A high-resolution-electron-microscopy study of a γ/γ′-α directionally solidified eutectic alloy

The microstructure of a /- directionally solidified (DS) eutectic alloy with a nominal composition of Ni-30.26Mo-6.08Al-1.43V (wt%) was investigated by means of high-resolution electron microscopy (HREM) and analytical electron microscopy. The -fibres exhibited a typical morphology with a rectangular cross-section and they displayed the Bain orientation relationship (OR) with the / matrix; that is, [001][001] and (110)(010). Misfit dislocations and lattice strain fields existed at the / interface for different habit planes; that is, (110)(010) and (100)(110) were analysed. EDAX (Energy dispersive X-ray) analysis showed that the composition of the -phase was approximately Ni₄(Mo, Al, V); it contained 90° rotational domains of Ni₃(Mo, Al, V) with a DO₂₂ structure and Ni₂(Mo, Al, V) with a Pt₂Mo structure.     

Heat conduction in a multilayer composite wedge

A new method for analytically solving a problem of steady-state heat conduction for multilayer composite wedge-shaped bodies is suggested based on a generalization of the integral Mellin transform.Notation T temperature - _rr, thermal conductivity coefficients - thickness of composite material layers (1) - N₁(), N ₂ ⁽¹⁾ (), N ₂ ⁽²⁾ () auxiliary local functions from the rapid variable =r/ - m(r, p) auxiliary function entering the core of the generalized integral Mellin transform - ₀ half of the wedge aperture angle Moscow Institute of Chemical Engineering. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 4, pp. 487–491, April, 1993.     

Question of determining the composition of composites by a tomographic method

One possible method of determining the volume content of composite components by using x-ray calculational tomography is examined.Notation , _T, _fi, P_b, _b, _w, _im material densities, theoretical, fiber, binder, pore, water, impregnating fluid - _fi, _b, _p fiber, binder, pore volume contents - f_fi, f_b, f_p, f_di, f_di ^*, f_cij, f_im linear coefficients of attenuation of the fiber, binder, air of the i-th layer of the dry specimen - n quantity of cells in the i-th layer, m_fi, m₁ m₂, weight of the dry and impregnated specimens in air and in water - C_cl closed porosity - S_f rms deviation of the linear attenuation coefficients - volume closed pore content Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 5, pp. 738–745, May, 1989.     

Radiation of internal waves during vertical motion of a body through a nonuniform liquid

Energy losses to radiation of internal waves during the vertical motion of a point dipole in two-dimensional and three-dimensional cases are computed.Notation _o(z), p_o(z) density and pressure of the ground state - z vertical coordinate - v, p, perturbed velocity, pressure, and density - H(d 1n _o/dz)^–1 characteristic length scale for stratification - N=(gH^–1–g²c _o ^–2 )^1/2 Weisel-Brent frequency - g acceleration of gravity - c_o speed of sound - vertical component of the perturbed velocity - V vector operator - k wave vector - frequency - d vector surface element - W magnitude of the energy losses - (t), (r) (x)(y)(z) Dirac functions - v_o velocity of motion of the source of perturbations - d dipole moment of the doublet - _o,l length dimension parameters - _o intensity of the source Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 4, pp. 619–623, October, 1980.     

Unsteady periodic contact heat-transfer

This paper presents results of an investigation of unsteady periodic heat-transfer, carried out on a special experimental facility.Notation _ch contact heat-transfer coefficient - q, q_st specific and steady heat flux through the contact zone - P_c contact pressure - , _f, _m thermal conductivities of the materials of the contact pair, the thermally insulating film, and the intercontact medium - _re reduced thermal conductivity - _t strength limit of the material - h₁, h₂ heights of contact-surface profile irregularities - h_f thickness of the thermally insulating film - relative area of actual contact - contraction coefficient - _c/_cy duty factor (ratio of contact duration to working cycle duration) - fcy/f_o relative frequency (ratio of contact cycle frequency to a fixed frequency) - a thermal diffusivity - t_st steady temperature at depth x from the contact surface - k order of harmonic - cyclic frequency - A_c, B_c Fourier series coefficients - k_a amplifier gain - y_q heat-flux coordinate on the oscillogram - c_s constant stub - l absolute distance of separation - intercontact gap at zero load - b, coefficients describing the surface roughness - relative separation of surfaces - thermocouple sensitivity - r specific electrical resistance Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 898–904, November, 1979.     

Response of differently axially excited spinning liquid columns

Summary A solidly rotating finite liquid column consisting of frictionless liquid is subjected to various axial excitation modes. The response of the free liquid surface displacement and velocity distribution has been determined in the elliptic (>2₀) and hyperbolic range (<2₀). Differences of the various cases are presented.List of symbols a radius of liquid bridge - h length of liquid bridge - I ₀,I ₁ modified Besselfunctions - J ₀,J ₁ Besselfunctions - p liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution in rotating liquid - axial excitation amplitude - elliptic case (>2₀) - hyperbolic case (<2₀) - liquid density - surface tension - liquid surface displacement - _n damping factor - phase angle - acceleration potential - ₀ rotational speed - , ₁,₂ axial forcing frequency - natural frequency of rotating system - _0n natural frequency of harmonic axial response     

Mixed convection flow of micropolar fluid over an isothermal plate with variable spin gradient viscosity

Summary A steady two-dimensional mixed convection flow of viscous incompressible micropolar fluid past an isothermal horizotal heated plate with uniform free stream and variable spin-gradient viscosity is considered. With appropriate transformations the boundary layer equations are transformed into nonsimilar equations appropriate for three distinct regimes, namely, the forced convection regime, the free convection regime and the mixed convection regime. Solutions of the governing equations for these regimes are obtained by an implicit finite difference scheme developed for the present problem. Results are obtained for the pertinent parameters, such as the buoyancy parameter, in the range of 0 to 10 and the vortex viscosity parameters, =0.0, 1.0, 3.0, 5.0 and 10.0 for fluid with Prandtl number Pr=0.7 and are presented in terms of local shear-stress and the local rate of heat transfer. Effects of these parameters are also shown graphically on the velocity, temperature and the couple stress distributions. From the present analysis, it is observed that both the momentum boundary layer and the thermal boundary layer increase due to an increase in the vortex viscosity of the fluid.List of symbols f, F, dimensionless stream function for forced convection free convection and mixed convection, respectively - g acceleration due to gravity - Gr_x local Grashof number - j micro-inertia density - m ₂₃ distribution of couple stress - N microrotation component normal to (x, y)-plane - p pressure of the fluid - q dimensionless rate of heat transfer - Re_x local Reynolds number - T temperature of the fluid in the boundary layer - T temperature of the ambient fluid - T temperature at the surface - u, v thex andy-components of the velocity field - U free stream velocity - x, y axis in direction along and normal to the plate Greek thermal diffusivity - coefficient of volume expansion - vortex viscosity parameter - stream function - , , nondimensional similarity variables - buoyancy parameter (=Gr _x Re _x ^/5/2 ) - vortex viscosity - density of the fluid - v kinematic coefficient of viscosity - spin-gradient viscosity - stream function - dimensionless skin-friction - fluid viscosity     

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.     

1 : 2 Long-range ordering and defect mechanism of WO3-doped perovskite Ba(Mg1/3Ta2/3)O3

The nature of the B-site cation ordering and the associated defect process necessary to stabilize the ordered domains were investigated using the WO₃-doped BaMg_1/3Ta_2/3O₃ BMT system as a typical example of BaB_1/3B_2/3O₃-type complex perovskites. It was shown that only the 1 : 2 long-range ordering of the B-site cation existed in both undoped and WO₃-doped BMT perovskites. The atomic defect mechanism associated with the stoichiometric 1 : 2 long-range ordering was systematically investigated. It is concluded that the substitution of W⁶⁺ for Ta⁵⁺ in the WO₃-doped BMT enhances the degree of the 1 : 2 long-range ordering and produces the positively charged W _Ta sites with a concomitant generation of tantalum vacancies V_Ta and mobile oxygen vacancies V _O for the ionic charge compensation.     

The transverse acoustic impedance of He II

The complex shear acoustic impedance of liquid He II has been measured at frequenciesf(=/2) of 20.5, 34.1, and 47.8 MHz from 30 mK to the -point T (2.176 K). The impedanceZ was found from the temperature dependence of the quality factor and the resonant frequency of a thickness shear mode quartz crystal resonator immersed in the liquid. The relationship for a hydrodynamic viscous liquidZ(T)=(1–i)(f _n )^1/2 was used to measure the temperature dependence of the viscosity (T) using tabulated values of the normal fluid density _n (T). Deviations from hydrodynamic behavior occurred when the viscous penetration depth was less than the superfluid healing length, the phonon mean free path, and the roton mean free path. Near the -point,Z(T)/Z(T) was frequency dependent and a value for the superfluid healing lengtha=(0.10±0.01)^–2/3 nm was found, where =(T–T)/T. The effects of van der Waals forces near the crystal surface were also observed and a layer model was used to interpret the measurements. Below 1.8 K only rotons contribute significantly toZ and we determined the roton relaxation time as _r =8.5×10^–14 T ^–1/3 exp (8.65/T) sec. Below 1.2 K, _r >1 and we investigated the breakdown of hydrodynamics in this region. ForT<0.6 K the resonant frequency of the crystals decreased by f/f=2×10^–7, but the origin of this effect is not yet known.Financial support provided by the SERC, Bedford College, and the Central Research Fund, University of London.     

Critical properties of4He in aerogel near the λ-line

We measured the superfluid fraction _s/ and the isobaric thermal expansion coefficient _P of⁴He confined in an aerogel. Data were obtained near the -line along several isobars. Powerlaw fits to the results for _s/ as a function of tT/T_c–1 (T_c is the transition temperature) give a pressure—independent exponent =0.755 when a confluent singular term is included. Fits to the _P data of power laws yield the specific-heat exponents –0.6 and –1.0 above and below T_c respectively. When an analytic background term a×t is included in the fit, the pressure-independent value =–0.59 is permitted, but the amplitude ratio A/A is found to be near zero and the coefficient of the analytic term is large. The measured values for and or are inconsistent with hyperscaling in three dimensions.     

On the measurement and physical meaning of the cleavage fracture stress in steel

Elastic-plastic two-dimensional (2D) and three-dimensional (3D) finite element models (FEM) are used to analyze the stress distributions ahead of notches of four-point bending (4PB) and three-point bending (3PB) specimens with various sizes of a C-Mn steel. By accurately measuring the location of the cleavage initiation sites, the local cleavage fracture stress _f and the macroscopic cleavage fracture stress _F is accurately measured. The _f and _F measured by 2D FEM are higher than that by 3D FEM. _f values are lower than the _F, and the _f values could be predicted by _f=(0.8––1.0)_F. With increasing specimen sizes (W,B and a) and specimen widths (B) and changing loading methods (4PB and 3PB), the fracture load P _f changes considerably, but the _F and _f remain nearly constant. The stable lower boundary _F and _f values could be obtained by using notched specimens with sizes larger than the Griffiths–Owen specimen. The local cleavage fracture stress _f could be accurately used in the analysis of fracture micromechanism, and to characterize intrinsic toughness of steel. The macroscopic cleavage fracture stress _F is suggested to be a potential engineering parameter which can be used to assess fracture toughness of steel and to design engineering structure.     

Generalized sufficient conditions for modular termination of rewriting

Modular properties of term rewriting systems, i.e. properties which are preserved under disjoint unions, have attracted an increasing attention within the last few years. Whereas confluence is modular this does not hold true in general for termination. By means of a careful analysis of potential counterexamples we prove the following abstract result. Whenever the disjoint union _{1 2} of two (finitely branching) terminating term rewriting systems ₁, ₂ is non-terminating, then one of the systems, say ₁, enjoys an interesting (undecidable) property, namely it is not termination preserving under non-deterministic collapses, i.e. ₁ {itG(x, y) x, G(x, y) y} is non-terminating, and the other system ₂ is collapsing, i.e. contains a rule with a variable right hand side. This result generalizes known sufficient criteria for modular termination of rewriting and provides the basis for a couple of derived modularity results. Furthermore, we prove that the minimal rank of potential counterexamples in disjoint unions may be arbitrarily high which shows that interaction of systems in such disjoint unions may be very subtle. Finally, extensions and generalizations of our main results in various directions are discussed. In particular, we show how to generalize the main results to some restricted form of non-disjoint combinations of term rewriting systems, namely for combined systems with shared constructors.This research was supported by the Deutsche Forschungsgemeinschaft, SFB 314 (D4-Projekt).     

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     

Ordinary size effects and deviations from Matthiessen's rule in the resistance of fine wires

Contrary to previous statements in the literature, large deviations from Matthiessen's rule in fine wiresare to be expected on the basis of a straight-forward solution of the ordinary transport equation, assuming the relaxation-time approximation and imposing the idealized condition of diffuse scattering of electrons at the boundaries. Using Chambers' path-integral method to evaluate the current density in a wire of arbitrary cross-sectional shape, the effects of boundary scattering on the resistivity in the regimed 0.1 have been calculated for two model Fermi surface geometries. For the temperature-dependent part of the resistivity, _d (T) _d (T)– _d (0), two distinct types of behavior are found in the alternative cases: (1) for a spherical Fermi surface, _d(T) increases logarithmically with _d(0); (2) for a cylindrical Fermi surface, _d (T) increases essentially linearly with _d (0). [In each case the qualitative dependence of _d(0) on /d is, for practical purposes, linear. However, the correct value of the product in the cylindrical case is not simply given in the ordinary way by the slope of an empirical plot of _d (0) vs.d ^–1.] A comparison of theoretical results for the two simple models with the published data for indium and gallium shows that the actual temperature-dependent size effects are consistent, both qualitatively and, by a rough estimation, quantitatively, with the expected behavior.     

Use of adjoint functions in investigations of heat conduction and transfer processes

An examination is made of the use of adjoint functions in heat conduction and convection theory. Formulas of perturbation theory are obtained for steady and unsteady cases, an interpretation of the physical meaning of adjoint temperature is given, and some applications of the theory are discussed.Notation (r,) thermal conductivity - t(r,) temperature - t *(r,) adjoint temperature - q_V(r,) density of heat release sources - p(r,) a parameter of adjoint equation - r generalized coordinate - time - (r_s, ) heat transfer coefficient - I linear functional of temperature - (r,;r₀,₀) and *(r,; r₀,₀) Green's function for t(r, ) and t *(r, ) - C(r,) volume specific heat - W(r, ) vector distribution of flow velocities - V, S volume and surface areas of body - R radius of HRE - r, radial and angular coordinates - F_in, F_out inlet and outlet flow areas of channel     

An apparatus for measuring the thermal conductivity and diffusivity of solid materials

An apparatus is described for measuring the thermal conductivity and diffusivity on small specimens of solid materials; also the results are shown which have been obtained for refractive high-alumina concrete by such measurements.Notation thermal conductivity at the mean temperature of specimens, W/m· °C - Q power of the central heater, W - F cross section area of a specimen, m² - t_1,2 temperature drop across the specimens, °C - ₁, ₂ difference in heights between the thermocouple beads, center-to-center, in the first and in the second specimen respectively, m - t temperature, °C - time coordinate, min - d₁= (d_1u+d_1l )/2 mean distance between specimen contact plane and nearest thermocouple beads, for the upper and lower specimen, m - d₂= (d_2u+d_2l )/2 mean distance between specimen contact plane and farthest thermocouple beads, for the upper and lower specimen, m - dt(d₁,)/d rate of temperature rise at section d₁ of the specimen at time, °C/h - t=t₁+t₂ sum of temperature drops in the specimens at time, °C - m heating rate, h^–1 - a thermal diffusivity of specimens, referred to their mean temperature, m²/h - =m/a, m^–1 b=¦(t_u–t_l)/t_u¦ heating nonuniformity factor Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 6, pp. 1049–1054, June, 1972.     

Effects of Orthorhombic Distortion on Magnetic Excitation in t-J Model

Neutron scattering experiments on La_2–x Sr _x CuO₄ (LSCO) have revealed the incommensurate antiferromagnetic peaks do not lie exactly on the symmetry axes (q _x=± and q _y=±), but, are slightly shifted from them. In this paper, a scenario is presented for such shift in terms of the anisotropy of t (next-nearest-neighbor hopping integral on the square lattice) in the slave-boson scheme of the two-dimensional t-J model. Since the predictions of the present theory are different from those based on the spin-charge stripes hypothesis, further studies of the shift may clarify the factor responsible for the incommensurate antifcrromagnetic fluctuations in LSCO systems.     

Stress intensity factors in a fully interacting,multicracked, isotropic plate

An essential part of describing the damage state and predicting the damage growth in a multicracked plate is the accurate calculation of stress intensity factors (SIF's). Analytical derivations of these SIF's for a multicraked plate can be complex and tedious. Recent advances, however, in intelligent application of symbolic computation can overcome these difficulties and provide the means to rigorously and efficiently analyze this class of problems. Here, the symbolic algorithm required to implement the methodology for the rigorous solution of the system of singular integral equations for SIF's is presented. The special problem-oriented symbolic functions to derive the fundamental kernels are described, and the associated automatically generated FORTRAN subroutines are given. As a result, a symbolic/FORTRAN package named SYMFRAC, capable of providing accurate SIF's at each crack tip, has been developed and validated.Simple illustrative examples using SYMFRAC show the potential of the present approach for predicting the macrocrack propagation path due to existing microcracks in the vicinity of a macrocrack tip, when the influence of the microcracks' location, orientation, size, and interaction are accounted for.List of symbols offset angle between inner tips of two parallel cracks - _lr, _mz direction cosines between two local coordinate systems - _jl strain tensor - offset of notch-microcracks system with respect to Y axis - _k four roots of the characteristic equation - v Poisson's ratio - _jl ^o , _jl ^T far-field and total stress field, respectively - _XX ^o , _YY ^o , _XY ^o components of stress in global coordinate system - _j angle defining local frame orientation - , normalized real variable - (s, y) Fourier transform of Airy stress function with respect to x variable - a _j half crack length - a ₁₁, a₁₂, a₂₂ coefficients of strain-stress relationship - d normalized radial (tip) distance - f _nj auxiliary functions - k ₁, k₂ mode-I and mode-II stress intensity factors - ker _inf ^sup Fredholm kernels - p _j normal traction at crack surface - q _j shear traction at crack surface - s Fourier variable - r _j, r_kX, r_kY position vector and its components, for an origin of local frame - u, v x, y component of displacement, respectively - w weight function - x _j y_jand X, Y local and global coordinates - [A] matrix of coefficients - C' _j, C_j functions of s in Fourier space (i.e., constrants in x, y-real space) - E Young modulus - F _j(x_j, y_j) Airy stress function - G_nj(_p) discrete auxiliary function - {} loading function vector     

A note on the solution of a differential equation arising in boundary-layer theory

Summary The differential equation f + ff + f² = 0 (where dashes denote differentiation with respect to the independent variable ) subject to the boundary conditions f(0)=0, f()=0 and either f(0)=1 or f(0)=–1 is considered. It is shown that by using pf as dependent variable and =C–f (where C=f()) as independent variable and then expanding in powers of , a very good approximation to the solution can be obtained using only a few terms in the expansion.