Volume 26, Issue 7, 01 July 1955

Vibroscope Measurements of the Elastic Moduli of Nylon 66 and Dacron Filaments of Various Draw Ratios
View Description Hide DescriptionBy use of the electrostatic vibroscope method, dynamic measurements have been made of the Young's modulus derived from bending and the torsional modulus of nylon 66 and Dacron filaments ranging in draw ratio from one (undrawn) to six. Quasistatic measurements have also been made to obtain the Young's modulus derived from extension. The dynamic values of the Young's modulus increase from draw ratio one to draw ratio six by a factor of 3.5 for nylon 66 and 5.8 for Dacron. The torsional moduli of both filament types exhibit no appreciable changes with increasing draw ratio.
The ratio of the Young's modulus to three times the torsional modulus, which ratio is unity for a homogeneous isotropic material with a Poisson's ratio of ½, is about three for nylon 66 and greater than five for Dacron at a draw ratio of six. These results, along with those obtained at lower draw ratios, indicate that both filaments become progressively anisotropic with drawing, the extent of the anisotropy reflecting mainly the changes in the Young's modulus. As a check on the experimental procedures, the elastic moduli have also been measured for a 1‐mil drawn tungsten wire.

Theory of Non‐Newtonian Flow. I. Solid Plastic System
View Description Hide DescriptionThe relaxation process of viscous flow may be visualized as the sudden shifting of some small patch on one side of a shear surface with respect to the neighboring material on the other side of the shear surface. Any shear surface will divide a mosaic of such patches lying on the two sides of the surface. Except for the simplest systems, this mosaic of patches will be heterogeneous and can be described by groups each characterized by its mean relaxation time β_{ n }, by x_{n} the fractional area of the shear surface which the group occupies and by α_{ n }, a characteristic shear volume divided by kT. The resulting generalized expression for viscosity is ,where ṡ is the rate of shear. This equation is applied to masticated natural rubber, polystyrene, X‐672 GR‐S, X‐518 GR‐S rubber, and Vistanex LM‐S polyisobutylene. All applications give good agreement with experiment. The known criticisms of Eyring's simple relaxation theory for viscous flow are reviewed, and are apparently taken care of in this general treatment.

Theory of Non‐Newtonian Flow. II. Solution System of High Polymers
View Description Hide DescriptionThe authors' theory developed in the preceding paper I is applied to solutions of polystyrene, polyisobutylene, X‐518 GR‐S rubber, and lime base grease with good agreement with experiment. The parameters, x_{n}/α_{n} and β_{ n } (see the abstract of the paper I), were calculated, and are tabulated; these parameters are proportional to the surface concentration and the relaxation time of the nth group of flow units, respectively. The effects of the molecular weights of polymers, concentration, solvent, and temperature on these parameters were studied. Our results establish the following facts:
(1) The heterogeneity of flow units increases with increasing molecular weight.
(2) In the range of low concentration, β_{ n }(relaxation time) is independent of concentration, while the areal concentration of non‐Newtonian units increases more rapidly than proportional to the bulk concentration of a polymer.
(3) A ``good'' solvent increases the concentration of non‐Newtonian units, while the contrary is true for a ``poor'' solvent.
(4) In poor solventsolutions, the concentration of non‐Newtonian units increases with increasing temperature, while the concentration is independent of temperature in good solvents.

Effect of Molecular Weight Distribution on the Creep Behavior of Cellulose Acetate
View Description Hide DescriptionCreep measurements were carried out at 80°C on cellulose acetate fractions characterized as to molecular weight distribution by the equilibrium ultracentrifuge. Stress levels were low enough that linear viscoelastic behavior was observed. Although the effect of molecular weight was not marked, the presence of low molecular weight material in a sample decreased the amount of permanent set and increased the recoverable deformation. In all cases, more than half of the recoverable deformation occurred in less than 10 sec. The results suggest that there was present some sort of a network, although no direct x‐ray evidence for crystallinity could be seen.

Effect of Pressure on Sound Propagation in Water
View Description Hide DescriptionMeasurements of the ultrasonicabsorption of water have been made up to pressures of 2000 kg/cm^{2}. The data show that both the shear and compressional losses decrease as the pressure is raised. Comparison of these results with the values predicted by Hall's theory of sound absorption in water shows that the theory must be modified to be in agreement with the experimental data. The modification consists of assuming that the open or ice type of packing is associated with the higher free‐energy state. If this modification is made, the observed data is in excellent agreement with theory. This result leads to the conclusion that even at 0°C less than 30 percent of the molecules in water are arranged in the ice type of packing. The results also indicate that the free‐energy difference between the two states of packing in water is temperature dependent.

Application of the Superposition Principle and Theories of Mechanical Equation of State, Strain, and Time Hardening to Creep of Plastics under Changing Loads
View Description Hide DescriptionThe superposition principle and the theories of mechanical equation of state, strain, and time hardening were applied to the creep under changing loads of four unfilled thermoplastics—polyethylene; monochlorotrifluoroethylene (Kel‐F), crystalline; polyvinylchloride (Geon‐404), annealed; and polystyrene.
A comparison of the theoretical results predicted by these theories with the experimental results indicated the accuracy with which these theories described the creep behavior under changing loads for the above materials.

Diffusion Controlled Stress Relaxation
View Description Hide DescriptionThe action of water solutions of dimethyl formamide on Dinitrile A fibers was studied using the stress‐relaxation technique. After prior conditioning and stress relaxation in water, the addition of dimethyl formamide‐water solutions produced an exponential stress relaxation. It was found that the rate and extent of stress relaxation in dimethyl formamide‐water solutions is dependent on the dimethyl formamide concentration. The rate of stress relaxation in dimethyl formamide‐water solutions is also dependent on the cross‐sectional area and the state of orientation of the fiber. These data can best be explained by postulating that the rate of diffusion of the dimethyl formamide‐water solution into the fiber controls the rate of stress relaxation. The diffusion coefficient is found to be concentration dependent, and the diffusion process has an activation energy of 14 kcal.

Viscosity and Elasticity of Oil Surfaces and Oil‐Water Interfaces
View Description Hide DescriptionA study of the rheological properties of lubricating oils was made by means of semiquantitative measurements of the viscosity and elasticity of surface and interfacial films. A torsion‐pendulum type, surface viscometer was used. A refined, uncompounded mineral oil was shown to possess neither surface nor interfacialviscosity or elasticity. One additive in mineral oil showed surface viscosity and elasticity, and two additives developed these properties at an oil‐water interface. The aged, viscous surface and interfacial films studied were found to be non‐Newtonian.

Contribution to the Study of Transport Phenomena in Gases at High Densities
View Description Hide DescriptionThe results of recent measurements of the viscosity and thermal conductivity of argon have shown the importance of studying these transport phenomena over a large density range in different regions of the reduced temperature. It appears that the Chapman‐Enskog theory cannot give an adequate description of the new experiments. It has not yet been possible to give a full account of the observations. However, a less rigorous theoretical discussion demonstrates the relevant physical features of the problem. For the moment it serves to indicate a new experimental program. This research may contribute to a more clear understanding of the transport properties in different states of a material, including the difficult intermediate region between the gas and liquid state.

Preliminary Results in Measuring Dynamic Compressibilities
View Description Hide DescriptionIn order to supplement dynamic measurements in shear and bending, the vibration tester of the Franklin Institute Laboratories was used to measure the bulk compressibility of plastics using harmonic vibrations. Polyethylene and plasticized polyvinyl chloride were investigated. The values of the compressibility were comparable to the static values as far as they are known. A noticeable phase shift between pressure changes and volume changes could not be detected with certainty so that the bulk modulus B in dynes/cm^{2} is not a complex quantity. Especially for the polyethylene, a temperature range from −25 to +95°C and a frequency range from 0.0003 to 5 cps was used. The isothermals obtained could be shifted together using the method of reduced variables of Ferry. From the frequency shifts a_{T} , an activation energy of 60 kcal/mole was obtained.
 REGULAR ARTICLES


Elastic‐Plastic Instability Caused by the Size Effect and Its Influence on Rubbing Wear
View Description Hide DescriptionThe yield strength of many materials is much higher for minute specimens than for bulk samples. The region around the point of highest shear stress in a solid undergoing deformation by a small spherical indenter can be regarded as such a minute specimen which may be ``protected'' by the size effect against plastic yielding if it is small enough. Formulating the effective yield strength and the elastic stress under the indenter in terms of a common parameter provides a basis for assessing the influence of size scale on the plastic yield threshold. Four size categories are identified, including a critical case for which a small change of loading may cause a discontinuous transition from the elastic to the plastic regime throughout the region of contact, and another, more frequently encountered, in which the supportable pre‐yield elastic stress is materially enhanced. The latter effect may exert an important influence on the rate of rubbing wear since it can make available a wider range of loading for which a low wear rate prevails. Reported wear tests on steel riders and on sapphire phonograph styli confirm these predictions qualitatively.

Specification of Thermally and Mechanically Induced Nonequilibrium States in AuCu by the Resistivity and Magnetoresistivity
View Description Hide DescriptionStudies were made of the change in the resistivity and magnetoresistivity of samples of AuCu, which had been thermally disordered, while annealed at 150°C, of samples, completely disordered by cold work, while annealed at 150°C and 265°C, and of initially ordered samples when subjected to varying amounts of cold work. The curves of magnetoresistivity against resistivity for the last three cases agree with one another, but differ from that for the thermally disordered sample annealed at 150°C and from a previously obtained curve for the annealing of a thermally disordered sample at 265°C. These last two curves are also markedly different from each other. All five curves appear distinct from the previously obtained curve for AuCu in equilibrium. An interpretation of the results in terms of the production of a more or less pronounced admixture of AuCu II during certain stages of the cold working or annealing process is presented.

Elastic Constants of Germanium between 1.7° and 80°K
View Description Hide DescriptionThe elastic constants of germanium (c _{11}, c _{12}, and c _{44}) increase on cooling and approach constant values for very low temperatures.

Electron Microscopy of Monodisperse Latexes
View Description Hide DescriptionA series of monodisperse polystyrene latexes has been prepared by carefully controlled emulsionpolymerizations. The particle diameters of three of these latexes were determined by electron microscopy. The latex particles were dispersed on collodion membranes supported by copper grids. The microscopes had previously been calibrated with collodion replicas of a 30 000 line/inch diffraction grating. In general, the reproducibility of measurements from many photographic exposures was good; however, a few exposures yielded particle diameters considerably higher than the averages.
An investigation of this technique indicated that: (1) polystyrene latex particle diameters (collodion membranes—copper grid supports) increased considerably on electron irradiation, (2) collodion diffraction grating replicas (copper grid supports) shrank slightly on electron irradiation, and (3) the magnification of the electron microscope varied slightly from exposure to exposure. It was found that variations of particle diameter resulting from the foregoing sources of error were negligible when the particles were dispersed directly on a silicon monoxide diffraction grating replica supported by a stainless steel grid.
The particle diameters of the latexes determined in this manner ranged from 880 to 11 720 A. Many photographic exposures of each latex were used for these measurements. The monodispersity of the latex particles is evident from the small values of the standard deviations of the over‐all particle‐size distributions. The reproducibility of particle diameters determined from different exposures is evident from the small values of the standard deviations of the means of the exposure averages.

Study of the Kinetics of Ordering in the Alloy AuCu
View Description Hide DescriptionOrdering in the alloy AuCu was studied by measurements of the electrical resistivity as a function of time and temperature of ordering for samples disordered at various temperatures above the critical point. It has been established experimentally that the disordering temperature has a profound affect upon the rate of ordering. The higher the disordering temperature the faster is the rate of subsequent ordering. The dependence of the rate of ordering on the ordering temperature seems to indicate that the transformation is nucleated even at very low temperatures. The appearance of a twin‐like structure during the disorder‐to‐order transformation has also been studied as a function of the previously mentioned variables.

Thermionic Emission Microscopy of Metals. II. Transformations in Plain Carbon Steels
View Description Hide DescriptionThe direct observation of transformations in plain carbon steels at temperatures above about 625°C is demonstrated for both the A _{3} and A _{1} transformations.
It is concluded from emission studies of the decomposition of austenite below the A _{3} line that the transformation is of a diffusionless type rather than carbondiffusion controlled. It is shown that carbon is associated with ``memory'' in the austenite grain structure, the memory improving with increasing carbon content. The emission images also indicate that the growth of a ferrite grain in austenite induces a recrystallization of the surrounding austenite. A model to account for the memory is advanced based on thin sheets of retained austenite in newly transformed ferrite.
Studies of a 0.77 percent carbon steel below the A _{1} line illustrate the formation of pearlite. The images suggest that these decompositions take place in two distinct steps. The first is the formation of a metastable crystal which subsequently decomposes by carbondiffusion to the final ferrite‐carbide products. Austenite recrystallization about a growing pearlite nodule is demonstrated. A model for the transformation based on a diffusionless type reaction followed by a diffusion decomposition is suggested to explain the emission images.

A Rheological Equation of State which Predicts Non‐Newtonian Viscosity, Normal Stresses, and Dynamic Moduli
View Description Hide DescriptionAn equation of state is formulated from the classical Maxwell assumptions of superposition of the effects due to strain and rate of deformation in a strained fluid. Except for the form of the time derivative, these assumptions result in the usual expression for a Maxwell element. The time derivative of the stress, however, is computed with respect to a set of axes in the fluid which are rotating (with respect to fixed axes) at a rate measured by the vorticity of the assumed velocity distribution. The usual transformation between rotating and fixed reference axes introduces cross terms between the stress and vorticity components.
The resulting equation of state predicts non‐Newtonian behavior and the simultaneous appearance of normal stresses. It reduces to the Newtonian case for low rates of shear (or for small relaxation times) and, if the cross terms are sufficiently small (but not otherwise), to the usual Maxwell element expression in the dynamic case. A common origin is thus assigned to these several phenomena. Reduced variable and distribution function procedures, at least in principle, should be as applicable to the viscosity and pressure phenomena as to dynamic data.

Analysis of Electrode Phenomena in the High‐Current Arc
View Description Hide DescriptionAn analysis is made of the phenomena at the electrodes of a high‐current short‐time arc. It is shown that the input power density to the anode spot is in the range 5×10^{4} to 1×10^{6} watts/cm^{2}. To a first‐order approximation, all this power can be carried off by evaporation. Power conducted into the metal and lost by radiation is negligible in the probable operating range. For most materials, the anode spot is probably considerably above the boiling temperature. The process of evaporation holds the spot temperature constant at a value such that the input power and evaporation power are equal. Experimental data indicate that for any given metal the anode spot temperature is that for which the evaporation power density is at least 3×10^{5} watts/cm^{2}. As an example, for copper the theoretical limits of temperature are 2490 to 3040°K, while experimental data indicate a temperature of 2920°K. Other metals considered are: Ag, Al, C, Fe, Mo, Sn, Ti, W, Zn, Zr. It is also shown that for the maximum power input that can be expected at the cathode, the thermionic emissioncurrent density is very small compared to the observed values of current density.

Condition of High‐Velocity Ductile Fracture
View Description Hide DescriptionThe Griffith energy criterion, dW = −dU (dW = crack propagation work, −dU = released elastic energy), cannot be applied to essentially ductile fractures. In particular, it does not represent the condition of rapid ductile fracture propelled by the elastic energy of the specimen. The condition of such fractures is where x is the plastic extension accompanying the propagation of the crack.
