Plastic deformation mode of retainedβ phase inβ-eutectoid Ti-Fe alloys

Plastic deformation mode of-eutectoid Ti-Fe alloys has been investigated at 300 and 77 K in a retained single phase (containing athermal phase). Surface analysis and transmission electron microscopy show that {332}1 1 3 twinning and 1 1 1 slip appear to be dependent on orientation, composition and deformation temperature. The {3 3 2} 1 1 3 twinning appears only in metastable regions adjacent to the M_s curve in good agreement with previous work in-isomorphous alloys. Orientation dependence for occurrence of the preferential {332} 1 1 3 twinning among the twelve equivalent twinning systems can be explained in terms of the Schmid factor and the polarization of twinning shear. It is concluded that the {332} <1 1 3 twinning is common for-titanium alloys and related to the instability of the phase.     

Streamline curvature effects in side-channel spillway flow

Summary Steady flow in side channel spillways is investigated, thereby accounting for the effects of the streamline slope and curvature on the free surface profile. The governing system of equations is linearized in order to discuss the main features of the solutions. Subsequently, the non-linear version is solved by an implicit numerical procedure; particular attention is paid to the stability of the chosen scheme. Finally, the solutions are compared to observations and an almost perfect agreement is found.Notation a reference flow depth - b channel width - F Froude number - g gravitational acceleration - h flow depth - J average energy gradient - K Strickler's roughness coefficient - L lateral inflow length - m root of characteristic polynomial - n Manning's roughness coefficient - p lateral inflow intensity per unit channel width - q lateral inflow intensity - Q discharge - R hydraulic radius - S specific momentum - S _f frictional slope - S ₀ bottom slope - V average cross-sectional velocity - x longitudinal coordinate - X normalized longitudinal coordinate - y normalized flow depth - factor, 01 - factor, 01 - perturbative change in flow depth - relative discharge intensity - relative specific momentum With 7 FiguresSeveral symbols may appear with indices u, d, N, c and then refer to the up-and downstream end of the lateral inflow zone, and to uniform and critical flow conditions, respectively. Primes indicate derivatives with respect to the longitudinal coordinate.     

Change of pressure in wells opening up highly inhomogeneous porous collectors

We consider a generalized averaged model of the filtration of a weakly compressible liquid in a highly inhomogeneous medium. We construct an approximate analytical solution of the problem that describes the change in the pressure field around a well in a circular bed. We investigate the effect of the parameters of a highly inhomogeneous bed on the form of the well pressure stabilization curve.Notation c Euler constant - D diameter of a weakly permeable block - Ei symbol of the integral exponential function - h bed thickness - K(t), K _* (t) kernels of integral operators - K ₀ symbol of the Macdonald function - k permeability - P pressure - Q constant discharge of the well - r radius - s complex variable - t time - t _* time of the relaxation of a weakly permeable block - U(r, t) reduced pressure - U(t) function taking into account the internal flow of the fluid from one medium to the other - fraction of the volume of the bed per block - ^* reduced coefficient of compressibility - characteristic scale of inhomogeneity - ratio of piezoconductivities of a block and a crack - Laplace operator - piezoconductivity - ratio of elastic amounts of weakly permeable blocks and systems of cracks - viscosity of the fluid - dimensionless time - integration variable. Indices: 1, weakly permeable blocks - 2 system of cracks - 0 initial value - w value in the well - e effective value - overbar Laplace transform Institute for the Problems of Oil and Gas of the Russian Academy of Sciences, Moscow. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 3, pp. 444–450, May–June, 1995.     

Hydrodynamics of a vortex ring

We considered the kinematics and dynamics of a vortex ring in an incompressible fluid in toroidal coordinates. We obtained the change in the pressure difference along the boundary between two flow regions in the case of a moving torus.Notation , , toroidal coordinates - (V ;V ;V ) velocity of a fluid particle and its projections in toroidal coordinates - g ,g ,g metric tensor components - the Jacobian of transition to curvilinear coordinates - V ₀ velocity at the center of a vortex ring on its symmetry axis - x, y, z Cartesian coordinates - z, y, cylindrical coordinates - a distance from the axis of a torus (V=0) to its axis of symmetry (Oz) - angle between the Oy axis and the line that connects a fluid particle on the streamline =const, which represents a circle [16], with the center of this circle - U _z,U _y velocities in the cylindrical system of coordinates - ₀ stream function of a stationary vortex ring - velocity circulation - U V ₁, velocity of a rectilinear flow at infinity - ₁ stream function of a rectilinear flow - = ₀ + ₁ superposition of two flows - n=k ⁴=V ₁/V ₀ velocity ratio coefficient - R radius of a vortical region - U velocity of fluid particles at the boundary in polar coordinates (r, ) with the center at the coordinate origin (point 0) - fluid density - p ₀,p pressure at infinity and at a certain point of flow - pressure difference Polotsk State University, Polotsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 4, pp. 531–536, July–August, 1995.     

The mechanism of adhesion of moist powders to solid surfaces in the presence of a temperature field

An examination is made of the basic factors which influence the creation of forces causing powders to adhere to solid surfaces in the presence of a temperature field. An experimental investigation has been conducted on an apatite concentrate.Notation p_c capillary pressure - density of fluid - g acceleration due to gravity - h_cap, h limiting and actual height of capillary rise - surface tension - r radius of equivalent capillary - q specific suction force - k_w water saturation coefficient - V_w volume of water in pores - V_pore volume of pores - Wg humidity by weight - R particle radius - polar angle - _c area of contact - N total adhesive force - _m, _w specific weight of powder and water     

Viscosity of steam in the critical region

The shear viscosity of fluids exhibits an anomalous enhancement in the close vicinity of the critical point. A detailed experimental study of the viscosity of steam in the critical region has been reported by Rivkin and collaborators. A reanalysis of the experimental data indicates that the behavior of the viscosity of steam near the critical point is similar to that observed for other fluids near the critical point. An interpolating equation for the viscosity of water and steam is presented that incorporates the critical viscosity enhancement.Nomenclature a critical region equation of state parameter - a _k coefficients in equation for ₀ - a _ij coefficients in equation for ¯ - b critical region equation of state parameter - c _p specific heat at constant pressure - c _v specific heat at constant volume - k critical region equation of state parameter - k _B Boltzmann constant - P pressure - P _r 22.115 MPa - P ^* P/P _r - P _c critical pressure - P _i coefficients in critical region equation of state - R~P (P-P _c )/P _c - q parameter in equation for critical viscosity enhancement - r parametric variable in critical region equation of state - T temperature in K (IPTS-48) - T _r 647.27 K - T ^* T/T _r - T _c critical temperature - T (T–T _c )/T _c - V volume - critical exponent of specific heat - critical exponent of coexistence curve - critical exponent of compressibility - critical exponent of chemical potential at T=T _c - dynamic viscosity - ₀ lim ₀ - ¯ normal viscosity - critical viscosity enhancement - ¯ thermal conductivity - normal thermal conductivity - critical thermal conductivity enhancement - parametric variable in critical region equation of state - correlation length - ₀ correlation length amplitude above T _c at = _c - critical exponent of correlation length - density - _r 317.763 kg/m³ - ^* / _r - _c critical density - (– _c )/ _c - _p estimated error of pressure - _T estimated error of temperature - estimated error of viscosity - exponent of critical viscosity enhancement - _t (/P) _T symmetrized compressibility - _T ^* _T P _r / _r ² - _{t t} P _c / _c ²     

Temperature field in a plate containing a system of heat sources

The temperature field is determined in a circular plate with a system of thin extrinsic heat sources.Notation T temperature in the plate with the inclusions - r polar radius - polar angle - time - (r,) coefficient of thermal conductivity - (r,) heat transfer coefficient - C(r,) volume heat capacity - W(r,, ) specific intensity of the heat sources - half thickness of the plate - (x) Dirac's delta function - ¯T finite Fourier cosine transform of the temperature - p parameter for this transformation - T Laplace transform of the temperature - s its parameter - Iv(x) Bessel function with imaginary argument of order - K _v (x) the MacDonald function of order - and dimensionless temperature - Po Pomerantz number - Bi Biot number - Fo Fourier's number - dimensionless polar radius - b₁ ^* dimensionless radius of the circle on which the inclusions are placed - R^* dimensionless radius of the plate Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 495–502, March, 1981.     

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.     

Anisotropic spin diffusion and multiple spin echoes in3He-4He solutions

We propose a ₁-t₁-₂ pulse-NMR experiment to detect the spin-diffusion anisotropy, =D-D, in degenerate spin-polarized³He-⁴He mixtures, where D and dare the transverse and longitudinal spin diffusion coefficients. In such an experiment the nonlinearity of the dynamics produces multiple spin echoes (MSE). At the ³He concentration x₃ 4% the spinrotation parameter vanishes (M 0), so that the nonlinearity of the equations of motion is entirely due to the anisotropy. In this situation, detection of MSE amounts to observation of D. For slight anisotropy, i.e. D/D 0.25, we use a perturbation scheme similiar to that developed by Einzel et al. (in that case, for small M and small demagnetizing field) to calculate the second and third echo heights. For larger anisotropy we numerically calculate the echo heights. We find that for D/D = 0.5 the heights are 2 % of the first echo, and should be detectable. The (₁, ₂) tip-angle dependence of the D echoes is different from that of the M and demagnetization echoes, and furthermore, they occur at right angles to these echoes (in spin space). Thus, even when small spin-rotation and demagnetization effects are present, the ₁-t₁-₂ experiment provides a sensitive means of detecting the anisotropy.     

EPR studies of the valence states of thulium in thulium monochalcogenides

We have studied theGd ³⁺ EPR at 9.2 HGz in 0.1 at % GdS inTmS, 1 at %GdTe inTmTe, and 1 at %GdSe inTmSe. From the temperature dependence of theGd ³⁺ linewidth we have concluded thatTm inTmS is trivalent. The temperature variation of theGd ³⁺ linewidth inTmTe has been interpreted as the result of the delocalization of the extra electron localized aroundGd ³⁺ . Theg-value and linewidth data are consistent with the identification thatTm inTmTe is divalent. The linewidth and theg-value of theGd ³⁺ resonance inTmSe have been found to be temperature independent. These striking results have been attributed to the motional narrowing effect arising from valence fluctuations ofTm inTmSe.Work performed under the auspices of the U.S. ERDA.Supported in part by NSF.     

The effect of temperature on the transition from crazing to shear deformation in crosslinked polystyrene

Thin films (0.7m thick) of polystyrene (PS) are bonded to copper grids and crosslinked by exposure to electron irradiation. By controlling the exposure time it is possible to produce samples of PS having a range of network strand densities (entangled and crosslinked). After physical ageing at 75° C for 10 to 12 h the PS films are then strained in tension at various temperatures. Transmission electron microscopy is used to characterize the ensuing deformation as well as measure the local extension ratio in either a craze or a deformation zone. A transition from crazing to shear deformation is observed to occur with increasing values of . At a slow strain rate of 4.1×10^–6 sec^–1 and a temperature of 23° C this transition in the aged PS occurs at (10 to 14)×10²⁵ strands m^–3, whereas at the same strain rate and 90° C the transition occurs at (5.8 to 8)×10²⁵ strands m^–3. The transition from crazing to shear deformation with increasing v may be rationalized by considering the extra energy required to break more main-chain polymer bonds to form the craze fibril surfaces in the high- networks. As the temperature is increased the yield stress _y (which is assumed to be independent of ) decreases almost linearly to zero as T _g is approached. On the other hand the crazing stress may be approximated by S _c [ _y(T) ^1/2]^1/2. Thus at higher temperatures the transition from crazing to shear deformation is expected to occur at lower values of as observed.     

Heat exchange in two-phase flow about a surface located in a rectangular channel

Similitude equations are obtained on the basis of the principle of superposition of separate effects to calculate heat exchange between surfaces with complexshaped cross sections located in a rectangular channel during their cooling by a two-phase flow.Notation T, q temperature and heat flux - T_w mean surface temperature - I, R current and electrical resistance - V volume of the material - , , anda heat-transfer coefficients, thermal conductivity, and linear expansion of the material - relative functions - =_m; ^* = _m ^{* *} _s ^* ; temperature factor - X relative weight content of liquid phase Indices w surface - f incoming flow - v volume - m two-phase flow - angle of attack - s shape of surface - * pertains to surface with swirl vanes Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 5, pp. 780–786, May, 1980.     

The effective surface energy of brittle materials

The effective surface energy of four brittle materials, alumina, poly(methylmethacrylate), glass, and graphite, is calculated from load/deflection curves of notched bars deformed in three-point bending. Two of the methods, which are commonly used in fracture mechanics studies,viz the modified Griffith treatment and the compliance analysis method, are concerned with the effective surface energy at the initiation of fracture, _I . The third method, the work of fracture test, is concerned with the mean effective surface energy over the whole fracture process, _F . The two estimates of _I give consistent values, and there is no systematic variation of _I with notch depth. Values of _F decrease with increasing notch depth as the fracture process becomes more controlled. For alumina _{I F} . For PMMA and glass _I > _F because of a multiplicity of crack sources during fracture initiation. For graphite _I < _F because of subsidiary cracking as fracture proceeds.     

Regularizing algorithm for inverting the Abel equation

The article presents a regularizing algorithm for solving the Abel equation using information on the statistics of the error of measurement of the right-hand side of the equation.Notation (r), f(x) solution and right-hand side of the Abel equation, respectively - f_i value of the right-hand side measured at point x_i - _i uncertainty of the i-th measurement - n number of measurements of the right-hand side - V correlation matrix of the uncertainty of measurement - smoothing parameter - S_n(x) interpolating spline - S_n,(x) smoothing spline - a_i, b_i, c_i, d_i coefficients of the smoothing spline - (r) regularized solution of the Abel equation - e() discrepancy vector - Sp[V] trace of the matrix V Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 2, pp. 270–274, August, 1980.     

Effect of Intense Self-Irradiation on the Phase Composition of Metallic Plutonium

The crystal structure of film samples of "high-level" (based on ²³⁸Pu) and low-level (based on ²³⁹Pu) metallic plutonium during their prolonged (up to 343 days) storage (self-irradiation) at room temperature was studied by X-ray diffraction. In the samples of high-level plutonium, the -Pu and -Pu lattices coexist. In the period of 40-60 days, the other known crystal modifications of plutonium (-Pu, -Pu, -Pu, and -Pu) are also present. Low-level plutonium had only the -Pu lattice. A possible origin of this phenomenon is discussed.     

Formation of Friction Layers and Wear Resistance of Steels under Conditions of Boundary Friction

We studied the influence of the lubricant compositions Grafitol with 10% graphite (1), Aerol containing 17% MoS₂ (2), Limol containing 60% MoS₂ (3), Limol + 10% chlorine-paraffin (4), and Limol + 10% copper powder (5) on the wear rate and formation of the fine structure of surface friction layers of structural steels. We established a correlation between the tribological characteristics of steels and lubricants. The abrasive wear of 40KhFA steel was minimum if it was lubricated with Limol + 10% copper powder. In this case, its wear was smaller by a factor of 10, 2, 1.25, and 7.25 as compared with lubricant compositions 1–4, respectively. In the course of minimum wear of 40KhFA steel, in the surface friction layers, we observed the minimum values of second-kind distortions (a/a) and of the true size of domains of X-ray coherent scattering (D) as well as the minimum difference between the crystal lattice constants (a) of steel before and after friction.     

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.     

Relationship between superconductivity and band structures of electrons and phonons

The relationship between superconductivity and band structures of electrons and phonons is established on the basis of a generalized Bardeen-Cooper-Schrieffer model in which the interaction strengths (V ₁₁,V ₁₂,V ₁₂) among and between electron (1) and hole (2) Cooper pairs are differentiated. Elemental superconductors must have local hyperboloidal Fermi surfaces called necks or inverted double caps.     

A flat jet in a granular bed of finite height

The distribution of gas flows in the vicinity of the jet is discussed and the conditions of disruption of the static equilibrium of the bed, the formation and growth of a cavity, and the jet breakthrough of the bed are investigated qualitatively.Notation a, b functions calculated in [11] - C, C constants in (7) - F derivative of the complex potential - f function in (6) - G function defined in (19) - H dimensionless height of bed - h height of cavity - k coefficient introduced in (15) - p, po pressure inside bed and in cavity - p dimensionless pressure drop - Q, q dimensional and dimensionless jet flow rates - q₁, q₂ critical values - T dimensionless height of cavity - T₀, T₁ T₁, T₂ characteristic values of T - u,v filtration velocities - u, u_* initial filtration velocity in the bed and minimum fluidization velocity - u_o velocity scale introduced in (14) - u * velocity scale introduced in (14) - u* velocity of fictitious flow defined in (15) - U complex velocity - Z=X+iY, z=x+iy dimensionless coordinates - z=x+iy dimensional coordinates - coefficient of hydraulic resistance - parameter from (5) - specific weight of particles' material - porosity - =+i coordinates in the plane obtained from z=x+iy as a result a of conformai transformation - _m value of giving a minimum of the function G - f complex and real flow potentials - angle of internal friction - stream function - angle of inclination of boundaries of the region of plastic flow to the vertical Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 804–812, November, 1979.     

An extension of the theory of oscillating cup viscometers

The theory of the fluid motion in the interior of an oscillating or rotating cup is reexamined. The quantity of interest in viscometry is the torque exerted by the fluis on the sides and rims of the cup. In this paper expressions for the torque are obtained for geometries for which the cup height approaches a fluid boundary layer thickness. Interest in such geometries is due to viscosity measurements made in mixtures in the critical region where cups of small height are used in order to minimize gravity effects.Nomenclature D() Torque on the cup, Eq. (5) - E() Truncation error term, Eq. (24) - h Internal half-height of a filled cup or the height of the liquid in a partially filled cup - I Moment of inertia of cup and suspension system - I Moment of inertia of fluid inside cup - I _n Modified Bessel function of order n - J _{i, n} Defined in Eq. (13) - R Radius of the cup - S _n Defined in Eq. (7) - S _n Defined in Eq. (10) - x Variable 2 ₀/ - z Variable 2 ₀^1/2 - () Angular displacement of the cup - Boundary layer thickness - Logrithmic decrement - Laplace transform variable - ₀ Dimensionless height h/ - Frequency ratio / ₀ - Kinematic viscosity - ₀ Dimensionless radius R/ - Density of liquid - Dimensionless time ₀ t - Phase angle of oscillation - Angular frequency of oscillation with liquid present in cup - ₀ Angular frequency of oscillation in a vacuum