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Volume 20, Issue 11, 01 November 1949

An Analysis of the Mechanics of Metal Cutting
View Description Hide DescriptionAn attempt is made to go beyond an idealized description of the process of metal removal. The details of two‐dimensional orthogonal cutting are investigated, and several concepts and hypotheses are introduced which apply equally well to the most general cutting operation. Of these, the most significant is the great importance of the small time available for the plastic deformation to occur. Ekstein's paradox is explained, and the influences of speed of cutting, depth of cut, and rake angle are correlated by the consideration of dynamic plasticity. In addition, the effect of non‐homogeneity of the material is analyzed and shown to account for the gradual change from the discontinuous to the continuous type of chip as the cutting speed is increased, and for the marked increase in the specific cutting force as the depth of cut is decreased. A partial theoretical analysis of the state of stress, in the chip and the workpiece, and energy considerations are also found helpful in the description of what probably happens when metal is cut.

Antennas and Open‐Wire Lines. III. Image‐Line Measurements
View Description Hide DescriptionA new type of open‐wire line is described for which many disadvantages, notably radiation and unbalance, are overcome by replacing one of the physical conductors by the image of the other in a semi‐infinite, highly conducting plane.
The characteristics of a line driven at both ends and loaded at the center are examined; it is shown that the impedances measured on both sides of such a line are equal and simply related to the load impedance, provided that electrical symmetry is maintained about the load point. The double‐ended drive requires no dielectric supports and permits the line conductor to continue past the load.
The construction and operation of an image line with double‐ended drive is described. The characteristics of the new line compare very favorably with those of a good coaxial measuring line.
Finally, use of the line in the measurement of the apparent impedance of a cylindrical dipole antenna as a function of the line spacing is described.

Convection Currents in Porous Media: II. Observation of Conditions at Onset of Convection
View Description Hide DescriptionSmall‐scale experiments have been carried out for determining the minimum vertical thermal gradient which is required to cause convection in liquids entrapped in porous media. Observations relative to the onset of convective flow in unconsolidated sands indicate that the present theories predict minimum gradients which are excessive by considerable amounts, possibly because they neglect the temperature‐dependence of viscosity. The ratio of theoretical to observed gradients is found to be roughly,where h ^{2} is the thermal diffusivity, μ_{Av} is average viscosity,k is flow‐permeability, ρ is density of liquid, α is the coefficient of cubical expansion of the liquid, and where K = 10^{−3} sec.^{2} per cm^{2} °C for c.g.s. units. By extrapolation, it is possible to strengthen the earlier conclusion that convection occurs in the Woodbine sand near the Mexia fault zone.

A Direct Method of Determining Preferred Orientation of a Flat Reflection Sample Using a Geiger Counter X‐Ray Spectrometer
View Description Hide DescriptionA new reflection method is described for determining pole figures of flat samples with a Geiger counter x‐ray spectrometer. The chief advantage of the method is that the experimental data may be used directly without corrections for changes in geometry during rotation of the sample. Beginning from an initial position identical with the usual reflection arrangement the sample is rotated about an axis defined by the intersection of the sample surface with the plane of the spectrometer. During this motion a randomly oriented sample of sufficient thickness will yield a constant counting rate because the absorption and effective scattering volume of the sample remain unchanged. As a result, no correction formula is required. The experimental arrangement requires three horizontal slits; two are used to collimate the incident beam, and the third is placed in front of the counter. A mathematical analysis of the optical elements of the arrangement is given together with the results from a practical application.

Determination of Preferred Orientation in Flat Transmission Samples Using a Geiger Counter X‐Ray Spectrometer
View Description Hide DescriptionA method employing a diverging x‐ray beam is described for the determination of preferred orientation in flat transmission samples with a Geiger counter x‐ray spectrometer. It is shown that for a certain range of sample thickness the counting rate is independent of the rotation of the samples, and therefore, no correction formula is required.

Propagation of Transverse Waves in Viscoelastic Media
View Description Hide DescriptionIn calculating elastic constants of viscoelastic media from transverse wave propagation, it has been customary heretofore to assume a plane disturbance in a medium of infinite extent. Equations have now been derived for conditions which approach much more closely the experimental arrangement, namely, propagation from a finite source plate in a rectangular cell, and representative numerical calculations have been made. The new theory shows that the finite dimensions of cell and source should have very little influence on the wave‐length as determined from observations of strain double refraction, but the attenuation should be perceptibly different from that of the plane wave case. Experimental data confirm these conclusions. Nevertheless, the simple plane theory is adequate within present experimental error for the majority of cases. Only in certain specified ranges of mechanical consistency will it be necessary to apply corrections taking into account the sizes of the cell and source.

A Study of the Mechanism of Sintering of Metallic Particles
View Description Hide DescriptionAn investigation has been carried out on the mechanism of sintering of metallic particles. Single layers of spherical copper particles have been sintered under varying conditions of time and temperature in a dry hydrogen atmosphere. Analysis of the rate of interface contact between the particles has shown metallic sintering to be a diffusion process, in agreement with the theory of Kuczynski. The heat of activation of self‐diffusion of copper has been calculated and found to be 55,000 cal./mole. This is in close agreement with Kuczynski and also values obtained by other workers using the radioactive tracer method.

Harmonic and Subharmonic Response for the Duffing Equation ẍ+αx+βx ^{3} = F cosωt (α>0)
View Description Hide DescriptionThe Duffing equationẍ+αx+βx ^{3} = F cosωt (α>0) is known to possess periodic solutions with frequency ω/n for all integral n, provided that β is sufficiently small. For n=1 and n≠1, these solutions are designated in the literature as harmonic and subharmonic solutions respectively. In this paper, a classification of the various types of periodic solutions is given, in which it is shown that there are two types of harmonic solutions and two types of subharmonic solutions for sufficiently small β. The perturbation method is employed to find the approximate response curves for each of the four types of periodic solutions. A comparison is made between the response curves obtained in the non‐linear case (β≠0) and linear case (β=0) and some properties of the solutions in the non‐linear case are discussed. A comparison is then made between the perturbation method and the Rauscher method, which is an iteration method that assumes F small instead of β. This comparison is not made in all generality, but only for one particular type of subharmonic solution. The main result obtained is that for F small, the two methods yield similar results for larger values of β than might have been anticipated.

New Interpretation of the n‐Power Law in Plastic Deformation
View Description Hide DescriptionIt is shown that the n‐power law describing a true stress‐strain curve, normally written as S = kδ^{ n }, can be placed in the form
A plot of S/S _{0} as a function of n, for a fixed value of the logarithmic strain δ, provides a general description of the behavior of all materials in plastic deformation. Experimental data from the literature are in good agreement with the curves.

A Technique for the Preparation of Grease or Solid Samples Dispersed in Grease‐Like Media for Examination with the Electron Microscope
View Description Hide DescriptionThe nature of grease as a dispersion of solid particles in oil is briefly discussed, and the value of the electron microscope in studying this solid phase is pointed out. The requirements of a satisfactory grease specimen mounting technique are outlined and a new technique fulfilling these requirements is described. Electron micrographs are presented which demonstrate the usefulness of the technique in disclosing pertinent information on grease structure. The factors involved in the preparation of powder specimens for electron micrography are discussed in relation to the adoption of a modification of the grease mounting technique for this purpose. The modified technique for powders is outlined and illustrated with micrographs.

Increasing Space‐Charge Waves
View Description Hide DescriptionAn earlier paper presented equations for increasing waves in the presence of two streams of charged particles having different velocities, and solved the equations assuming the velocity of one group of particles to be zero or small. Numerical solutions giving the rate of increase and the phase velocity of the increasing wave for a wide range of parameters, covering cases of ion oscillation and double‐stream amplification, are presented here.

The Effect of Cold Work in Metals on Powder Pattern Intensities
View Description Hide DescriptionUsing crystal monochromated CuKα‐radiation and a Geiger counter spectrometer, integrated intensity measurements have been made for powder samples of cold‐worked and annealed α‐brass. The effect of cold work is to increase the integrated intensity of the strong lines and make practically no change in the weak lines. The increase for the strong lines is presumably due to a reduction in extinction.Measurements were made of the (400) reflection on a cold‐worked sample and on an annealed sample held at high temperature to demonstrate the difference between the effects of cold work and temperature vibration.

The Structure of Porous Materials from Gas Penetration Rates
View Description Hide DescriptionGas penetration rates have been used to study the structure of three commercial grades of sintered Pyrex glass. Specific surface areas, ``average pore diameters,'' pore population densities, average particle diameters, and particle population densities have been calculated on the basis of the data obtained.

Application of a Variational Principle to Biconical Antennas
View Description Hide DescriptionA theoretical examination is made of the impedance of a biconical antenna, based upon a method devised by Schwinger in studying the discontinuity problems of a wave guide. In the present analysis, an integral equation to determine the aperture field is obtained by matching the tangential electric and magnetic fields along the boundary sphere. Using this integral equation, the effective terminating admittance of the antenna can be expressed in a form that is stationary with respect to small variations in the aperture field. It is shown that the zeroth‐order solution of the admittance function thus obtained is the same as the one that Smith derived by neglecting all the high order waves in the interior region except the principal mode. For small‐angle cones, the present formulation yields the same exact solution obtained previously, based upon several different methods. The paper also contains a discussion of the first‐order approximate solution which is applicable to both small‐ and wide‐angle cones. The analysis includes a detailed treatment of a method by which the characteristic values and characteristic functions for a given cone may be found approximately, but very accurately; as well as certain integrals involving the product of Legendre functions.

Erosion of Electrical Contacts on Make
View Description Hide DescriptionWhen an electric current is set up by bringing two contacts together, they necessarily discharge a capacity. If the discharge takes place through an arc before the metallic circuit is established, erosion of the electrodes results. In a low voltage circuit the occurrence of an arc is dependent upon the condition of the electrodesurfaces and upon the circuit inductance. For ``inactive'' surfaces, and a voltage of the order of 50, an arc does not occur if the inductance is greater than about 3 microhenries. Surfaces of various metals can be ``activated'' by vapors of certain unsaturated organic compounds, and in the active condition they give arcs even when the circuit inductance is greater than this limiting value by a factor of more than 10^{3}. The study of arcs between active metal surfaces is not yet complete, and most of this paper and all of the remainder of this abstract have to do with surfaces which are inactive.
When an arc occurs at the make of inactive metal surfaces, its energy, which in low voltage circuits of practical interest is drawn entirely from a charged condenser, is dissipated almost entirely upon the positive electrode, and melts out a crater intermediate in volume between the volume of metal which can be melted by the energy and that which can be vaporized. Some of the melted metal lands on the negative electrode and, with repeated operation, results in a mound of metal transferred from anode to cathode. This transfer is about 4×10^{−14} cc of metal per erg.
The arc voltage is of the order of 15. If the initial circuit potential is more than about 50 volts there may be more than one arc discharge, successive discharges being in opposite directions and resulting in the transfer of metal in opposite directions— always to the electrode which is negative.

The Scattering Cross Section of Spheres for Electromagnetic Waves
View Description Hide DescriptionThe problem discussed in this paper is that of the scattering of electromagnetic waves by a spherical obstacle. The classical theory is well known. Stratton's ``Electromagnetic Theory,'' for instance, contains a very good summary of that discussion. The computation of the scattering cross section, according to this theory, leads to some difficulties. In the case of large spheres, where geometrical optics should apply, the rigorous theory yields a scattering cross section equal to twice the actual cross section of the sphere!
The discussion presented in this paper explains this strange result and shows the role played by the shadow and by the diffraction fringes surrounding the shadow. A reasonable system of approximations yields the well known ``Babinet's principle.'' The physical interpretation is of such general character that it must certainly apply to a variety of similar problems in acoustics or wave mechanics. The spherical shape of the obstacle is essential in the present discussion, but similar results would certainly be found for other shapes of the obstacle. The case of a circular cylinder, investigated by E. B. Moullin and L. G. Reynolds, also leads to a total cross section twice as large as the actual cross section, for large cylinders. The explanation is the same as for the spheres. Experiments very carefully designed by Dr. Sinclair and Professor V. K. LaMer gave a very precise check of the theoretical predictions.

Measurement of the Complex Conductivity of an Ionized Gas at Microwave Frequencies
View Description Hide DescriptionThe positive column of a glow discharge is placed along the axis of a cylindrical cavity excited in the TM_{010} mode. The transmission of 3‐cm waves through the cavity and the shift in resonant frequency are observed as a function of discharge current. It is shown that from these measurements values of the complex conductivity, σ_{ r }+iσ_{ i }, of the electron gas can be calculated. Curves of the measuredconductivity components as functions of pressure and current are given. Using a theoretical formula for the conductivity (see reference 6) values of electron density can in turn be calculated from both σ_{ r } and σ_{ i }. Langmuir probe studies are carried out to check the results obtained, and adequate agreement is found.

Thermionic Emitting Properties of Two Refractories
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Papers by Hadrian D. Stahl
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