Showing papers in "Journal of Applied Physics in 1945"

Mechanics of the Metal Cutting Process. I. Orthogonal Cutting and a Type 2 Chip

Abstract: An analysis of the chip geometry and the force system found in the case of orthogonal cutting accompanied by a type 2 chip has yielded a collection of useful equations which make possible the study of actual machining operations in terms of basic mechanical quantities. The shearing strain undergone by the metal during chip formation, and the velocities of shear and of chip flow are among the geometrical quantities which can be quantitatively determined. The force relationships permit calculation of such quantities as the various significant force components, stresses, the coefficient of friction between chip and cutting tool, and the work done in shearing the metal and in overcoming friction on the tool face. The experimental methods by which such analyses can be readily made are described. Observed and calculated values from typical tests are presented.

Theory of Filler Reinforcement

Abstract: For small loadings (up to about 10 percent volume parts) the colloidal carbon black spheres may be considered as suspended in a continuous rubber matrix. In the present paper this model is generalized for ellipsoidal (including plate‐ and rod‐like) filler particles and it is extended to the computation of various properties of the suspension in terms of the properties of the matrix and of the fillers. Viscosity, Young's modulus, stress‐strain curve below crystallization, and dielectric constant of the suspension are derived as linear functions of the volume concentration for small, and as quadratic functions for higher loadings. The stress‐strain curves for varying amounts of fillers are similar. For small loadings the tensile strength first decreases because of the stress concentrations occurring around the carbon black spheres when the samples are stretched. The increase of the tensile strength observed for greater loadings is caused by the tendency of the carbon black spheres to form chains and finally...

Convection Currents in a Porous Medium

Abstract: The problem is considered of the convection of a fluid through a permeable medium as the result of a vertical temperature‐gradient, the medium being in the shape of a flat layer bounded above and below by perfectly conducting media. It appears that the minimum temperature‐gradient for which convection can occur is approximately 4π2h2μ/kgρ0α D2, where h2 is the thermal diffusivity, g is the acceleration of gravity, μ is the viscosity, k is the permeability, α is the coefficient of cubical expansion, ρ0 is the density at zero temperature, and D is the thickness of the layer; this exceeds the limiting gradient found by Rayleigh for a simple fluid by a factor of 16D2/27π2kρ0. A numerical computation of this gradient, based upon the data now available, indicates that convection currents should not occur in such a geological formation as the Woodbine sand of East Texas (west of the Mexia Fault zone); in view of the fact, however, that the distribution of NaCl in this formation seems to require the existence of ...

Mechanics of the Metal Cutting Process. II. Plasticity Conditions in Orthogonal Cutting

Abstract: The analysis of the mechanics of orthogonal cutting with a type 2 chip as presented in the first paper of this series can be extended by introducing those physical properties of the work material which control its plastic behavior. One evident plasticity condition is the equality of the shear stress on the plane of shear to the shear strength of the metal. If it is also assumed that the shear strength of the work material is a constant and is the only quantity controlling its plastic behavior, then a very simple additional plasticity condition is obtained by application of the principle of minimum energy. This condition is 2φ+τ−α=90°, where φ is the shear angle, τ the friction angle, and α the rake angle. This condition, however, is found by experiment to be a poor approximation in the case of polycrystalline metals. A very good approximation is obtained, though, if use is made of the fact that the shear strength of the polycrystalline metal is actually a function of the compressive stress on the shear pl...

The General Theory of Stresses and Displacements in Layered Systems. I

Abstract: The problems of airport and foundation engineering have become increasingly important in the war construction program. These problems frequently involve the consideration of stresses and settlements in layered soil deposits. The well‐known Boussinesq equations apply strictly only to homogeneous soil deposits. The general theory of stresses and displacements in a twolayer system is developed in order to provide the engineer with a useful tool which is more directly applicable to the analysis of actual conditions encountered in soil deposits. The basic equations of stresses and settlements are derived. The numerical evaluation of the surface settlement equation for the simplest case of Poisson's ratio equal to one‐half has been completed as the first of a series, and is presented in the form of influence curves for the analysis of practical problems.

The Methods of Specifying the Properties of Viscoelastic Materials

Abstract: Seven methods (Voigt model, Maxwell model, operator equation, mechanical impedance function, creep curve, relaxation curve, and dynamic modulus function) of specifying viscoelastic behavior are discussed. A number of exact relations between these methods of specification are worked out in detail. The majority of these relations are simple enough to be of practical value although a few are too cumbersome. Approximate relationships between the creep curve, the relaxation curve, Maxwell model, and Voigt model are discussed; and numerical examples show the magnitude of errors introduced by the approximation to be small even in quite unfavorable cases. A consideration of the practical utility and physical meaning of the various methods of specification distinguishes between (1) those of general descriptive value and those of direct experimental value; (2) those useful in a phenomenological study of mechanical behavior and those more suited to a formulation of molecular theory. A summary of the present molecular theories is presented together with their interpretation in terms of the Voigt and Maxwell specifications.

The Structure of Certain Muscle Fibrils as Revealed by the Use of Electron Stains

Abstract: Fibrils from certain molluscan muscles, in particular the adductor muscles of the clam Venus mercenaria, were examined with the electron microscope and found to possess periodic variations in structure. In order to make these structural variations visible, it was necessary to treat the fibrils with reagents of high electron scattering power (electron stains). Phosphotungstic acid was found to be particularly suitable. This stain combines with specific regions in the fibrils, forming a remarkably regular geometrical pattern of which the most prominent feature is a regular cross striation, representing a fiber‐axis spacing of about 145A. Within each stained band, the stain is more highly concentrated in spots spaced about 193A from center to center across the band. A line drawn through any such spot parallel to the fiber axis passes through other similar spots, spaced five cross bands apart, making the length of the fiber‐axis period precisely five times the fiber‐axis spacing. X‐ray diffraction data obtained by Bear from the intact muscles are compared with the electron microscope observations. The small angle diffractions are in close agreement with those which would be expected from the observed structure except for the magnitude of the lateral spacing. Electron microscope values for this spacing are significantly smaller than the 325A indicated by the x‐ray data, probably as a result of lateral shrinkage in the vacuum‐dried electron microscope specimens. No significant difference in axis spacing has been observed in fibrils isolated from muscles fixed with alcohol in contracted and extended states.

Strain Hardening Under Combined Stresses

Abstract: Experimental investigations of the strain hardening of metals under combined stresses are usually conducted so that the directions of the principal stresses as well as the ratios of their magnitudes remain constant during any one test. The paper is concerned with incompressible isotropic materials which are stressed in this manner and deform in accordance with certain postulates. The most general stress‐strain relation which can arise under these circumstances is established, and some special cases of this relation are discussed.

Numerical Solution of Ordinary and Partial Differential Equations by Means of Equivalent Circuits

Abstract: Numerical methods are developed to solve certain types of linear and nonlinear partial differential equations to any desired degree of accuracy with the aid of equivalent electrical networks. The methods of solution of ordinary differential equations, both linear and nonlinear, follow as special cases. Three types of problems are considered:1. Initial‐value problems. If the field quantities are known along a surface, the networks may be solved by a straight‐forward step‐by‐step calculation. The networks may also be looked upon as supplying a ``schedule'' of operations that can be put on a digital calculating machine.For time‐varying problems new types of networks are developed in which time appears as an extra spatial variable. Examples of new networks for the elastic field and for the general nonlinear wave equation are given. Sample calculations and theoretical checks of a transient heat flow problem and of an ordinary differential equation are also included.2. Boundary‐value problems. Four methods of s...

Solution of the Diffusion Equation Applicable to the Edgewise Growth of Pearlite

Abstract: The diffusion equation is transformed to a set of coordinates moving with the pearlite interface and a solution applicable to the problem obtained in the form of an infinite series of terms. Using the first three terms, the edgewise velocity of pearlite growth is calculated for a plain carbon eutectoid steel using data most of which are obtained by extrapolation. The values obtained show reasonable agreement with values for the rate of pearlite nodule growth determined by Hull, Colton, and Mehl. The velocity increases with decreasing temperature, as expected, and it is shown that this is caused by the change in the solubilities of ferrite and cementite in austenite with temperature. The theory predicts curved ferrite‐austenite and cementite‐austenite interfaces and the carbon concentration in austenite is shown to vary across each of these interfaces.

Gas Flow in the Mass Spectrometer

Abstract: If a mass spectrometer is to be used successfully for gas analyses, the gas flow through the system must meet a number of requirements. The three modes of gas flow—molecular, intermediate, and viscous—are reviewed, and their working ranges are discussed in terms of the pressure of the system. The upper limit for molecular flow, through capillaries or through small openings, is found to lie at a pressure where the mean free path of the molecules is between 15 and 40 times the diameter of such a gas leak. Expressions are developed to show that, for molecular flow, the ion beam intensity is independent of molecular weight but is a linear function of the sample pressure, and that the principle of linear superposition applies to mixture peaks. Since the composition of a gas mixture in a reservoir is found to change with time (a numerical example is worked out), the necessity for analyses of short duration becomes evident. The practical aspects of designing the gas system for molecular flow and for efficient ion production are discussed in detail. The various flow requirements are best met by a gas leak consisting of a small hole in a diaphragm, or several holes in parallel. A relatively high gas pressure within the electron beam boundaries and resulting large ion currents are produced by introducing the gas as a molecular beam into a gas‐tight ionizing region.

Thermal Expansion and Second‐Order Transition Effects in High Polymers: PART II. Theory

Abstract: The nature of the thermal expansion anomaly in high polymers, known as the second‐order transition, is examined in some detail. It is suggested that below the transition temperature, Tm, polymer chains can expand sidewards but not parallel to their length. At Tm lengthwise expansion becomes prominent, thus accounting for the sudden increase in thermal expansion. Experimental results are presented showing the anisotropic expansion of oriented polymers below Tm. The transition effect is then treated as a problem in viscous flow, which gives rise to various semi‐empirical plots connecting Tm with applied forces, plasticizer content, and time effects. The brittle point, Tb, involves highly elastic deformation, and is shown to be a fundamentally different test, although Tm and Tb are sometimes numerically equal. Various factors influencing the brittle point are reviewed briefly.

The Determination of Molecular‐Weight Distribution in High Polymers by Means of Solubility Limits

Abstract: By means of polymer fractions of known molecular weight, dissolved in solutions of known compositions, it is possible to determine the solubility law which relates the point of solution saturation to the molecular weight and concentration of the dissolved polymer. Having established such a calibration, it is possible to determine the molecular‐weight distribution in a heterogeneous sample of the polymer by suitable operation on a curve relating the mass of polymer precipitated to the amount of precipitant added to the solution. Optical means, making use of scattering from the precipitate, are used to obtain this latter curve. The method is applied to cellulose acetate butyrate and is shown to give results in agreement with gravimetrically obtained distribution curves.

A High Temperature, High Pressure Rheometer for Plastics

Abstract: A modified Bingham‐type rheometer, designed for operation at temperatures up to 500°F and at pressures up to 2000 p.s.i. is described. Interchangeable orifice plates permit wide variation of shear conditions. With this instrument flow properties may be studied under conditions approximating those encountered in the actual processing of thermoplastics, e.g., by molding or extrusion. Typical results are presented for cellulose acetate, polystyrene, and polyvinyl resin plastics, and correlation with practical experience is pointed out. The instrument is slow, and this limits its usefulness for other than research investigations.

The Thermodynamics of Rubber at Small Extensions

Abstract: On analyzing their own data, Meyer and Ferri have concluded that at small extensions, rubber is an ideal elastomer according to the definition that (∂E/∂L)P,T=0. Further analysis of Meyer and Ferri's data does not sustain their conclusion. If, however, (∂E/∂L)V,T=0 is taken as a new criterion for an ideal elastomer, Meyer and Ferri's data do indicate that rubber is ideal, at least for extensions up to 166 percent. The new criterion implies that the valence angles do not store an appreciable amount of energy when the rubber is stretched. However, both the molecular orientation and the interatomic displacements do influence the energy required for extension.

The Production Histories of Oil Producing Gas‐Drive Reservoirs

Abstract: A theory has been developed for predicting the behavior of solution gas‐drive oil producing reservoirs, on the basis of previously established empirical laws on the flow of heterogeneous fluids through porous media Treatments are given both for the simple pressure depletion history without gas injection, and those for systems in which gas is injected during the course of oil production The specific results provided by the theoretical analysis include the ultimate oil recovery, and the pressure decline, gas‐oil ratio, and productivity factor histories Two types of gas injection have been considered, namely: (1) that in which the returned gas is supposed to diffuse through and be produced continuously with the oil zone; and (2) that in which the injected gas remains locked in the gas cap, which merely expands as oil production and gas injection proceed In the latter case the rate of growth of the gas cap is also obtained as a function of the cumulative oil recoveryThe theory is illustrated by numerical

The Secondary Electron Emission of Pyrex Glass

Abstract: The total secondary emission of Pyrex glass is measured by a method utilizing the conductivity of the heated glass to carry the current. Necessary precautions for this type of measurement are pointed out. The secondary emission is measured over the bombarding voltage range of 50 to 10,000 volts. No temperature variation of secondary emission is observed.

Crystal Interference Phenomena in Electron Microscope Images

Abstract: The observation of electron reflections in electron microscope images is reviewed and further data are presented. The observations of the reflected beams with the objective limiting diaphragm removed and the determination of the planes responsible for the reflections by this means are described. The results of the dynamical theory of electron diffraction are briefly discussed and the values of the ``characteristic'' crystal thickness D0 are computed. These values of D0 are compared with the experimental values and are in reasonably good agreement for the MgO (200) reflections at 60, 96, and 103 kv, MgO (220) reflections and CdO (200) reflections at 60 kv. The dynamical theory accounts satisfactorily for the intensity variations except as modified by inelastic scattering and the results may be considered as experimental verification of the theory.

Electron Microscopical Replica Techniques for the Study of Organic Surfaces

Abstract: The problem of examining opaque surfaces in the electron microscope is discussed and it is shown that none of the methods heretofore described is completely satisfactory for the examination of organic surfaces. Two new methods, a low pressure polystyrene‐silica technique and a silver‐silica double evaporation method, are described and it is demonstrated that they allow observation of organic as well as metallurgical surfaces. Electron micrographs of fiber surfaces, biological material, paint films, ores, and metals are included to illustrate the utility of these techniques.

Virtual Masses of Rectangular Plates and Parallelepipeds in Water

Abstract: The following is a report on experimental results obtained for the virtual masses of thin rectangular plates and rectangular parallelepipeds moving in water. Experimental data, together with an empirical equation, showing the manner in which the virtual mass of a rectangular plate varies with dimensions and direction of motion are given. Data and an empirical equation giving the virtual mass of a rectangular parallelepiped as a function of dimensions and direction of motion, for the special case in which the motion is parallel to one face, are also listed.

Techniques for Evaporation of Metals

Abstract: Thirty‐four elements have been observed for evaporation behavior, the results being summarized for each element and the best techniques then listed in Table I. Heaters studied fall into two general classes, wires and crucibles. Tungsten, iron, nickel, and chromel wires were used and these were formed into close wound conical baskets and helical coils. Each element was studied for evaporation behavior from as many of these forms as was possible. Alundum and BeO crucibles formed by painting suspensions of these materials on a tungsten conical basket followed by baking at a high temperature were exceptionally satisfactory heaters for almost all of the elements studied. These crucibles served well for the evaporation of metals whose evaporation temperatures approached 2000°C as well as for those with lower evaporation temperatures.The 18‐inch evaporation system was designed and constructed along fairly standard lines. An externally operated, four‐inch vacuum valve between the diffusion pump and the bell jar a...

Data on Rate of Capillary Rise

Abstract: General aspects of the dynamics of capillary rise are considered with references to extant theories. A stroboscopic method used to study the rise of a liquid in a capillary tube is discussed. Tables are presented showing the observed heights at various times during the rise for the liquids—water, ethyl alcohol, and glycol in each of three capillaries of different diameters.

The Frictional Properties of Some White Metal Bearing Alloys: The Role of the Matrix and the Hard Particles

Abstract: A previous paper has described an investigation of the frictional properties of alloys of the copper‐lead type which consist of a hard matrix (copper) in which are dispersed particles of a soft material(lead). It was shown that these alloys function by the extrusion and smearing of the soft phase over the hard matrix, so providing metallic‐film lubrication. This paper describes experiments on a typical lead‐base bearing alloy which consists of a soft matrix in which are dispersed numerous hard crystallites. Measurements of the friction were made at room temperature and at elevated temperatures for clean and for lubricated surfaces. Comparison with a special alloy consisting of the matrix material alone, showed that the hard particles played no appreciable part in the basic frictional and wear properties of the bearing alloy. It is suggested that the frictional behaviour of the bearing alloy is determined essentially by the properties of the matrix material itself although in practical running operations there may be other properties which determine the suitability of the alloy for use in bearings. Similar experiments are described on a typical tin‐base bearing alloy and a corresponding tin‐base ``matrix'' alloy.

A 100‐Million Volt Induction Electron Accelerator

Abstract: The plan and construction of a device capable of accelerating electrons to energies as high as 100 million electron volts are described together with the special building to house it. A more detailed description of the device and its construction will appear in the General Electric Review. The accelerator has a pole face 76 inches in diameter, weighs 130 tons, and operates on 60‐cycle current requiring at full load 200 kilowatts. The machine is air cooled and is capable of continuous operation at full voltage. The toroidal glass vacuum tube of oval section has an external diameter of 74 inches and consists of 16 sectors cemented together. At 100 million volts the x‐ray output, measured in a thick‐walled (¼ inch lead) ionization chamber, is 2600 Roentgens per minute at one meter target‐thimble distance and the half‐value width of the x‐ray beam is 2.0 degrees. The penetrating power of the x‐rays in iron at various voltages has been measured and the radiographic possibilities studied.

On Maximum Gain‐Band Width Product in Amplifiers

Abstract: By introducing an electrostatic problem analogous to the impedance function problem it is found possible to prove that, under simple and quite broad assumptions, the maximum possible gain‐band width products for two‐terminal coupling, four‐terminal low‐pass coupling and four‐terminal band‐pass coupling are, respectively, 1, 2.47, and 2.53 times g/πC. The first result was conjectured by Wheeler long ago, and it and the second have recently been proved by Bode. The last result covers a case more general than those considered by Bode.

The Effects of Temperature and Humidity on the Physical Properties of Tire Cords

Abstract: Apparatus by means of which tire cords may be conditioned and tested at elevated humidities (1.6–65 percent R. H.) and temperatures (20–165°C) is described. The apparatus consists of a portable conditioning unit which is used with a standard tensile testing machine. Equipment for measuring creep of tire cords under dead load at elevated temperatures is also described. Five representative types of tire cord were employed in the experiments, medium stretch cotton, low stretch cotton, viscose rayon, Fortisan, and Nylon. Tenacity, ``10 pound‐stretch,'' and ultimate stretch are studied as functions of relative humidity, temperature, and moisture regain. It is shown that the tensile properties are best represented as functions of temperature at constant regain. The tenacity of viscose rayon cords decreases with increasing temperature at constant regain in the range of regains 0–5 percent. The tenacity of the medium stretch cotton cords at constant regain falls off with increasing temperature in the range of 20–...

Flexural Vibration of Unrestrained Cylinders and Disks

Abstract: Solutions are given for the free flexural vibration of a cylinder vibrating as a rod would vibrate and for the free flexural vibration of a disk vibrating as a circular plate would vibrate. The solutions are based upon the mathematical theory of elasticity. Curves are given showing the correction factors which, when applied to the elementary solutions, will give results in agreement with those obtained by means of the more rigorous solutions given here.