Effect of magnesium content on the stress exponent and effective stress in the steady state creep of Al-Mg alloys

The stress exponent of steady state creep,n, and the internal ( _i) and effective stresses ( _e) have been determined using the strain transient dip test for a series of polycrystalline Al-Mg alloys creep tested at 300° C and compared with previously published data. The internal or dislocation back stress, _i, varied with applied stress,, but was insensitive to magnesium content of the alloy, being represented by the empirical equation _i=1.084 ^1.802. Such an applied stress dependence of _i can be explained by using an equation for _i of the form _i (dislocation density)^1/2 and published values for the stress dependence of dislocation density. Values of the friction stress, _f, derived using the equation _e/=(1–c) (1– _f/), indicate that _f is not dependent on the magnesium content. A constant value of _f can best be rationalized by postulating that the creep dislocation structure is relatively insensitive to the magnesium content of the alloy.On leave from Engineering Materials Department, University of Windsor, Windsor, Ontario N9B 3P4, Canada.     

The athermal α → ω transformation in Zr-2 at% Nb alloy

The athermal transformation in Zr-2 at.% Nb alloy has been investigated by transmission electron microscopy. Analysis of the selected-area diffraction pattern has shown that the orientation relationships between the omega and the parent-phase in quenched Zr-2 at.% Nb alloy are the same as have been previously observed for the reaction in pure zirconium. Thus it was deduced that the direct transition has taken place in the alloy during cooling. The-originated -particles were visualized using the dark-field technique. The formation of the athermal omega in the-region of-stabilized Zr-Nb alloy is discussed in terms of the relative positions of the free energy equilibrium curvesT ₀ ,T ₀ ,T ₀ and the correspondingM _s ,M _s andT _s start curves. It is concluded that the omega phase can occur over a much wider range of alloy compositions than is usually recognized on the basis of transformation data.     

Natural convection in a rectangular enclosure in the presence of a magnetic field with uniform heat flux from the side walls

Summary A numerical study is presented for magnetohydrodynamic free convection of an electrically conducting fluid in a two-dimensional rectangular enclosure in which two side walls are maintained at uniform heat flux condition. The horizontal top and bottom walls are thermally insulated. A finite difference scheme comprising of modified ADI (Alternating Direction Implicit) method and SOR (Successive-Over-Relaxation) method is used to solve the governing equations. Computations are carried out over a wide range of Grashof number, Gr and Hartmann number, Ha for an enclosure of aspect ratio 1 and 2. The influences of these parameters on the flow pattern and the associated heat transfer characteristics are discussed. Numerical results show that with the application of an external magnetic field, the temperature and velocity fields are significantly modified. When the Grashof number is low and Hartmann number is high, the central streamlines are elongated and the isotherms are almost parallel representing a conduction state. For sufficiently large magnetic field strength the convection is suppressed for all values of Gr. The average Nusselt number decreases with an increase of Hartmann number and hence a magnetic field can be used as an effective mechanism to control the convection in an enclosure.List of symbols Ar aspect ratio,H/L - B ₀ induction magnetic field - H ₀ magnetic field,H ₀=B ₀/ _m - g gravitational acceleration - Gr Grashof number,gq(L/k)L ³/v ² - H height of the enclosure - Ha Hartmann number, - k thermal conductivity - Nu local Nusselt number - average Nusselt number - p pressure - Pr Prandtl number, / - q heat flux - t time - T dimensionless temperature, (–₀)/q(L/k) - u vertical velocity - U dimensionless vertical velocity,uL/ - v horizontal velocity - V dimensionless horizontal velocity,vL/ - x vertical coordinate - X dimensionless vertical coordinate,x/L - y horizontal coordinate - Y dimensionless horizontal coordinate,y/L - thermal diffusivity - thermal expansion coefficient - temperature - ₀ reference temperature - density - kinematic viscosity - viscosity - _m magnetic permeability - electrical conductivity - stream function - dimensionless stream function, / - dimensionless time,t/L ² - vorticity - dimensionless vorticity, L ²/ - X grid spacing inX-direction - Y grid spacing inY-direction - time increment - ² Laplacian operator     

Theory of helium under heat flow near the λ point. I. Interface of He I and He II

A He I-He II interface is shown to exist under heat flow and is studied near the point. The temperature in the superfluid region is found to be of the form T –T Q^3/4 if dynamic scaling is assumed, where T is the critical temperature andQ is the heat flow. In the normal region the temperature has a finite gradient. Here we are neglecting a small thermal resistance due to vortices in the superfluid region. In a finite system with size much greater than the correlation length a first-order phase transition occurs as an inverted bifurcation as the temperature at the cooler boundary is lowered slightly below T. Namely, the system will jump from the disordered state to a state in which the two phases are separated by an interface. The theory can be constructed analogously to the theory of superconductors in a magnetic field.     

Thermal transport properties of helium near the superfluid transition. II. Dilute3He-4He mixtures in the superfluid phase

Measurements of the average thermal conductivity _exp hQ/T and of the thermal relaxation time to reach steady-state equilibrium conditions are reported in the superfluid phase for dilute mixtures of³He in⁴He. Hereh is the cell height,Q is the heat flux, andT is the temperature difference across the fluid layer. The measurements were made over the impurity range 2×10^–9<X(³He)<3×10^–2 and with heat fluxes 0.3<Q<160 µW/cm². Assuming the boundary resistanceR _b , measured forX<10^–5, to be independent ofX over the whole range ofX, a calculation is given for _exp. ForQ smaller than a well-defined critical heat fluxQ _c (X) X ^0.9, _exp is independent of Q and can be identified with the local conductivity _eff, which is found to be independent of the reduced temperature = (T–T)/T for –10^–2. Its extrapolated value at T is found to depart forX10^–3 from the prediction X ^–1 , tending instead to a weaker divergence X ^–a witha0.08. A finite conductivity asX tends to zero is not excluded by the data, however. ForQ >Q _c (X), a nonlinear regime is entered. ForX10^–6, the measurements with the available temperature resolution are limited to the nonlinear conditions, but can be extrapolated into the linear regime forX2×10^–7. The results for _exp(Q),Q _c (X), and _eff(XX) are found to be internally consistent, as shown by comparison with a theory by Behringer based on Khalatnikov's transport equations. Furthermore, the observed relaxation times (X) in the linear regime are found to be consistent forX>10^–5 with the hydrodynamic calculations using the measured _eff(X). ForX<10^–5, a faster relaxation mechanism than predicted seems to dominate. The transport properties in the nonlinear regimes are presented and unexplained observations are discussed.     

AC electrical conductivity of electron beam evaporated Cu-GeO2 thin cermet films

AC electrical properties of 410 nm think 30 at.wt% Cu-70 at.wt% GeO₂ thin films are reported for the frequency range 10⁴ to 10⁶ Hz and temperature range 150 to 425 K. The loss tangent (tan ) and the dielectric loss (/₀) are found to show striking minima around a cut-off frequency 10⁵ Hz. In the lower frequency range (10⁵ Hz), ₁() ^s T ⁿ is obeyed with s (0 to 0.51) increasing as a function of temperature and n (0.10 to 0.14) showing a very weak temperature dependence. In the higher frequency region (10⁵ Hz), ₁() and /₀ increase sharply leading to the quadratic behavior of ₁() with s equal to 2. These processes are discussed by analyzing an equivalent circuit which shows that at lower frequencies, the effects of series resistance in leads and contacts can be neglected, while at higher frequencies such effect give rise to spurious ² dependance for the conductance. A weakly activated AC conductivity and a frequency exponent s that increases with increasing temperature suggest that the low frequency behavior originates from carrier migration by tunneling process.     

Retention of a metastable bcc ε-Pu solid solution: ε-Pu(Ti)

A metastable -Pu (bcc) solid solution has been retained to room temperature by rapid quenching of Pu-rich Pu-Ti alloys from the liquid state. Until now, -Pu solid solutions were limited to high temperatures and had not been successfully quenched to room temperature without transformation. The apparatus used to quench the specimens was a modified gun-type splat-cooling unit, capable of producing extremely high cooling rates of from 10⁶ to 10⁸ ° C sec^–1. -Pu(Ti) was retained in the composition region from 20 to more than 45 at.% Ti, and extrapolation of the lattice parameter/composition curve yielded a value of a ₀ = 3.53₀ Å for -Pu at 20° C. This modification differs from the -Pu modification derived by extrapolating from high temperature to 20° C by a small valence increase of 0.1. Metastable -Pu (Ti) (fcc) solid solutions were also quenched-in with alloys containing lesser amounts of Ti, and evidence was found to indicate that the was probably a product of -Pu(Ti) solid-state decomposition.     

A note on the similarity solutions for free convection on a vertical plate

Summary The similarity solutions for free convection on a vertical plate when the (non-dimensional) plate temperature is x and when the (non-dimensional) surface heat flux is –x are considered. Solutions valid for 1 and 1 are obtained. Further, for the first problem it is shown that there is a value ₀, dependent on the Prandtl number, such that solutions of the similarity equations are possible only for >₀, and for the second problem that solutions are possible only for >–1 (for all Prandtl numbers). In both cases the solutions becomes singular as ₀ and as –1, and the natures of these singularities are discussed.     

Application of a new iterative method for elastic-plastic stress analysis

A new iterative method for elastic-plastic stress analysis based on a new approximation of the constitutive equations is proposed and compared with standard methods on the accuracy and the computational time in a test problem. The proposed method appears to be better than the conventional methods on the accuracy and comparable with others on the computational time. Also the present method is applied to a crack problem and the results are compared with experimental ones. The agreement of both results are satisfactory.List of symbols u = (u ₁, u ₂) displacements u ^(H) = u ⁽ⁿ⁺¹⁾ - u ⁽ⁿ⁾ u _k ⁽ⁿ⁾ = u _(k ^{(n + 1)} - u ⁽ⁿ⁾ (n, k = 0, 1, 2, ...) - = ₁₁, ₂₂, ₁₂) stresses - = (₁₁, ₂₂, ₁₂) strains - = (₁₁, ₂₂, ₁₂) center of yield surface - D elastic coeffficient matrix, C = D ^–1 - von Mises yield function. The initial yielding is given by f() = _Y - f {f/} - ^* transposed f - H hardening parameter (assumed to be a positive constant for kinematic hardening problems) - time derivative of - [K] total elastic stiffness matrix - T traction vector - = [B] relation between nodal displacements and strains     

Interaction between a dislocation and an impurity in KCl: Mg2+ single crystals

The interaction between a dislocation and the impurity in KCl: Mg²⁺ (0.035 mol% in the melt) was investigated at 77–178 K with respect to the two models: one is the Fleischer's model and the other the Fleischer's model taking account of the Friedel relation. The latter is termed the F-F. The dependence of strain-rate sensitivity due to the impurities on temperature for the specimen was appropriate to the Fleischer's model than the F-F. Furthermore, the activation enthalpy, H, for the Fleischer's model appeared to be nearly proportional to the temperature in comparison with the F-F. The Friedel relation between effective stress and average length of the dislocation segments is exact for most weak obstacles to dislocation motion. However, above-mentioned results mean that the Friedel relation is not suitable for the interaction between a dislocation and the impurity in the specimen. Then, the value of H(T _c) at the Fleischer's model was found to be 0.61 eV. H(T _c) corresponds to the activation enthalpy for overcoming of the strain field around the impurity by a dislocation at 0 K. In addition, the Gibbs free energy, G ₀, concerning the dislocation motion was determined to be between 0.42 and 0.48 eV on the basis of the following equation ln / = G ₀/(kT_p0)1 – (T/T _c)^{1/2 –1}(T/T _c)^1/2 + ln ₀/where k is the Boltzmann's constant, T the temperature, T _c the critical temperature at which the effective stress due to the impurities is zero, _p0 the effective shear stress without thermal activation, and ₀ the frequency factor.     

Correlation of burst pressure of GRP cylinders with the stress wave factor

Glass fibre-reinforced plastic (GRP) cylinders are increasingly used for highly stressed structural elements. The higher the demands on the materials, the higher are the fault detection requirements to be met by non-destructive materials testing methods. Acousto-ultrasonics is a valuable aid for the non-destructive evaluation of GRP composite materials, because it may be the answer to evaluating effects of subtle defects in composites. The aim of the research is to evaluate the burst pressure of GRP cylinders by acousto-ultrasonics techniques. The theoretical results have been found to be in good agreement with the experimental values. Hence the results strongly suggest that stress wave factor measurements can be exploited successfully to predict burst pressure of GRP cylinders.Nomenclature P Internal pressure, kgf cm^–2 - d Internal diameter, cm - t Thickness of cylinder, cm - (N ,N ,N ) Resultant forces, kgf - (M ,M ,M ) Moments, kg cm - [A] Extensional stiffness matrix - [B] Bending stretching coupling matrix - [D] Flexural stiffness matrix - ( ⁰ , ⁰ , ⁰ ) Midplane strains - (k ,k ,k ) Curvatures - n Number of laminae - Z Distance from midplane, cm - _u Ultimate tensile strength of GRP composite, kg cm^–2 - S _W Stress wave factor - m Material parameter - Filament winding angle     

Experimental evaluation of relative mode parameters in the irregular earth-to-ionosphere waveguide

Conclusions A model for representing the propagation of superlong waves was selected. Certain relative mode parameters ()₁, ()₂, ()₃, (V)₁, (V)₂, (V)₃, C₁, C₂, and C₃ can be used in order to account for the time-measurement error produced as a resuit of the double-mode signal propagation, to determine in a semiempirical manner the ionosphere's effective reflection height at night and in the daytime, to calculate and apply signal-propagation corrections which take into account phase velocity changes due to variations in the ionosphere height from day to day, and to calculate the fields of transition paths.Translated from Izmeritel'naya Tekhnika, No. 8, pp. 75–78, August, 1974.     

Nonlinear axisymmetric response of orthotropic thin truncated conical and spherical caps

Summary An approximate analytical solution of the large deflection axisymmetric response of polar orthotropic thin truncated conical and spherical shallow caps is presented. Donnell type equations are employed. The deflection is approximated by a one term mode shape satisfying the boundary conditions. The Galerkin's method is used to get the governing equation for the deflection at the hole. Nonlinear free vibration response and the response under uniformly distributed static and step function loads are obtained. The effect of various parameters is investigated.Notations A, A ^* Inward and outward amplitudes - a, b, h Base radius, inner radius and thickness of the cap - D M h ³/[12(–v ² )] - E ,E Young's moduli - H ^*,H Apex height, dimensionless apex heght:H ^*/h - N _, Stress resultants - p ^1/2 - q Uniformly distributed load - Q,Q₀ Dimensionless load: , dimensionless step load - Q, Q ₀ Dimensionless load: , step load - t, Time, dimensionless time: t - T _A Ratio of nonlinear periodT for inward amplitudeA and the linear periodT _L - w ^* Normal displacement at middle surface - w Dimensionless displacement:w ^*/h - ₁ Linear parameter of static response - Orthotropic Parameter:E /E - Mass density - ₂,₃ Quadratic and cubic nonlinearity parameters - b/a - v ,v Poisson's ratios - Dimensionless radius:r/a - ^*, Stress function, dimensionless stress function: - ₀ ^* ,₀ Linnear frequency, dimensionless frequency: With 7 Figures     

Mixing displacement of viscoplastic fluids feom a channel with a rectangular cavity

Different mixing displacement regimes for viscoplastic fluids are investigated theoretically and experimentally.Notation x and y Cartesian coordinates - h half-width of the gap - H, L dimensionless depth and length of the cavity - v_x, v_y velocity components - density - _ik components of the viscous stress tensor - e_ik components of the deformation rate tensor - dynamic viscosity - dynamic viscosity for infinitely high displacement velocity - ₀ analog of the limiting shear stress in Bingham's fluid - W parameter in Williamson's model - =/gh dimensionless viscosity - stream function - vorticity - ₀, ₀ distributions of and at the inlet - r,a, b, and c auxiliary constants - C concentration of the displacing fluid - D diffusion coefficient - Pe Peclet's number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 432–439, March, 1981.     

Microdeformation in partially compatible blends of poly(styrene-acrylonitrile) and polycarbonate

Dilute 3-component 1-phase solutions in methylene chloride of poly(styrene-acrylonitrile) PSAN and polycarbonate PC are used to cast phase separated thin films. Films of pure PSAN, pure PC and five intermediate compositions are examined. The films are bonded to copper grids and strained at a constant rate of 4.1 × 10^–6sec^–1. The median tensile strain _v for void formation is determined using an optical microscope and the regions surrounding the voids are examined by TEM. At room temperature and slow strain rates both PSAN and PC plastically deform by shear yielding. For pure PSAN _v was found to be 0.13 whereas for PC _v exceeds 0.23. The addition of the more ductile polymer PC to PSAN at weight fractionsx forx 0.4 decreases _v. In this case voids form in crazes at the boundaries between the PC-rich inclusion and the PSAN-rich matrix. When the PC content is increased tox = 0.8, _v approaches 0.23. The effect of physical ageing (annealing belowT _g the glass transition temperature) on the mode of plastic deformation was also examined over the same compositional range. Physical ageing was found to suppress shear deformation and favour crazing in PSAN and PSAN-rich phases. Because crazes are more susceptible to breakdown than DZ's (shear deformation zones), physical ageing results in a marked decrease in _v. The breakdown statistics of these phase separated partially compatible blends was found to follow a Weibull distribution in strain from which two parameters may be extracted: the Weibull modulus and _w the Weibull scale parameter. is a measure of the breadth of distribution of void initiation and _w is a measure of the median strain to void formation in the films. The behaviour of _w was found to approximately mirror _v. The Weibull modulus appears to be primarily controlled by the matrix phase.     

Analysis of the complex impedance data for β-PbF2

Previously published complex impedance plots for the ionic conductor -PbF₂ show the familiar depressed circular arcs with an angle 0.7 /2 and an activation energy for the volume conductivity W _v=0.45 eV. A detailed analysis of this behaviour in terms of the recently developed non-Debye model shows the real part of the relative dielectric permittivity to have a frequency dependence ^0.7–1, with a high frequency limit of 50 Hz and with only weak dependence on temperature. The low-frequency spurs on the impedance plots are shown to indicate an interfacial barrier at each electrode having a similar non-Debye frequency characteristic to the bulk but showing a strong temperature dependence with an activation energy equal to W _v/2. This suggests the presence of low Debye-screened barriers of about k T height, resulting from depletion and accumulation of ionic carriers at incompletely transmitting electrodes. There is no visible effect of inter-grain boundaries on the flow of direct current.     

High frequency dielectric properties of MgO,Fe/MgO and Cr/MgO

The study of the dielectric constant and loss in pure single-crystal MgO and in Fe- and Cr-doped crystals, the low frequency results of which have been reported [1], has now been extended to cover frequencies from 500 Hz to 9 GHz. Measurements were made on the same specimens, at room temperature, using bridge, cavity, slotted-line and cavity-resonator techniques. Over the whole frequency range, a good fit is obtained to the Universal Laws of dielectric response: _ac ⁿ and (–) ^n–1 with n=0.98±0.02 for both pure and doped MgO. At any point in this frequency range the addition of iron or chromium increases and decreases , the changes being more pronounced with iron. These effects are discussed in terms of hopping mechanisms.     

Similarity solutions in axisymmetric mixed-convection boundary-layer flow

The similarity equations for mixed-convection axisymmetric boundary-layer flow are considered. The equations involve a buoyancy parameter and a curvature parameter . The equations are solved numerically and it is found that for large , and of O(1), an asymptotic solution is approached, the nature of which is discussed. When is also large, of O(^1/4), the problem, at leading order, becomes independent of the mainstream and the free-convection limit is obtained. This problem is also discussed, including the behaviour for large values of ₀, the free-convection curvature parameter. For < 0 we find that the solution can be continued past the point where the wall heat transfer becomes zero (where previous mixed-convection similarity solutions in plane geometry were terminated) with the solution ending as 0^–. The nature of this limit is also discussed. For < 0 it is also found that there are solutions only in _b = < 0 with two branches of solution bifurcating out of = _b , and values of _b are computed for a range of . The behaviour of the solution for large values of the curvature parameter , and of O(1), is discussed where it is shown that the solution proceeds in inverse powers of log .     

Dynamic scaling and ultrasonic attenuation in 4He near the superfluid transition point

Attenuation of first sound has been measured in ⁴He under saturated vapor pressure near the lambda temperature T at frequencies /2 ranging from 10.2 to 271 MHz. The frequency dependence of the critical part of the attenuation is determined and the dynamic scaling hypothesis is examined. Above the lambda point, it is found that the critical attenuation is described by a scaling function (, ) = ^1+y F(), where = ₀^–x and = T/T – 1, with the results x = 1.02±0.05 and y = 0.33±0.03. The characteristic frequency of the order-parameter fluctuation with the wave number k equal to the inverse correlation length is then proportional to ^x , which is in an excellent agreement with the prediction of dynamic scaling. Below the lambda point, a characteristic relaxation time or times shorter than previously expected at lower frequencies appears to exist in the present frequency range.Based on a Ph.D dissertation submitted by K. Tozaki to the University of Tokyo (1977).