Elasticity Of Metals Research Articles

Residual stresses due to gas arc welding of aluminum alloy joints by numerical simulations

This study deals with the numerical simulation of the gas arc welding process of Aluminum tee joints using finite element analysis and evaluation of the effect of welding parameters on residual stress build up. The 3D simulations are performed using ABAQUS code for thermo-mechanical analyses with moving heat source, material deposition, solid-liquid phase transition, temperature dependent material properties, metal elasticity and plasticity, and transient heat transfer. Quasi Newton method is used for the analysis routine and thermo-mechanical coupling is assumed; i.e. the thermal analysis is completed before performing a separate mechanical analysis based on the thermal history. The residual stress build up and temperature history state in a three-dimensional analysis of the tee joint is then compared to experimental results. Hole drilling method is used for measuring the residual stress, while temperature history is measured by thermocouples. After carrying out numerical simulations, the effects of voltage/current, welding speed, material thickness and size of electrode on residual stress build-up and resulting distortions are evaluated.

Correlation between Diffusion Parameters and the Temperature-Dependent Modulus of Elasticity of Metals

It is shown using the Debye model and an equation of state for solids that the diffusion parameters of anomalous and conventional metals correlate with the temperature variation of their shear moduli.

Self-consistent fluctuation-phonon (SCFP) approach to the theory of magnetism

The thermodynamics of itinerant electron ferromagnets based on the self-consistent fluctuation-phonon (SCFP) approach are discussed. Temperature dependences of the magnetic properties of typical ferromagnetic metals are elucidated. We demonstrate how the dynamic theory of metal elasticity permits to obtain the bulk modulus at constant magnetization. The new longitudinal complex permeability of electrons at constant magnetization is introduced.

Dinamicheskie uravneniya teorii uprugosti v metallakh

Dinamicheskie uravneniya teorii uprugosti v metallakh

Radiation effects on elasticity of metals

For a metal containing a periodically arranged (three-dimensional) system of voids, explicit analytical expressions are developed for the bulk and the shear moduli (and, consequently, Young's modulus and the Poisson ratio), on the assumption that the metal is initially (nonirradiated) homogeneous and isotropic. These expressions include the effect of the interaction between adjecent voids and the void size, but do not take into account the effects of the void shape. The results are compared with previous estimates by other investigators who did not include the influence of the interaction between adjacent voids. The interaction effect becomes more pronounced with the increasing volume fraction of the voids. Hence, the present results provide more realistic estimates of the material elasticity. These and related results are illustrated by means of numerical examples. Then the mechanism of void and gas bubble formation in irradiated metals is briefly discussed and some relevant theoretical and experimental results are summarized. In particular, curves are developed which relate the reduction in elastic moduli to the neutron fluence, temperature, and other relevant parameters. Finally, on the basis of an approximate model we give a rough estimate for the reduction in the yield stress due to irradiation.

Note on the elasticity of metals as affected by temperature

When two solids or structures, identical in form and differing only in the material of which they are composed, are subjected to stress, their strengths depend on the limits of the strains which those particular materials will bear without permanent set or rupture, but their stiffnesses are directly proportional to the elastic constants. It is with the strength of structures that engineers are mostly concerned, and a great deal of work has been done on the strength of materials for various classes of strains, of which some, though not much, relates to the variation of strength with temperature.

Societies and Academies

LONDON. Royal Society, February 6.—Sir J. J. Thomson, president, in the chair.—A. Mallock: Note on the elasticity of metals as affected by temperature. The present note is an account of some preliminary experiments on the variations with temperature of Young's modulus for fifteen selected metals. The choice was influenced largely by the ease with which specimens could be procured. No alloys are included. The metals chosen were rhodium, platinum, iron, palladium, nickel, copper, gold, silver, magnesium, aluminium, zinc, lead, cadmium, bismuth, and tin. The procedure was to determine the frequency of the vibrations of a stiff rod carried at its lower end by a small thin plate of the material to be tested, the other end of the plate being clamped to a fixed support. The plate and its support could be immersed in fluid of any desired temperature without wetting the rod or in any way interfering with the mounting. The temperatures employed were those of liquid air, 0° Centigrade, ordinary temperature (10°–15°), and as near 100° C. as was practicable. The measured frequencies of vibration at these temperatures furnished the necesary data for determining the changes in Young's modulus. The results showed that the more infusible the metal, the less the modulus was affected for a given change of temperature, and this suggested that there might be a real connection between the variation of the modulus (M) and the melting point θM in Absolute temperature. A diagram is given comparing the experimental results with what they would have been had the relation dM/dθ = θM been true. If this relation holds, and 11, θ2 are two temperatures for which the moduli are M1, M2, then would M1/M2=θM-θ1/θM-θ2, and if θ1 is Absolute zero and θ2=0° C., then in this M1/M3 = melting point Absolute/melting point Centigrade for any two temperatures differing by 270° C. The experimental results show a distinct resemblance to those obtained on this supposition.—W. L. Cowley and H. Levy: Vibration and strength of struts and continuous beams under end thrusts. In a previous communication, “The Critical Loading of Struts and Structures,” the authors investigated the stability of a strut under end thrust and simply supported at a number of intermediate points. The method of analysis has been extended in the present paper to include the more general problem of the vibration of such a system when the lateral load is periodic and the supports are assumed in a state of vibration. The flexural rigidity and the end thrust, constant along each bay, are taken for further generality to vary from bay to bay. These conditions correspond closely with those originated in a wing spar of an aeroplane when in flight and influenced by engine-throbbing. A very general form of the equation of three moments is derived, and the conditions for resonance and crippling are expressed in a convenient determinantal form. The general case where the end thrust, the flexural rigidity, and the mass per unit length vary between the supports according to any assumed law is discussed, and the method of solution illustrated in the particular case of the crippling of a strut of variable flexural rigidity. The result is expressed in a form extremely convenient for graphical treatment.—A. Dey: A new method for the absolute determination of frequency. (With a prefatory note by C. V. Raman.)

Scientific Serials

Annalen der Physik, May.—Researches on the normal cell, especially the Weston element, by W. Jaeger and St. Lindeck. This paper contains the results of an exhaustive experimental study of the Clark and Weston cells. The researches of E. Cohen had thrown some doubts upon the suitability of the Weston cell as a standard, especially in the neighbourhood of 0° C. In the present paper it is shown that these irregularities only occur about 0° C. and with the cell containing 14.3 per cent. amalgam, no trace of any irregular deviations appearing when the cell is used at 10° C. or higher temperatures. Further, if the amalgam is made slightly weaker in cadmium, 12 per cent. or 13 per cent., these irregularities near 0° disappear, and the measurements are trustworthy at all temperatures. It is concluded that the strictures of Cohen with regard to this cell are not justified, and that the Weston element is eminently suitable as a standard of electromotive force.—The calculation of isotherms, by C. Dieterici. The fundamental equation of condition of van der Waals is modified, in part empirically, without assuming that the cohesion pressure and the volume correction are determined, and the results applied to the measurements of Young on isopentane and benzene, of Ramsay and Young on ether andwater, and of Cailletet and Matthias on sulphur dioxide and carbonic acid.—Contribution to the theory of electric discharges in gases, by J. Stark.—On the variation of the dielectric constant with pressure and temperature, by J. Koenigsberger.—The constancy of the sparking potential, by K. R. Johnson.—On Jaumann's clear J-surface, by A. Korn. A discussion of a phenomenon first observed by Jaumann in a vacuum tube.—The internal friction of argon and its variation with temperature, by H. Schultze. The absolute value found for the viscosity coefficient of argon is practically identical with that previously determined by Lord Rayleigh, but the alteration of viscosity with temperature is found to be somewhat greater according to the author's experiments. The formula suggested by Sutherland gives a good approximation to the results of the experiments.—On the internal friction of gases and its change with the temperature, by P. Breitenbach. An application of Sutherland's formula to the experiments previously published by the author on the temperature coefficient of the viscosity of air, ethylene, carbonic acid, hydrogen and methyl chloride. The agreement between the calculated and experimental results is so good as to amount to a proof of Sutherland's theory.—The equilibrium figures of powders, by F. Auerbach.—On the influence of temperature on the elasticity of metals, by C. Schaefer. Experiments were carried out on nine metals, and the value of the torsion modulus measured at - 186°C., - 70° C. and about 20° C. If the temperature coefficients of the different metals are plotted as ordinates, and the melting points as abscissae, a smooth curve passes through the whole of the results.—Remarks on a paper of T. Middel on the cause of the thermal change of delicacy in balances, by W. Felgentraeger.—Liquid crystals, by O. Lehmann. A reply to some remarks of G. Tammann.—On the distribution of electricity on an ellipsoid, by G. Jaeger.

XXI. Preliminary experiments on the effects of long-continued stress on the elasticity of metals

The following paper is intended to describe the results of experiments on elasticity of wires which have been carried on during the past two years, in the Natural Philosophy Laboratory in the University of Glasgow. In 1875, at the Glasgow meeting of the British Association, a Committee was appointed, at the suggestion of Sir William Thomson, for the purpose of commencing secular experiments on the elasticity of wires, and a grant of money was placed at the disposal of the Committee.

IV. On the elasticity and viscosity of metals

Among the experimental exercises performed by students in the physical laboratory of the University of Glasgow, observations on the elasticity of metals have been continued during many years. Numerous questions of great interest, requiring more thorough and accurate investigation, have been suggested by these observations; and recently they have brought to light some very unexpected properties of metallic wires. The results stated in the present communication are, however, with one or two exceptions, due to the careful experimenting of Mr. Donald Macfarlane, official assistant to the Professor of Natural Philosophy, whose interested and skilful cooperation have been most valuable in almost everything I have been able to attempt in the way of experimental investigation. The subject has naturally fallen into two divisions, Viscosity, and Moduli of Elasticity.