Clarence Zener

Effect of Strain Rate Upon Plastic Flow of Steel

An experiment has been designed to check a previously proposed equivalence of the effects of changes in strain rate and in temperature upon the stress‐strain relation in metals. It is found that this equivalence is valid for the typical steels investigated. The behavior of these steels at very high rates of deformation may, therefore, be obtained by tests at moderate rates of deformation performed at low temperatures. The results of such tests are described. Aside from changing the isothermal stress‐strain relation, an increase of strain rate tends to change the conditions from isothermal to adiabatic. It is found that at low temperatures, the adiabatic stress‐strain relation in the plastic range is radically different from the isothermal, having an initial negative rather than a positive slope. This initial negative slope renders unstable homogeneous plastic deformation.

Theory of Growth of Spherical Precipitates from Solid Solution

The radius of a spherical precipitate particle growing in a solid solution of initially uniform composition may be shown to be equal to α(Dt)½, where D is the atomic diffusion coefficient, t the time of growth, and α, the growth coefficient, is a dimensionless function of the pertinent compositions. In this paper the precise dependence is found of this function upon the pertinent concentrations. A similar computation is made for the growth coefficient corresponding to the one‐dimensional growth of a plate.

Theory of Do for Atomic Diffusion in Metals

The theory of the entropy of activation ΔS previously given for interstitial diffusion in metals is herein extended to self‐ and to chemical diffusion. It is concluded that this entropy of activation will always be positive; and it is shown that in the case of self‐diffusion and of chemical diffusion at very low concentrations, the better the empirical ΔS the better does it correlate with the theoretical positive ΔS. The large negative apparent ΔS frequently found for chemical diffusion at higher concentrations must be attributed either to inaccuracies in experiments or to the presence of short circuiting diffusion paths. It is predicted that the presently reported negative values of ΔS will become positive when very small concentrations are used in large grain size specimens.

Interference of Growing Spherical Precipitate Particles

The exact theory of the rate of growth of spherical precipitate particles has previously been developed for the initial stage where the individual precipitate particles do not interfere with one another. In the present paper this theory is carried one stage further to include their mutual interference. It is found that in the particular case of a very dilute solution this interference may be accounted for in a relatively simple manner. The applicability of the theory has been tested by new observations upon the precipitation of carbon from α‐iron. Good agreement is found up to 95 percent completion of precipitation.

Relation between residual strain energy and elastic moduli

It is shown that the presence of residual strain energy necessarily results in a lowering of the overall tensile and shear moduli, and a quantitative relation is derived between the density of residual strain energy and the decrease in tensile and shear moduli. An interpretation is thereby given to the recent observations of Koster that solute atoms of only a small solubility lower the tensile modulus when they are atomically dispersed.

Internal friction in solids

The various causes of internal friction in solids are discussed. Internal friction depends in general on thermal currents which occur owing both to the inhomogeneous strains set up by the vibrations in the solid, and to the variations in the elastic constants from point to point in polycrystalline materials. The influence of ferromagnetism also is considered.

Problems in Non‐Elastic Deformation of Metals

In this article an attempt is made to examine the goals of current and of possible future types of research concerned with the non‐elastic deformation of metals. It is found that an understanding of non‐elastic deformation would be enhanced by research upon the following topics: 1. The anelasticity associated with the viscous behavior of grain boundaries and the at least temporary viscous behavior of slip bands. 2. The mechanics of the initiation and growth of twin bands. 3. The mechanics of the initiation and growth of slip bands, including the drop in resistance to deformation which accompanies the initial slip bands. 4. The mechanics of the segregation of solute atoms in solid solution, such as of carbon and nitrogen in iron. 5. The conditions under which strain hardening is not removed by recovery or by recrystallization, and hence under which a mechanical equation of state exists, i.e., under which a relation exists between strain rate, strain, stress, and temperature. 6. Variation of the heat of activation for plastic strain rate upon stress and upon the microstructure. 7. Anisotropy introduced by deformation.

Foam Solar Sea Power Plant

In the accompanying report Beck suggests a new type of open-cycle system for obtaining power from the oceans thermal gradient. A modification of this open-cycle plant which will ensure a high efficiency, and also a low capital cost per unit power output, is described here.

Mechanical Behavior of High Damping Metals

The relation between the various measures of internal friction are independent of the precise mechanism of the dissipation of energy when the internal friction is small, but not when it is large. In this paper the relation between the two measures most commonly used, logarithmic decrement and tangent of the angle with which strain lags behind stress, is deduced for all levels of internal friction in the important case in which the dissipation of energy is due to a relaxation process having a single time of relaxation. The conditions are further derived under which a specimen of such a metal will not vibrate, but returns aperiodically to its equilibrium configuration.

Equation of state for strong electrolytes

I develop an equation of state for strong electrolytes (nonassociated) by combining the Debye–Huckel electrostatic interaction with the van der Waals excluded volume for hard elastic spheres. This equation of state gives essentially perfect agreement with published data up to 5M negative ion concentration for all the systems I have studied: HCl, LiCl; MgCl2, CaCl2, SrCl2; AlCl3. I use two adjustable parameters: the Debye–Huckel closest distance of approach a0 between positive and negative ions, and the van der Waals’ excluded volume b0 at infinite dilution. These two parameters approximately satisfy an equation stating that all the water of hydration is absorbed by the small positive ion.