Grain growth in the two-phase Al-Cu alloys

Grain and phase growth in the two-phase Al-Cu alloys containing 6, 11, 1 7, 24 and 33 wt % Cu were investigated by annealing at 535 °C for 0.5–100 h. The grain and phase sizes of the phase are seen to be larger than that of the phase. The size of phase decreases whereas the size of phase increases with increasing copper content in the alloy. As such, the phase- and grain-size distributions are broader than the phase- and grain-size distributions, but the size range depends on annealing time and alloy composition. The grain sizes of the ,d , and ,d , phases can be related to the volume fraction of the phase,f , according to the equationd = 0.497d /f .     

Thermal stresses in a thin circular disc of orthotropic material due to an instantaneous point heat source

Summary In this paper, we have analysed the transient plane thermal stress problem of a circular disc of orthotropic material with instantaneous point heat source. The variation of with time along different radius vectors is exhibited graphically and compared with that of the isotropic case.

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Wärmespannungen in einer dünnen Kreisscheibe aus orthotropem Material zufolge einer punktförmigen instantanen Wärmequelle

Zusammenfassung In dieser Arbeit wurde das instationäre ebene Wärmespannungsproblem einer Kreisscheibe aus orthotropem Material zufolge einer punktförmigen instantanen Wärmequelle untersucht. Die Veränderung von über die Zeit für verschiedene Radien ist graphisch dargestellt und wird mit dem isotropen Fall verglichen.

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Nomenclature r, polar coordinates - T temperature rise - ² ratio of conductivities - ² thermal diffusivity in -direction - J _n Bessel function ofn-th order - t time - p introduced in equation (2) - h heat transfer coefficient - a radius of circular disc - f(r, ) temperature distribution at initial state - r ₀, ₀ a point on the disc - T ₀ strength of point heat source - Dirac delta function - F stress function in two dimensions - ₁, ₂ coefficient of thermal expansion - a ₁₁,a ₁₂,a ₂₂,a ₆₆ elastic constants With 9 Figures     

The interdependence between the incidence angles associated with quasi-stable intersections during ion erosion

A general discussion, which is valid for any angular dependence of sputtering yieldS=S(), concerning the interdependence between the incidence angles _e and ₀, associated with quasi-stable intersections during ion erosion, is given. The object was firstly to establish the location of _e roots as a function of ₀ and secondly to identify the stationary points and general trend for the complex dependence _e= _e( ₀). The results obtained are applied to a quasi-stability analysis of some specific surface features during ion erosion. Various possible types of quasi-stable intersections (surface-surface, plane-surface, plane-plane) are reviewed from the point of view of their evolution caused by ion bombardment.     

Breakup of an anomolously viscous liquid film in a centrifugal force field

An equation is obtained for the breakup radius with consideration of tipping moments and Laplacian pressure forces acting on the liquid ridge at the critical point.Notation K, n rhenological constants - density - surface tension - r current cup radius - R maximum cup radius - r_c critical radius for film breakup - ¯r=¯r=r/R dimensionless current radius - ¯r_c=r_c/R dimensionless critical radius - ₀, _c actual and critical film thicknesses - current thickness - R_r ridge radius - h₀ ridge height - h current ridge height - ₀ limiting wetting angle - current angle of tangent to ridge surface - angle between axis of rotation and tangent to cup surface - angular velocity of rotation - q volume liquid flow rate - v₁ and v meridional and tangential velocities - =4vv _lm/r,=4v_m/r dimensionless velocities - M moments of surface and centrifugal forces - M_v moment from velocity head - p_r pressure within ridge - P_vm pressure from velocity head - p_m, p_pm pressures from centrifugal force components tangent and normal to cup surface - deviation range of breakup radius from calculated value - ¯r_max, ¯r_min limiting deviations of breakup radius - _c angle of tangent to curve _c/°₀=f(¯r) at critical point - t random oscillation of ratio _c/_c Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 51–56, July, 1980.     

In-Plane Fourfold Symmetry of the Upper Critical Field Observed in La(Sr)214 Single Crystals

In order to establish the existence of in-plane anisotropy of the upper critical field H _c2 (), the out-of-plane resistivity _c measurements were performed on La(Sr)214 single crystals with rectangular and cylindrical shape under rotating magnetic field applied within the ab-plane. Although observed _c shows non-sinusoidal twofold symmetry, clear fourfold symmetry was obtained after subtracting twofold sinusoidal component in _c which is due to the unavoidable misalignment of the magnetic field with respect to ab-plane. H _c2 () is estimated from the extracted fourfold component of _c with the flux flow theory. Angular dependence of H _c2 () was well fitted by cos(4). Since the fourfold component of H _c2 () was largest at = n/2, which corresponds to the a-axis direction, the present results strongly suggest the type symmetry in La(Sr)214. In addition, the difference in fourfold component of H _c2 at = n/2 and n/2+/4 was found to increase with decreasing temperature.     

A boundary layer theory for the end problem of a circular cylinder

Summary This paper discusses the nature of an approximate solution for the hollow circular cylinder whose fixed ends are given a uniform relative axial displacement and whose cylindrical surfaces are free from traction. We shall take the solution of this problem to be given by a super-position of the following two problems: problem I considers a finite length cylinder whose ends are given a relative axial displacement, but are no longer fixed; problem II removes the radial displacement at the end of the cylinder obtained in problem I.Nomenclature a mid-surface radius of cylinder - c half-height of cylinder - E, in-plane elastic moduli - E_t, _t, G_t transverse elastic moduli - _z, , _r axial, circumferential, and normal strain - _rz transverse shear strain - h cylinder thickness - _z, , _r axial, circumferential, and normal stress - _rz transverse shear stress - z, r axial and radial coordinates - u_z, u_r axial and normal displacements     

Effect of crack shape,inclination angle,and friction coefficient in crack surface contact problems

In rolling/sliding contact fatigue, it is known that the crack propagates at a characteristic angle =15–30 deg to the surface. To analyze the mechanism, however, the body force method has been widely used assuming 3D crack models for =45–90. In this study, therefore, the unknown body force densities are newly approximated by using fundamental density functions and polynomials. Then, a semi-elliptical crack model is analyzed for =15–90 under compressive residual stresses and Hertzian contact loads. The stress intensity factors K _II, K _III are calculated with varying the crack shape b/a, inclination crack angle , and crack face friction coefficient . The calculations show that the present method is useful for the analysis for =15–30 deg with high accuracy. It is seen that the K _II-values when b/a0 are larger than the ones when b/a=1 by 0–24% for both under compressive residual stress and Hertzian contact load. Regarding the maximum K _II values under Hertzian contact load, the results of =15 deg are smaller than the ones of =45 deg by 23–34%. Regarding the amplitude of (K _{II max}–K _{II min}), the results of =15 deg are smaller than the ones of =45 deg by 4–24%. With increasing the value of friction coefficient for crack faces the value of K _II decreases significantly. When the crack is short and the inclination angle is small, the value of friction coefficient f for Hertzian contact load largely affect the K _II value.     

Disappearance of Bose-Glass Behavior in Transport Properties of YBa2Cu3O y Films with Columnar Defects

The glass transitions of the vortex system in Au-ion irradiated YBa₂Cu₃O _y films have been studied by the measurements of transport properties as a function of magnetic field B and angle of B to the direction of columnar defects. At =0°, we find an anomalous upturn behavior of the glass transition line B _g(T) at BB /3, where B is the matching field. In B>B /3, the dependence of glass transition temperature T _g reveals cusplike behavior with a peak at =0°, which is consistent with the Bose glass theory. In B<B /3, on the other hand, T _g is almost independent of , suggesting the system undergoes the vortex glass transition induced by the inherent point-like defects.     

On the nucleation ofθ′ and T1 on Al3Zr precipitates in Al-Li-Cu-Zr alloys

Two quaternary Al-Li-Cu-Zr alloys have been investigated using electron microscopy. Ageing at 190° C resulted in the nucleation of precipitates on the Al₃Zr/matrix interface in addition to heterogeneous nucleation on matrix dislocations. In the majority of cases, the broad, coherent face of the plans ms in contact with the Al₃Zr precipitates. Similar evidence showed that nucleation of T₁ precipitates occurred on the Al₃Zr, but to a lesser extent than. Solid-solid nucleation theory has been used to account for the Al₃Zr acting as a nucleation substrate.     

Vibrations of axially compressed laminated orthotropic cylindrical shells,including transverse shear deformation

Summary The free vibrations, buckling and the effect of initial prestress upon the frequency spectrum of orthotropic composite cylindrical shells are examined in the context of a theory that includes transverse shear deformation. Results obtained are compared with the predictions of refined Love-type theory and simplified Donnell-type theory that do not consider shear deformation.The calculated examples indicate that transverse shear deformation can be significant not only for short composite shells but even for longer shells possessing low shear moduli.

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Schwingungen axial gedrückter, laminierter, orthotroper zylindrischer Schalen einschließlich Querschubverformung

Zusammenfassung Es werden die freien Schwingungen, das Beulen und der Einfluß einer Anfangsvorspannung auf das Frequenzspektrum orthotroper, kompositer, zylindrischer Schalen im Rahmen einer Theorie, die die Querschubverformung mitberücksichtigt, untersucht. Die erhaltenen Resultate werden mit den Vorhersagen der verbesserten Loveschen Theorie und der vereinfachten Donnellschen Theorie, welche keine Querschubverformung in Betrach ziehen, verglichen.Die durchgerechneten Beispiele zeigen, daß die Querschubverformung nicht nur für kurze, komposite Schalen sondern sogar für längere Schalen mit niederem Schubmodul Bedeutung gewinnen kann.

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Nomenclature a radius of reference surface of cylindrical shell - A _i amplitudes of displacements - A _ij elastic area - B _ij elastic statical moment - D _ij elastic moment of inertia - E _ij elastic stiffness modulus - h shell thickness - k ₄₄,k ₅₅ shear correction factors - l length of cylindrical shell - L _ij functional operator - m number of half-waves in axial direction - M ,M ,M axial, circumferential and twisting moments, respectively - n number of circumferential waves - N ⁰ axial compression force - N ,N ,N axial, circumferential and shear forces, respectively - Q ,Q transverse shear forces - R ₀,R ₁,R ₂ inertia terms - t time - T matrix defined in Eq. (25) - u, v, w displacements in axial, circumferential and radial directions, respectively - U _i time-independent displacement or rotation - nondimensional axial wave parameter - , , axial, circumferential and shear strains, respectively - radial coordinate, taken positive inward - polar angle - , , curvature changes - circular frequency - nondimensional axial coordinate - density - , , , , stress components - , rotations of normal to undeformed midsurface With 6 Figures     

The tensile strength and ductility of continuous fibre composites

The plastic instability approach has been applied to the tensile behaviour of a continuous fibre composite. It is shown that the combination of two components with different strengths and degrees of work-hardening produces a new material with a new degree of work-hardening, which may be determined by the present analysis. Expressions for the elongation at rupture and the strength of a composite have been obtained and the results of the calculation are compared with some experimental data.List of symbols V _f volume fraction of fibres in composite - , , true strain of fibre, matrix and composite - s true stress - , , nominal stress on fibre, matrix and composite - _*, _*, _* critical stress of fibre, matrix and composite (ultimate tensile strength) - _*, _* critical strain of separate fibre and matrix - _* critical strain of composite - Q external load - A cross-sectional area - A ₀ initial value of area     

Structure of unidimensional temperature stresses

Using the structural approach, the temperature stresses are examined in a semiinfinite rod, insulated on the lateral faces and rigidly fixed at the end. A comparative analysis is made for three heat-transfer models.Notation k(t) heat flux relaxation function - (t) internal energy relaxation function - T rod temperature - ambient temperature - t time - x coordinate along the rod - _xx(x, t) stress - u(x, t) displacement - (x, t) deformation - c₀=(E/)^1/2 speed of sound in the rod under isothermal conditions - E elasticity modulus - density of the material - _t coefficient of thermal expansion - thermal-conductivity coefficient - a thermal-diffusivity coefficient - b thermal-activity coefficient - c_q=(a/_r)^1/2 velocity of heat propagation - _r heat flux relaxation time - (t) unique Heaviside function Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 5, pp. 912–921, November, 1977.     

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     

Analysis of the effect of the decomposition of char-forming heat-insulating materials on the free discharge of a gas mixture

The article presents results of a numerical solution of a nonsteady problem on the free discharge of a mixture of gases from a hemispherical volume with allowance for thermal decomposition of heat-insulating materials.Notation V volume - S area - t - P p - T - u v - Q q, dimensional and dimensionless time, pressure, temperature, TIM decomposition rate, and heat flux - adiabatic exponent - R gas constant - density - H specific enthalpy - c specific heat - thermal conductivity - , , _s dimensionless complexes - coefficient expressing the radiative properties of the gas medium and the heat-transfer surface - Stefan-Boltzmann constant Indices 0 initial state and scale factors - s surface - coke - M TIM material - P pyrolysis front - A ablation front - v volatile degradation products - adiabatic conditions - c completion of discharge Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 5, pp. 787–793, May, 1988.     

Response of a spinning liquid column to pitch excitation

Summary The response of a solidly rotating liquid bridge consisting of inviscid liquid is determined for pitch excitation about its undisturbed center of mass. Free liquid surface displacement and velocity distribution has been determined in the elliptic (>2₀) and hyperbolic (<2₀) excitation frequency range.List of symbols a radius of liquid column - h length of column - I ₁ modified Besselfunction of first kind and first order - J ₁ Besselfunction of first kind and first order - r, ,z cylindrical coordinates - t time - u, v, w velocity distribution in radial-, circumferential-and axial direction resp. - mass density of liquid - free surface displacement - velocity potential - ₀ rotational excitation angle - ₀ velocity of spin - forcing frequency - _1n natural frequency - surface tension - acceleration potential - for elliptic range >2₀ - for hyperbolic range >2₀     

Evolution of transient thermal processes in layer counterflow apparatuses and heat exchangers

Results are given of an analytic investigation of transient processes inside counterflow apparatuses and heat exchangers with temperature disturbance in one of the heat carriers at the entry to the apparatus.Notation =(t–t₀)/(T₀–t₀),=(T–t₀)/(T₀ s-t₀) relative temperatures - t, T temperatures of material and gas respectively - t₀, T₀ same for the initial state - Z=[ _Vm₁/c(1–w/w_g)] [–(y₀–y)/w_g] dimensionless time - m₁=1/(1+Bi/) solidity coefficient - B₁=( _FR/) Biot number - _{F V} heat-exchange coefficients referred to 1 m² surface and 1 m³ layer - R depth of heat penetration in a portion - portion heat conductivity coefficient - shape coefficient (=0 for a plate,=1 for a cylinder,=2 for a sphere) - c, C_g heat capacities of material and gas respectively - , _g volumetric masses - w, W_g flow velocities of material and gas - y distance from the point of entry to the heating heat carrier - y₀ heat-exchanger length - Y= _Vm₁y/W_gC_{g g} dimensionless coordinate - m=cw/C_g– _gW_g water equivalent ratio Deceased.Translated from Inzhenerno-Fizicheskii Zhurnal, vol. 20, No. 5, pp. 832–840, May, 1971.     

Hot electrons in metals at low temperatures

Hot electrons in metals at helium temperatures under steady conditions can be produced by passing an electric current of moderate density ( 10⁶ A/cm²) through thin, narrow (~1 m wide) metallic films in good thermal contact with bulk single-crystal dielectric substrates. This paper is concerned with the theory of hot electrons in normal metals at low temperatures (when _D, where is the average electron energy and _D is the Debye temperature). The theory is formulated in terms of realistic electron and phonon dispersion laws, taking into account the experimental possibility of heat removal from the sample. In the case in which the temperature approximation of Kagnov, Lifshitz, and Tanatarov is not satisfied when elastic scattering of electrons is dominant in a steady state electric field, the kinetic equation is derived for the energy-dependent, hot electron distribution function, which determines the associated nonlinear responses. The solution of this equation is discussed for a simple model. It is shown that the experimental information on the electron-phonon interaction in a metal can be obtained in terms of the well-known spectral functions S() ² F() and g() _tr ² F(). This is illustrated by experiments determining the nonlinear field dependence of the resistance, by tunnel experiments, and by critical current hysteresis measurements (for superconducting metals). Theoretical estimates which support the observability of the effects under discussion are presented.     

Heat transfer in a “pseudoturbulent” bed of dispersed material

A two-phase model is proposed for the steady heat exchange between a surface and a pseudoturbulent bed of dispersed material. Expressions are obtained for the temperature fields of the gaseous and solid phases.Notation _g effective thermal conductivity of gaseous phase - _s effective thermal conductivity of the mixed solid phase - porosity - _m molecular thermal conductivity - d particle diameter - temperature of dispersed bed at a large distance from heat source - , g gas temperature - _p particle temperature - _w wall temperature - x current coordinate in the direction perpendicular to the wall - l bed thickness - q heat flux - coefficient of heat exchange between wall and pseudoturbulent bed of dispersed material - ^* coefficient of interphase heat exchange - _g=_g/_w dimensionless gas temperature - _p = _p/_w dimensionless particle temperature - Y = x/d dimensionless coordinate - L =l/d dimensionless bed thickness - A_h dimensionless coefficient of interphase heat exchange - Nu_g = d/_s Nusselt number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 465–469, September, 1981.     

A finite volume technique to simulate the flow of a viscoelastic fluid

Hydrodynamically developing flow of Oldroyd B fluid in the planar die entrance region has been investigated numerically using SIMPLER algorithm in a non-uniform staggered grid system. It has been shown that for constant values of the Reynolds number, the entrance length increases as the Weissenberg number increases. For small Reynolds number flows the center line velocity distribution exhibit overshoot near the inlet, which seems to be related to the occurrence of numerical breakdown at small values of the limiting Weissenberg number than those for large Reynolds number flows. The distributions of the first normal stress difference display clearly the development of the flow characteristics from extensional flow to shear flow.List of symbols D rate of strain tensor - L slit halfheight - P pressure, indeterminate part of the Cauchy stress tensor - R the Reynolds number - t time - U average velocity in the slit - u velocity vector - u,v velocity components - W the Weissenberg number based on the difference between stress relaxation time and retardation time - W ₁ the Weissenberg number based on stress relaxation time - x,y rectangular Cartesian coordinates - ratio of retardation time to stress relaxation time - zero-shear-rate viscosity, ₁ + ₂ - ₁ non-Newtonian contribution to - ₂ Newtonian contribution to - ₁ stress relaxation time - ₂ retardation time - density - (, , ) xx, yy and xy components of ₁, respectively - determinate part of the Cauchy stress tensor - ₁ non-Newtonian contribution to - ₂ Newtonian contribution to      

Residual thermal stresses in the pull-out specimen: A finite element calculation

The residual thermal stress field in the pull-out specimen is calculated in the case of a high properties thermoset system (carbon-bismaleimide). The calculation is performed within the framework of the linear theory of elasticity by means of a finite element method. The specimen is modelled as a three-phase composite (holder-fibre-matrix). The meniscus which forms at the fibre entry is taken into account in order to provide a realistic stress concentration. The latter is far higher than the matrix strength. Evidence that fibre debonding propagates from the fibre end during cooling is then produced.Nomenclature T thermal load - L _e embedded length - r _f fibre radius - _c curvature radius of the meniscus (fibre entry) - r _c radial dimension of the finite element mesh - E _m,E _h matrix and holder moduli - E _A,E _T fibre axial and transverse moduli - _m, _h matrix and holder thermal expansion coefficients - _A, _T fibre axial and transverse thermal expansion coefficients - _rr, , _zz, _rz non-zero components of the residual stress field - _rr ⁱ , ^im , _zz ^im , _rz ⁱ stresses at the interface in the matrix (r=r _f + ) - _rr ⁱ , ^if , _zz ^if , _rz ⁱ stresses at the interface in the fibre (r=r _f–) - _p1 maximum principal stress - _zz ^f mean axial stress over the fibre section - _rupt ^m matrix strength - u _r ,u _z non-zero components of the displacement field