Rheological behaviour and modelling of semi-solid Sn-15% Pb alloy

The rheological behaviour and modelling of a semi-solid, Sn-15% Pb alloy characterized by a special coaxial-cylinder rheometer over a wide range of process conditions is reported. In particular, the effect of shear rate , volume fraction of solid (f _s), and cooling rate on the apparent viscosity () of the semi-solid Sn-15% Pb alloy under isothermal and various cooling conditions was studied. Based on the experimental data, the shear rate used in preparing the semi-solid alloy as well as the volume fraction of solid have the most dominant effects on the rheological properties of the semi-solid Sn-15% Pb alloy. A viscosity model expressed as is proposed in which f _s ^* is the critical solid fraction at which the apparent viscosity goes to infinity, (F _s) corresponds to the asymptotic viscosity at infinity shear rate, and characterizes the transition shear rate between the power-law and Newtonian regions. finally, measurements with a differential scanning calorimeter were made and used to correlate the temperature and volume fraction of solid which, in turn, was corroborated with available data from the literature.     

Superconducting critical currents in Nb-Cu-Nb sandwiches

A preparation method is presented for Nb-Cu-Nb sandwiches for proximity-effect measurements with a large junction area of about 150×150 µm and intermediate Cu layers of thicknesses between 0.2 and 1.5 µm. The thickness of the Nb layers is about 150 µm. These samples are used to study the dependence of the superconducting critical currentI _c through the Cu layer as a function of a magnetic field applied parallel and perpendicular to the layers. Furthermore, the effects of flux lines trapped in the Nb layers on the critical currentsI _c andI _c are investigated. The results are used to discuss the influence of proximity effects in microcomposite superconductors.     

The HREM study of precipitates in an Al−Zn−Mg alloy

A study of precipitate phases in an Al–Zn–Mg alloy in the T74 condition has been conducted by means of high resolution electron microscopy. It has been observed that G.P. zones, and phases exist simultaneously in the matrix. The G.P. zones are plate-like forming on (111) matrix plane. The phase has a hexagonal structure witha=0.496 nm,c=1.403 nm and the orientation relationship with the matrix is . A new orientation relationship between the phase and the matrix is found to be .     

Computer-aided design of small patch antenna using (Al, Mg)TaO2 ceramics

The microwave dielectric properties of (AMT) ceramics and the design of small coplanar waveguide fed antenna (CPWFA) have been investigated. ( and ( have orthorhombic and tetragonal structure, respectively. As ( concentration increased, AMT ceramics transformed into the tetragonal structure. Specimens having tetragonal single phase could be obtained above x=0.6. As ( concentration increased, the grain size, dielectric constant and quality factor (Q) significantly increased and the temperature coefficient of resonant frequency changed from negative to positive. The of was realized at x=0.65 and the Q · f _O value and for this composition were 112 470 GHz and 26.1, respectively. Newly developed dielectric materials were used for 1.5 GHz band CPWFA design and fabrication. The size of the CPWFA can be reduced by using high dielectric constant AMT ceramics, insetting slits into the patch, and fabricating CPW feed line in the ground plane. The slits play a role in not only lowering a center frequency but also fine tuning for the proposed antenna together with the open stub of CPW feed line. The CPWFA with slits has a lower center frequency than the conventional CPWFA, which suggests that the antenna size can be reduced by as much as 16.3%. The structure simulations of the CPWFAs have been performed to obtain impedance matching and to investigate the effects of slits. Experimental results of the fabricated device were in good agreement with the simulation.     

On the meaning of the impingement parameter in kinetic equations for nucleation and growth reactions

If certain preconditions are met, the Johnson-Mehl-Avrami-Kolmogorov (JMAK) kinetic equation is exactly accurate for nucleation and growth reactions with linear growth and is, at least, a good approximation for nucleation and growth reactions with parabolic growth. These preconditions include randomly distributed product phases, isotropic growth and constant equilibrium state. Mechanisms causing deviations from these preconditions include: capillarity effect, vacancy annihilation, blocking due to anisotropic growth. It is shown that deviations lead to a modification of the overall transformation, which can be approximated well by a single equation:

On a stability theory of non-selfadjoint mechanical systems

Summary The concept of the Hamiltonian functional is generalized in such a way that a bilinear functional results, which plays the role of the Hamiltonian for non-selfadjoint systems. For this generalized Hamiltonian the condition leads to the so called hybrid Galerkin's equations, and the condition , to the load-frequency reationship. This relationship can be interpreted as a surface in the load-frequency space, the projection of which on the load-planes yields the stability boundaries, i.e. the buckling loads.

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Zu einer Stabilitätstheorie nicht-selbstadjungierter mechanischer Systeme

Zusammenfassung Der Begriff des Hamiltonschen Funktionals wird in solcher Weise verallgemeinert, daß ein bilineares Funktional bei nicht-selbstadjungierten Systemen an seine Stelle tritt. Für dieses verallgemeinerte Hamiltonsche Funktional führt die Bedingung auf die sogenannten hybriden Galerkinschen Gleichungen und die Bedingung auf die Last-Frequenz-Funktion. Diese Funktion kann im Last-Frequenz-Raum als eine Fläche aufgefaßt werden, deren Projektion auf die Last-Ebenen die Stabilitätsgrenzen und damit die Knicklasten liefert.

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Dedicated to Professor Kurt Magnus in honor of his sixtieth birthday.     

On strong Dickson pseudoprimes

It is known that the Lucas sequenceV _n(,c)=aⁿ + bⁿ,a, b being the roots ofx ² – x + c=0 equals the Dickson polynomial .^n–2i Lidl, Müller and Oswald recently defined a number b to be a strong Dickson pseudoprime to the parameterc (shortlysDpp(c)) if [itg_n(b, c)b modn for all b. These numbers seem to be very appropriate for a fast probabilistic prime number test. In generalizing results of the above mentioned authors a criterion is derived for an odd composite number to be ansDpp(c) for fixedc. Furthermore the optimal parameterc for the prime number test is determined.     

Natural damped frequencies and axial response of a rotating finite viscous liquid column

Summary For a finite solidly rotating cylindrical liquid column the damped natural axisymmetric frequencies have been determined. The liquid was considered incompressible and viscous. The cases of freely slipping edges and that of anchored edges have been treated. It was found that instability appears in a purely aperiodic root for the spinning liquid bridge. This is in contrast to the instability appearing in the damped oscillatory natural frequency of a nonspinning liquid column at . The spinning viscous liquid column exhibits the same instability as the frictionless liquid. It appears at for axisymmetric oscillations.List of symbols a radius of liquid column - I _m modified Bessel function of first kind and orderm - s complex frequency ( ) - r, ,z polar cylindrical coordinates - p pressure - t time - u, v, w radial-, azimuthal- and axial velocities of liquid, respectively - Weber number - h height of liquid column - dynamic viscosity of liquid - v kinematic viscosity of liquid (v=/) - density of liquid - surface tension of liquid - _r , _rz shear stress - (r, z, t) circulation - (r, z, t) streamfunction - ₀ angular velocity of liquid column about the axis of symmetry - (,t) free surface displacement     

On primitive and free roots in a finite field

In this paper them-dimensional extension of the finite field of orderq is investigated from an algebraic point of view. Looking upon the additive group as a cyclic module over the principal ideal domain , we introduce a new family of polynomials over which are the additive analogues of the cyclotomic polynomials. Two methods to calculate these polynomials are proposed. In combination with algorithms to compute cyclotomic polynomials, we obtain, at least theoretically, a method to determine all elements in of a given additive and multiplicative order; especially the generators of both cyclic structures, namely the generators of primitive normal bases in over , are characterized as the set of roots of a certain polynomial over .     

Nonlinear liquid oscillations in spherical systems under zero-gravity

Summary Nonlinear free oscillations of the interface of a concentric frictionless immiscible liquid system in a spherical container are investigated in a zero-gravity environment. The natural frequencies are determined for the axisymmetric and asymmetric oscillations of the interfacial surface with the diameter ratio and density ratio as parameters. It was found that for small outer- to inner liquid density ratio the oscillations exhibit softening, while for large density ratios it renders hardening oscillation. The asymmetric oscillations exhibit in the softening range softer and in the hardening range harder liquid oscillations. For a liquid layer around a rigid center sphere the oscillations of the free liquid surface yields softening behavior, where for thinner layers the softening effect is more pronounced.Nomenclature a radius of spherical container, or radius of rigid center sphere - b radius of undisturbed interfacial surface, or radius of undisturbed free liquid surface - k=a/b diameter ratio - pressure - pressure (dimensionless) - , , spherical coordinates - dimensionless radius - R _i main radii of curvaturei=1, 2 time - dimensionless time - v _i liquid velocity (j=1 spherical layer region,j=2 inner liquid sphere region) - V volume of the liquid - Y _nm tesseral surface harmonics - _i density of liquids - velocity potential - dimensionless velocity potential - interfacial surface- or free surface elevation - dimensionless interfacial surface- or free surface elevation - ₀ maximum elevation - circular frequency - circular frequency - _n0 axisymmetric natural frequency - _n1 asymmetric natural frequencym=1 - _nm ⁽⁰⁾ natural frequency of linearized liquid system - mean curvature - _nm Kronecker symbol With 10 Figures     

Torsional boundary layer effects in shells of revolution undergoing large axisymmetric deformation

Numerical and asymptotic solutions are developed to the equations governing large torsional, axisymmetric deformation of rubberlike shells of revolution. The shell equations include large-strain geometric and material nonlinearities, transverse shear deformation, transverse normal stress and strain, and torsion. Both analyses allow ready incorporation of different strain-energy density functions. In the asymptotic analysis, the interior solution corresponds to that of nonlinear membrane theory and contains a primary boundary layer. The edge-zone solution gives a secondary boundary layer that, for large strain, divides into a bending-twisting moment component and a torsional-membrane component. The boundary layer behavior is illustrated for a clamped neo-Hookean cylinder subjected to internal pressure and axial torque.List of symbols Latin symbols a General dependent variable - a ^(mn) Terms of the asymptotic expansion of a(x) - b Characteristic length - c Scalar curvature components in the normal direction - c , c , , c Cosine of , respectively - C Material constant with units of a Young's modulus - e _i Deformed local orthonormal basis associated with (, s, n)(x ₁, x ₂, x ₃) coordinates - Undeformed cylindrical coordinate basis - Intermediate coordinate basis - g Shear correction factor - H Horizontal stress resultants - l ₁ Strain invariant - k Scalar curvature components - L Undeformed cylinder length - M Moment resultants - M _r, M , M _z Moment resultant components in the basis - N Membrane stress resultants - p Internal pressure - p _H, p _v Horizontal and vertical surface loads, respectively - p _i Thickness-averaged surface tractions - Q Transverse shear stress resultants - , r Radial coordinate prior to, after deformation - R Undeformed cylinder radius - , s Meridional coordinate prior to, after deformation - s , s _x, , s Sine of , respectively - , S Reference surface prior to, after deformation - S ₁, S ₂ Shear stress resultants parallel to the reference surface - S ₃ Average transverse normal stress resultant - t Undformed shell thickness - T Axial torque - V Vertical stress resultants - w Two-dimensional strain-energy density function - w _n Terms in expansion for w - W Three-dimensional strain-energy density function - x Undeformed axial coordinate in cylinder - , z Axial coordinate prior to, after deformation     

Heat flux measurement from the temperature field of a heated surface. 2. Inhomogeneous flux

Based on the previously obtained analytical solutions of the three-dimensional space-time problem of recalculating boundary conditions, algorithms are developed and a computational experiment is carried out to reconstruct the heat flux with arbitrary spatial distribution of the temperature field of the heated surface.Notation T(t, ) temperature over the plate surface - q(t ) heat flux to the plate surface - ={x,y} transverse coordinate - t time - k thermal conductivity - a ² thermal diffusivity - L plate thickness - Jacobi theta-function [4] - Fourier parameter - Jacobi theta-function [4] - transversal Laplacian Institute of Atmospheric Optics, Siberian Division, Russian Academy of Sciences, Tomsk, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 4, pp. 622–628, July–August, 1995.     

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     

Transmission electron microscope study of a directionally solidified Cu-MgCu2 eutectic

The crystallography and the interface structure of a unidirectionally solidified Cu-MgCu₂ eutectic alloy have been examined by transmission electron microscopy. The microstructure of the eutectic was found to be lamellar and regularly interrupted by faults. The preference of the particular orientation relationship could not be explained by relative atomic densities of the planes comprising the interface. Based on the defect contrast observed and extinction distance calculations, it is suggested that the fine array of defects observed at the interface may be characterized as steps with step vectors parallel to or Dislocations were also observed at the interface but they were rarely regular.     

Size effects and ductile-brittle transition of polypropylene

The influence of specimen width on fracture parameters has been investigated. The range examined was sufficiently large to obtain ductile and brittle fractures. With reference to previously published work, the phenomenology has been analysed by combining BCS model and Carpinteri's brittleness number approach.Nomenclature a crack length - f(a/W) shape function according to ASTM specification [16] - F(a/W) shape function according to Tada Paris notation [21] - E elastic modulus - K _IC plane strain fracture toughness - K _IC ^f fictitious plane strain fracture toughness - K _IC2 plane stress fracture toughness - J _IC ^f J-integral at maximum load - L span - weight average molecular weight - number average molecular weight - polydispersity - P _M maximum load - P _F load of brittle fracture - p _P load of plastic collapse - s brittleness number - V machine cross speed - W specimen width - _y yield stress - strain rate     

On a certain inverse problem of temperature and thermal stress fields

Summary The paper discusses the method of solution of an inverse problem of one-dimensional temperature and stress fields for a sphere, a circular cylinder and an infinite plate. The inverse problem describes the dependance of the boundary conditions of different types on the prescribed temperature state or stress state within the body under consideration, in contrast with the direct problem which relates the temperature and stress states to known boundary conditions. To obtain a function describing the temperature of a heating medium and/or the Biot number in a simple form use has been made of the Laplace transformation. The numerical examples for both types of the inverse problems are presented.

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Über ein inverses Problem der Temperatur- und Wärmespannungsfelder

Zusammenfassung Die Arbeit Antersucht die Lösungsmethode des inversen Problems eindimensionaler Temperatur-und Spannungsfelder für eine Kugel, einen Kreiszylinder und eine unendliche Platte. uas inverse Problem beschreibt die Abhängigkeit der Randbedingungen verschiedener Drt vom vorgegebenen Temperatur- oder Spannungszustand innerhalb des betrachteten Körpers im Vergleich zum direkten Problem, welches den Temperatur- und Spannungszustand zu bekannten Randbedingungen in Beziehung setzt. Zum Erhalt einer Funktion, die die Temperatur des erwärmten Mediums und/oder die Biot-Zahl in einer einfachen Form beschreiben, wurde die Laplace-Transformation verwendet. Numerische Beispiele für beide Arten der inversen Probleme werden angegeben.

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Notation a characteristic size of the body, [m] - _t coefficient of linear thermal expansion [1/°C]; [1/°K] - parameter describing a shape of the body; - Laplace transform of the functionf, G, ... - Fourier number (dimensionless time) - Biot number - G shear modulus, [kN·cm^–2] - I (z),K (z) modified Bessel 1^st and 2^nd kind functions of the order - J (z) 1^st kind Bessel function of the order ; - thermal diffusivity, [m²·s^–1]; - , Lame constants, [kN·cm^–2] - Poisson ratio - s parameter of Laplace transformation - _°°(°,Fo), (°,Fo) radial and circumferential stresses [kN·cm^–2] - T(,Fo) absolute temperature at a point (,Fo); [°C, °K] - T _f (Fo) absolute temperature of a medium that heats a body under consideration [°C, °K] - T _m the reference temperature [°C, °K] - dimensionless temperature - u(,Fo) dimensionless displacement - dimensionless coordinate of position With 11 Figures     

Anisotropic flow and fracture in beryl [Be3Al2(SiO3)6]

Flow and fracture resulting from Vickers indentation testing on {0 0 0 1} and {10 0 } planar orientations have been examined. Flow characterized by indent shape differentiation was analysed to belong to the slip system with planes of the types { 10 0} and {11 0}. The ensuing fracture paths were resolved to propagate along {1 0 0} and {1 1 } cleavage planes whileK _c values obtained for them were 0.196 and 0.248 MPam^1/2, respectively.     

The laminar stagnation-point flow against a solidifying moving shell

Summary This paper considers the two-dimensional laminar stagnation-point flow due to a jet impinging onto a solidifying moving boundary. The flow is of interest in connection with the horizontal belt strip casting process. An exact solution to the Navier-Stokes equations is found that is shown to depend on a single ordinary differential equation. The solution is useful in the study of morphological and hydrodynamic instabilities within the impingement region. Solutions for the steady-state shape of the initial stages as well as the asymptotic behavior of the solidifying interface are also discussed in a perturbative manner.Nomenclature A suction velocity in boundary layer variables - a jet width [m] - c specific heat of the solid metal [J/m³K] - h Newtonian heat transfer coefficient [W/m²K] - k velocity gradient in units ofU/a - m dS ^*/dX ^* local inclination of the solidifying phase - S ^* (L)/L average slope of the solidifying phase - S ^* local thickness of the solidified phase [m] - S, S local thickness of the solidified phase in units ofL and , resp. - T absolute temperature [K] - T _f fusion temperature of metal [K] - T ₀ temperature of cooling water [K] - U jet velocity [m/s] - V belt velocity [m/s] - +i complex velocity potential in units ofUa - x coordinate tangential to the solidifying interface in units ofa - X ^* coordinate tangential to the belt [m] - X, X coordinates tangential to the belt in units ofL and , resp. - y coordinate orthogonal to the solidifying interface in units ofa - Y ^* coordinate orthogonal to the belt [m] - Y, Y coordinates orthogonal to the belt in units ofL and , resp. - z x+iy complex coordinates in units ofa - unit vector along the belt - unit vector orthogonal to the belt - local unit normal vector to the solidifying interface - h _f latent heat of fusion of metal [J/m³] - thermal diffusivity of solid metal [m²/s] - belt velocity in units ofU - { _n }, { _n } asymptotic sequences of the outer and inner expansion, resp. - m suction velocity outer variables - velocity potential in units ofUa - jet inclination relative to the local solidifying interface - coordinate orthogonal to the solidifying interface in units of - x c thermal conductivity of solid metal [W/mK] - displacement thickness in units of - v kimematic viscosity of liquid metal [m ²/s] - arctan (dS ^*/dX ^*) local angle of inclination of the solidifying interface - =(T–T ₀)/(T _f –T ₀) dimensionless temperature - perturbation parameter - coordinate tangential to the solidifying interface in units ofa/k - stream function in units ofUa - magnified stream function valid within the boundary layer - solidification constant Dimensionless parameter P _eL VS ^* (L)/ Peclet number - Q h/(cV) Heat flux number - R Ua/v Reynolds number - St Stefan number     

EPR study of V2O5–P2O5–Li2O glass system

glass system, with 0 < x 50 mol%, was prepared and investigated by EPR method. For low content of V₂O₅ all the spectra present a hyperfine structure typical for isolated V⁴⁺ ions. With the increasing of V₂O₅ content, the EPR absorption signal showing hyperfine structure is superposed by a broad line without hyperfine structure characteristic for clustered ions. At high V₂O₅ content, the vanadium hyperfine structure disappears and only the broad line can be observed in the spectra. Spin Hamiltonian parameters g , g , A , A , dipolar hyperfine coupling parameters, P, and Fermi contact interaction parameters, K, have been calculated.The composition dependence of line widths of the first two absorptions from the parallel band and of the broad line characteristic to the cluster formations was also discussed.     

Thermal diffusion ratio of a3He/4He mixture near its λ transition: The onset of heat flush

We present experimental data on the thermal diffusion ratioK _T for a 15 molar % mixture near its transition obtained from measurements of the convection velocity of a mixture contained in a vertical column. The physical nature of the normal modes of heat and mass transfer near the transition is discussed. One possibility that arises from this discussion is that the temperature dependence ofk _T may be such that , where is the value ofk _T at the transition andD is the mass diffusion coefficient. There is limited support for this conjecture by the data over a restricted temperature range.