formulations of this problem, which are usually necessary for the derivation of workable solutions, are discussed in the chapters that follow. In addition, a brief treatment is given in Article 1.13 of a thermodynamic approach to the theory for a linear viscoelastic material; that theory is introduced here only parenthetically, a discussion of various types of inelastic problems from another viewpoint being postponed until Chapter 14.

1.2 Notation

It will be convenient in this and the following three chapters to use the compact notation often referred to as indicial notation. A short outline of this notation is given here for purposes of reference.¹ The discussions in which this notation will be used are of a general theoretical character and do not refer to any specific geometry or loading pattern; it is therefore sufficient at this point always to refer all quantities to a rectangular cartesian coordinate system. The coordinate axes of this system will be denoted by x₁, x₂, and x₃ or, more briefly, by x_i, i = 1, 2, 3. Consider now a vector f with components f₁, f₂, and f₃ in the x₁, x₂, and x₃ directions respectively; more simply, we may then say that f is a vector with components f_i, i = 1, 2, 3; or, more simply yet, a vector f_i. Clearly, it is immaterial what letter is used as subscript, provided of course that the values to be taken by it are prescribed. In what follows, Latin subscripts, unless otherwise specified, assume the values 1,2, 3, and this will not, in general, be stated explicitly; on the other hand, Greek subscripts or sup...