Technical Papers and Discussions - Properties of Metals; Sponge Iron - Anelasticity of Metals (Metals Tech., Aug. 1946, T. P. 1992, with discussion)

It is customary to regard the stress-strain relation as consisting of two parts, thc elastic region and the plastic region. The essential attribute of the plastic region is the presence of a permanent set, which remains upon removal of all stresses. The essential attribute of the elastic region is the absence of such a permanent set. Absence of a permanent set does not imply a linear relation between stress and strain, nor even a single valued relation. In fact, in no real metal is stress a single valued function of strain in the elastic region. The property of a solid in virtue of which stress and strain are not uniquely related in the elastic range will be called "anelasticity." The purpose of the present article is to review and correlate the past work upon the anelasticity of metals. The following paper by W. A. West124 describes investigations upon anelastic properties of iron. Many manifestations of anelasticity have been observed, the first as early as 1835 by Weber.l,2 In his experiments Weber subjected a specimen to a constant load (or deformation) for a given time, and then suddenly removed the load. He observed that most of the deformation suddenly disappeared, but that there remained a residual deformation, which disappeared only gradually with time, as is illustrated in Fig. I. The occurrence of a residual deformation which only gradually disappeared, Weber called the elastic after-effect (Elastische Nackwir-kung). An extensive review of the early work upon elastic after-effects has been given by Auerbach.3 Another manifestation of anelasticity is the dependence of the elastic constants---e.g., Young's modulus— upon the method of measurement. Thus, if dynamic methods are used, the measured value will depend upon the frequency of oscillation. Still another manifestation is dissipation of energy attending vibration, called damping or internal friction. One objective. of metallurgical science is the understanding of the plastic and fracture properties of metals in terms of their microstructure. Through such an understanding will come the ability to design microstructure to give the desired mechanical properties. A study of anelasticity will furnish an invaluable aid in the attainment of this objective. Such studies, when properly guided, yield information regarding the relation between stress and strain in the individual components of the microstructure. In order, however, that this type of information may be obtained, it is necessary that the experimental studies of anelasticity be interpreted by the appropriate mathematical analysis. This article, therefore, starts with the mathematical formulation of anelasticity.