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Elasticity and Anelasticity of Metals. By CLARENCEM. ZENER. ix 170 pp.; 56 figs. Chicago, Illinois : University of Chicago Press, 19-18, The principal topic of this monograph is the anelastic behavior of metals, a phenomenon which has been known for many years, but which has been greatly illuminated and clarified only during the past ten years by the work of the author and his shool. Anelasticity is the term chosen by the author to describe the behavior of metals in the region of small strain, where, however, strain is not a linear single-valued function of stress alone, but yet where no permanent plastic deformation takes place. Part I of the book describes the elements of classical elasticity theory, presents numerous data on the elastic constants of metal crystals, and discusses the relationship between these constants and crystal structure. Data on the tempetature dependence of the elastic constants, and the relevance of this to the stability of body-centered cubic versus face-centered cubic structures, are discussed. Chapter IV is devoted to the subject of “microelasticity,” which deals with the elastic behavior of elementary regions containing such a small number of atoms that one does not take account of departures from a perfect lattice; i.e., no imperfections such as holes or dislocations are invoked. I n such a region the deformation is considered to be homogeneous and elastic up to the theoretical limit of strength. An interest,ing description of the transition from one type of cubic structure to another during the strain of such a small region is given. This is related to the phase transformation from bodycentered cubic to face-centered cubic structures, an example of which occurs in lithium at low temperatures and was first predicted by Zener on the basis of the ideas described in this chapter. Part I1 deals with the formal theory of anelasticity, based on the generalizations that the stress components and their time derivatives are linearly related to the strain components and their time derivatives. With this assumption for the fundamental anelastic behavior, a description of the frequency dependence of the elastic constants and the energy losses per cycle in vibration experiments, and of creep and stress relation, is given. The anelastic behavior of a real metal can then be described with a spectrum of relaxationprocesses, and descriptions of the physical origin of the various bands present in such a spectrum sought for. A chapter on measurements describes the various techniques used to determine the details of this relaxation spectrum experimentally; an important point is the possibility of extending the available frequency range through the fact that the relaxation time, 7 , for a large group of examples obeys an activation energy law, so that the relaxation time can be varied by varying the temperature. This is equivalent to varying the frequency, for the quantity of importance is (TU). The last chapter, forming about two-thirds of the book, is the most important, for it describes the author’s major contributions to this field, the physical interpretation of the variety of relaxation processes that can be encountered in a real metal sample. The author and his coworkers have here exhibited their greatest ingenuity and physical insight into the nature of the relaxation processes experimentally observed. They have thus been able to make, from a subject before only rather hazily understood, a very new and useful tool for studying the motion of atoms within solids, the nature of grain boundary material, and the anelastic behavior of the materials within slip bands. This latter leads to a n interesting section on the plastic behavior and fracture of metals. Many diverse aspects of the anelastic behavior of solids are given a logical and coherent unity. The book as a whole is a very satisfying demonstration of the way in which a field originally rich in potential information, but rather obscure, may be made very useful and illuminating by the keen physical insight described here. The book is attractive in form, suffers only from the minor annoyance of using Roman numerals in the references, and should be of great value t o metallurgists and those interested in the physics of solids. Many of its ideas are capable of extension to materials other than metals,-for example, solid polymers.
SIDNEYSIEGEL.
