Three-dimensional surface singularity of an interface crack

The three-dimensional singularity field near the terminal point of an interface crack at the free surface of an elastic bimaterial is investigated. The Finite Element Iterative Method (FEIM) is used for evaluating the asymptotic field. A spherical coordinate system r, , is used and the singular displacement field is assumed to be of a product form r g(, ), where and g(.) are in general complex. To validate the model, the method is first applied to the three dimensional surface crack in a homogeneous elastic material. The results for this case show excellent agreement with previously published analytical and numerical results. For an extreme effect of bimaterial property mismatch, on the surface crack singularity, an elastic material bonded to a rigid substrate is investigated (E1/E2=). The results show that the complex power singularity depends strongly on Poisson's ratio . The real part of the stress singularity is greater than 0.5 of the plane strain case and the imaginary part becomes almost zero at 0·25 instead of at =0.5. The second term in the expansion of the asymptotic field was shown to have a singularity of 0.5.     

The Role of Dilatation in the Nonlinearly Viscoelastic Behavior of PMMA under Multiaxial Stress States

In order to better understand phenomena related to yield-like behavior of polymers, the nonlinear thermo-mechanical behavior of Polymethyl Methacrylate (PMMA) under combined axial (tension, compression) and shear stress states (torsion) is investigated on thin walled cylindrical specimens at temperatures between 22 and 110°C. In contrast to the mutual independence of shear and dilatational response under conditions appropriate for linearized viscoelasticity, one observes an increasingly strong influence of the first stress or strain invariant on shear creep at shear strains in excess of 0.5%. While shear stresses alone elicit nonlinear response in creep (rates) as intrinsically nonlinear shear response, the superposition of small positive dilatation accelerates shear deformations while negative dilatation retards it in qualitative agreement with free volume arguments when comparison is effected via maximum shear. In addition, an isochronal representation of the intrinsically nonlinear shear response demonstrates that the nonlinear behavior becomes more pronounced the closer one approaches the glass transition temperature from below.     

Thermodynamic properties of iron doped beta″-alumina by e.m.f. measurements with beta-alumina electrolytes

Thermodynamic studies of the non-stoichiometric iron doped beta-alumina (ID) phase were carried out by electrochemical measurements coupled with coulometric titration using the cell Na_liq/Li-alumina/ID. Hot pressing and glass sealing techniques were developed and employed to obtain a suitable and stable Li-alumina/ID interface. The equilibrium e.m.f. of the cell was determined as a function of sodium concentration over the temperature range 444 to 523 K. The range of sodium concentrations over which the ID phase is stable was also determined. The relative partial molar thermodynamic quantities of sodium, , , and in ID alumina as a function of sodium concentration were obtained from cell e.m.f. data.     

State of stress and strain of pressure vessels during pressurization

Kiev Polytechnic Institute, Kiev. Scientific and Production Association Kriogenmash, Balashikha, Moscow Region. Production Association Zhdanovtyazhmash, Zhdanov. Translated from Problemy Prochnosti, No. 6, pp. 69–74, June, 1988.     

Use of packed thermal diffusion columns to determine the soret coefficient in a benzene-carbon tetrachloride mixture

Experimental results of the determination of the Soret coefficient of a benzene-carbon tetrachloride mixture in a packed column with reservoirs at the ends are presented.Notation c concentration - density - z vertical coordinate - L length of the column - d diameter of the glass balls - coefficient of dynamic viscosity - coefficient of thermal expansion - k permeability of the packing - T temperature - B perimeter of the working gap - H and K transport coefficients - M mass of the fluid in the reservoir at the end of the column - M/BL - y Hz/K - H sg²k(T)²B/12) Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 503–506, September, 1981.     

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     

Temperature-density parameters of Freon-13 on the saturation line

Experimental data of a high degree of accuracy are presented on the temperature-density parameters of Freon-13 on the saturation line in the density range of (0.08246–1.6061)·10 kg/m³.Notation T absolute temperature of phase transition from two-phase to one-phase state (or vice versa) - T_c critical temperature - , densities of liquid and vapor, respectively, on saturation line - _c density at critical points - average density - =(T_c–T)/2 reduced temperature - parameter of order, equal to ' – _c – b for the liquid phase and _c + b – "for the vapor phase Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 830–834, November, 1979.     

Joule-Thompson effect in a disperse medium

An expression for the Joule-Thompson coefficient of a polydisperse medium subject to throttling is derived in the relaxation approximation of thermodynamics of irreversible processes, with both temperature and velocity relaxation in the phases taken into account.Notation A_qk, A_fk thermal and momentum interphase exchange affinities - _qk, _fk relaxation parameters - T, w temperature and velocity of a phase relaxation in the mixture - density of the mixture - T_o, T_k temperature of the carrier phase and of the k-th group of solid particles - p pressure of the carrier phase - h enthalpy of the mixture - W _o ² /2 specific kinetic energy of the carrier phase - _o, _k volume concentration of the carrier phase and of the k-th group of solid particles - _o, _k true density of the carrier phase and of the k-th group of solid particles - c_v and c_p constant-volume and constant-pressure specific heats of the mixture - c_k specific heat of the k-th group of solid particles - c_v, c_p constant-volume and constant-pressure specific heats, respectively, of the mixture referred to volume - _qk, _fk temperature and velocity relaxation times, respectively, of the k-th group of solid particles - t times - frequency in the Fourier series expansion - differential Joule-Thompson coefficient (adiabatic throttle effect) - N number of groups of particles in the mixture Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 825–829, November, 1979.     

Fast adiabatic heating and temperature relaxation in near-critical fluids under zero gravity

Heat transport in supercritical CO₂ is studied under microgravity conditions. A large temperature and density region around the critical point is explored (CO₂ cells were filled at critical density= _c and off-critical densities= _c±0.18 _c). Local heating is obtained by using a small thermistor located in the bulk fluid. Through interferometric observations, a new mechanism of thermalization has been evidenced. Thermal expansion of a warm diffusing boundary layer around the heating thermistor is responsible for rapid adiabatic heating of the bulk fluid through the emission of pressure waves at the border. The scaled thickness of the thermal boundary layer follows a power law. When the heat flow stops, the bulk adiabatic heating instantaneously vanishes and the temperature relaxation inside the thermal boundary layer follows locally a diffusive process.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Correlation between magnetic hysteresis and magnetic relaxation in YBaCuO single crystals

The dependence of the magnetic momentm obtained from the hysteresis loops on the speed of the magnetic field sweep =dH _ext/dt is explained on the basis of Anderson's interpretation of the magnetic flux creep. In addition, a phenomenological model is suggested which predicts a linear dependence ofm on ln with the slope m/ ln , numerically equal to the relaxation rate m/ ln(t) from the usual magnetic relaxation. Such linear relations betweenm and ln were observed experimentally in single crystals of YBaCuO. Preliminary experiments on the complementary time dependent relaxation ofm after a simulated step change ofH _ext gave mostly relaxation rates close to the predicted values. The model here presented also enables one to compare the critical state in the superconductor at a field sweep rate with the critical state at some timet _eff after a step change ofH _ext. The values of analyzed in our experiments actually correspond to the critical state at timest _eff between0.04 and4 sec after an imaginary large step change ofH _ext.     

The Nearly Classical Behavior of a Pure Fluid on the Critical Isochore Very Near the Critical Point Under the Influence of Gravity

Comprehensive measurements of the isothermal compressibility along the critical isochore in the critical region of pure sulfur hexafluoride (SF₆) and pure carbon dioxide (CO₂) were carried out. All measurements were performed with a multicell apparatus, especially designed for pT measurements in the critical region. The height of the measuring cells was either 30 or 11 mm. Independent of the cell height, we found for both fluids nearly classical values for the critical exponent in the limiting approach to the critical point. However, at a certain distance from the critical point {(T – T _c) 90 mK or 2.82 × 10^–4 for SF₆ and (T – T _c) 55 mK or 1.81 × 10^–4 for CO₂}, we observed a transition to values of the critical exponents which nearly meet the predictions of the renormalization-group theory. Since in the fitting range (T – T _c 1 mK) the correlation length ( 0.5 m) is very much smaller than the geometrical dimensions of the measuring cells, we conclude that the reason for the different behavior is an explicit gravity effect governing the inner critical region. The two different loci of the transition points for sulfur hexafluoride and carbon dioxide can be attributed to the different gravity impact on the fluid corresponding to the different critical densities of the two substances.     

Study of flow in a smectic liquid crystal in the X-ray Surface Forces Apparatus

We describe the newly invented X-Ray Surface Forces Apparatus (X-SFA) which allows the simultaneous measurement of forces and collective structures of confined complex fluids under static and flow conditions. The structure of the smectic liquid crystal 8CB (4-cyano-4-octylbiphenyl) f confined between two mica surfaces with separation ranging from 4000 to 20,000 A was measured. At small gaps and no shear, the smectic layers take on distinct stable orientations, including the bulk forbidden h orientation. which persist under low shear ( 30 s^–1). However, at higher shear rates 360 s^–1) the shear acts to dramatically order and align the smectic layers into a singlea orientation.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Viscoelastic and rheological behavior of concentrated colloidal suspensions

Molecular approaches are discussed to the density (), viscoeleastic (), and rheological () behavior of the viscosity(,,) of concentrated colloidal suspensions with 0.3 < < 0.6, where, is the volume fraction, the applied frequency, and ; the shear rate. These theories are based on the calculation of the pair distribution functionP ₂(r,,), wherer is the relative position of a pair of colloidal particles. The linear viscoelastic behavior(,,=0) follows from an equation forP ₂(r,,) derived from the Smoluchowski equation for small, generalized to large by introducing the spatial ordering and (cage) diffusion typical for concentrated suspensions. The rheological behavior(,,=0) follows from an equation forP ₂(r,) of a dense hard-sphere fluid derived from the Liouville equation. This leads to a hard-sphere viscosity^hs(,) which yields the colloidal one(,) by the scaling relation(,) ₀=^hs(,) _B, where ₀ is the solvent viscosity. _B is the dilute hard-sphere (Boltzmann ) viscosity and the's are appropriately scaled,(,) and(,) agree well with experiment. A unified theore for(,,) is clearly needed and pursued.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994. Boulder, Colorado, U.S.A.     

The process of heat and mass transport at the critical point of pure fluids

The effects of fast isentropic temperature propagation, called the piston effect, or critical speeding up, and slow mass diffusion, called critical slowing down, are investigated. A temperature propagation experiment in a spherical cell filled with pure SF₆ at critical density was performed during the Second German Spacelab Mission D2 in 1993. The results evidently confirm the presence of the piston effect both in the one-phase region and in the two-phase region. The numerical simulations are in remarkable good quantitative agreement with the experimental results.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Synthesis, crystal structure and X-ray powder diffraction data of the phosphor matrix 4SrO·7Al2O3

The white phosphor matrix 4SrO·7Al₂O₃ has been synthesized by firing the appropriate mixture of SrCO₃, Al(OH)₃ and H₃BO₃ in the molar ratios 1:3.5:0.135 at 1300°C for 4–7 h. The crystal structure of 4SrO·7Al₂O₃ has been determined as a orthorhombic Pmma space group with a=24.7451(2)Å, b=8.4735(6)Å, c=4.8808(1)Å, V=1023.41(3)ų, Z=2, and D=3.66 g cm^–3 by the Rietveld analysis. The refinement figures of merit are R_p=8.26, R_wp=11.60, R_bragg=4.44 and s=2.61 for 844 reflections with 2<119.94°. And the corresponding X-ray powder diffraction data are presented for search/match analysis.     

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.     

Structure of martensite formed in Cu-Al-Fe single crystals duringin situ HVEM pseudoelastic tensile experiment

Single crystals of the CuAlFe alloy, containing 14.5 wt% Al and 2.2 wt% Fe were subjected toin situ tensile experiment using straining attachment in a 1 MV electron microscope. Loadelongation curves were obtained for three foil plane/tensile direction orientations: (001) [0 1 0], (0 0 1) [1 1 0] and (1 1 0) [¯1 1 2]. Each crystal was subjected to two cycles of pseudoelastic deformation up to maximum 2% strain, showing almost complete shape recovery. Structure observations and electron diffraction pattern indicated that during deformation of samples of (0 0 1) [1 1 0] and (1 1 0) [1 1 2] orientations, formation of ₁ martensite was observed and only at later stages narrow needles of ₁ nucleate in front of ₁. During pseudoelastic deformation in the (0 0 1) [1 0 0] direction, martensite forms as a mixture of narrow plates possessing either 2H or 18R structures. The following crystallographic relationship between the parent phase and both types of martensite was observed: [1 00] ₁ [101] ₁ and (0 0 1) ₁ (0 1 0)₁;(0 0 1) ₁ (0 1 0) ₁ and [1 1 0] ₁ [0 0 1] ₁. From the character of sidebands reflections presence of 1 0 1 1 0¯1 static displacement waves was inferred.     

Hydrodynamic similarity in an oscillating-body viscometer

Hydrodynamic similarity can be used to calibrate simply and accurately an oscillating-body viscometer of arbitrarily complicated geometry. Usually, an explicit hydrodynamic model based on a simple geometry is required to deduce viscosity from the transfer function of an oscillating body such as a vibrating wire or a quartz torsion crystal. However, at low Reynolds numbers the transfer function of any immersed oscillator depends on the fluid's viscosity only through the viscous penetration depth(2/)^1/2. (Here and are the fluid's viscosity and density and/2 is the oscillator's frequency.) This hydrodynamic similarity can be exploited if the oscillator is overdamped and thus is sensitive to viscosity in a broad frequency range. Even an oscillator of poorly known geometry can be characterized over a range of penetration depths by measurements in a fluid of known and over the corresponding range of frequencies. The viscosity of another fluid can then be compared to that of the calibrating fluid with high accuracy by varying the frequency so that the penetration depth falls within the characterized range. In the present work, hydrodynamic similarity was demonstrated with a highly damped viscometer comprised of an oscillating screen immersed in carbon dioxide. The fluid's density was varied between 2 and 295 kg·m^–3 and the fluid's temperature was varied between 25 and 60°C. The corresponding variation of the viscosity was 50%.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

A scaling parameter for He II thermal counterflow and critical heat currents

A scaling parameter for He II thermal counterflow is developed from a consideration of the stability of the normal fluid component in the presence of superfluid vortex production. Observations of superfluid entrainment are combined with a reinterpretation of the mutual friction force to define the scaling parameter which is shown to be independent of temperature and geometry at the critical heat current.Work supported by National Science Foundation grants GP 13381 and GP 27242.