Effect of Grain Size on the Modulus of Elasticity and Strength of Synthetic Graphites

The effect of the grain size of the filler on the mechanical properties (compressive, bending, and tensile strength and modulus of elasticity) of synthetic graphite is analyzed using data for commercial structural graphites. As the mean particle size of the filler (_av) decreases from 3000 to 1 m, the modulus of elasticity increases, on the average, from 10 to 15 GPa, and the compressive, bending, and tensile strength increases by about one order of magnitude. The Griffith equation is used to evaluate the size of defects that initiate fracture (c _c) in different types of graphites. It is shown that the factors determining the critical defect size depend on the particle size of the filler. For _av > 150 m, c _c is comparable to _av or _max. In the range 30 < _av < 150 m, c _c is equal to or greater than _max. In graphites with _av < 30 m, c _c far exceeds _max and, presumably, corresponds to the particle size of the molding powder.     

Die Entwicklung von Längswirbeln in zeitlich anwachsenden Grenzschichten an konkaven Wänden

Zusammenfassung Messungen des Anwachsens von Längswirbeln in zeitlich anwachsenden Grenzschichten an konkav gekrümmten Wänden (Görtler-Taylor-Wirbel) ergaben drei deutlich getrennte Bereiche: Es traten zunächst Wirbel mit der Wellenläge 0,9 auf (=Grenzschichtdicke, =Höhe einer Zelle, die zwei gegensinnig drehende Wirbel enthält). Je nach Größe der mit der Verdrängungsdicke ₁ der Grenzschicht gebildeten Reynolds-Zahl erschienen dann kurze Zeit später Wirbel mit 2,5, wenn war. Im Bereiche dagegen traten stattdessen bei den hier durchgeführten Versuchen immer Wirbel mit der Wellenlänge 6,5 auf. Bei werden die ersten Tollmien-Schlichting-Wellen mit der Wellenlänge _TS 6· angefacht. In ihren wandnahen Bereichen der Wellentäler könnten sich dann die oben genannten Längswirbel der Wellenlänge 6,5· ausbilden, die die zwei-in eine dreidimensionale Störung allseits gleicher Größenordnung verwandeln können.

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The development of longitudinal vortices in boundary layers growing with time along concave walls

Summary Measurements of the growth of longitudinal vortices in boundary layers growing with time along concave walls (Görtler-Taylor vortices) rendered three distinctly separated regions. First, vortices with a wave-length 0.9 appeared (-boundary layer thicness, =height of a cell containing two counterrotating vortices). Then, depending on the Reynolds number R _{a 1}/v ₁=displacement thickness), vortices with 2.5 appeared shortly afterwards, provided . In the region , however, the wave-length was 6.5. For the first Tollmien-Schlichting waves with _TS 6 were excited. In the wave-throughs close to the wall the abovementioned longitudinal vortices with wave length 6.5 may then be formed. This might transform the two-dimensional into a three-dimensional flow of equal order of magnitude in all directions.

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Zeichenerklärungen R _a Innenradius - Re _a Reynolds-Zahl gebildet mit dem InnenradiusR _a - Reynolds-Zahl gebildet mit der Verdrängungsdicke ₁ - kritische Taylor-Zahl - h Standhöhe der Flüssigkeit im Zylinder - t Zeit - z Anzahl - Steigungswinkel der Geraden - Grenzschichtdicke - ₁ Verdrängungsdicke - Wellenlänge (enthält ein gegensinnig rotierendes Längswirbelpaar) - v kinematische Zähigkeit - Winkelgeschwindigkeit Indizes K Knickpunkt der Geradensteigung - L unterhalb des Knickpunktes der Geradensteigung - TS Tollmien-Schlichting - e Einsatz der Wirbelentstehung     

Nonlinear asymptotic theory of hypersonic flow past a circular cone

Summary The hypersonic small-disturbance theory is reexamined in this study. A systematic and rigorous approach is proposed to obtain the nonlinear asymptotic equation from the Taylor-Maccoll equation for hypersonic flow past a circular cone. Using this approach, consideration is made of a general asymptotic expansion of the unified supersonic-hypersonic similarity parameter together with the stretched coordinate. Moreover, the successive approximate solutions of the nonlinear hypersonic smalldisturbance equation are solved by iteration. Both of these approximations provide a closed-form solution, which is suitable for the analysis of various related flow problems. Besides the velocity components, the shock location and other thermodynamic properties are presented. Comparisons are also made of the zeroth-order with first-order approximations for shock location and pressure coefficient on the cone surface, respectively. The latter (including the nonlinear effects) demonstrates better correlation with exact solution than the zeroth-order approximation. This approach offers further insight into the fundamental features of hypersonic small-disturbance theory.Notation a speed of sound - H unified supersonic-hypersonic similarity parameter, - K hypersonic similarity parameter, M - M freestream Mach number - P pressure - T temperature - S entropy - u, v radial, polar velocities - V freestream velocity - shock angle - cone angle - density - density ratio, /() - ratio of specific heats - polar angle - stretched polar angle, / - (), (), () gage functions     

A gradient method of defining smooth solutions to inverse boundary-value problems in thermal conduction

An iterative algorithm is described for solving boundary-value inverse problems in thermal conduction by steepest descent, which utilizes information on the smoothness of the solution.Notation A, B linear operators - u element of solution space U - f exact reference data - f reference data uncertainty - value of reference data uncertainty - A^–1 inverse operator - u^(k)() k-th derivative of function u - _m length of observation interval - _i(t) polynomials of degree i–1 - A^*, B^*, L^* operators conjugate to the operators A, B, L - Jg discrepancy functional gradient - _n descent step along the discrepancy antigradient for the n-th iteration - K( –) kernel of integral equation - q() heat flux - T() measured temperature inside body Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 2, pp. 259–263, August, 1980.     

Piezoelectric and mechanical properties of ceria-doped lead zirconate titanate ceramics

Phases, microstructures and properties of lead-zirconate-titanate (PZT) ceramics with the compositions Pb(Zr_0.535– Ce Ti_0.465) O₃ where =0.0, 0.001, 0.01, 0.02 and 0.05 were studied. Rhombohedral and tetragonal phases were present at =0.0. The amount of the rhombohedral phase increased with increasing , and only the tetragonal phase was present for >0.001. Thec/a ratio of the tetragonal phase also increases with increasing . Particles of CeO₂ were found to be present in compositions with >0.01, indicating that the solubility of CeO₂ is less than 1a/o on the metals basis. The piezoelectric and electromechanical constants achieved maximum values for =0.001. The hardness increased monotonically with increasing . The modulus of rupture and the fracture toughness, however, went through a minimum and both stayed lower than their values for =0.     

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.     

Types of superplasticm-δ curves of Ti-6Al-4V alloy and their intertransformation

The superplasticm- curves of Ti-6Al-4 alloy have been determined at different temperatures and strain rates; all were of them _L=m _max type, and were of either fundamental, descending or ascending types. The latter two types were transformed from the former through the processes ofm _Lm _O, _LO andm _Lm _F, _LF, respectively. The highest total elongation, _F, was 1150% obtained at 950C and 1.55×10^–3 s^–1. The Chin Liu equation has been applied to all types ofm- curves. The parameters characteristic of all types ofm- curves have been obtained and were found to vary with temperature and strain rate. The total elongation, _F, is determined by the resultant effects of all other parameters, not by a singlem value, theoretically considered to be constant and determined practically by a tensile strain of about 30%–50% (m _30%–50%) as usual.Nomenclature C (=k/k _o ) the normalized slope ofm- curve corresponding to - a material constant corresponding to - m strain-rate sensitivity index corresponding to - m _max maximum on them- curve corresponding to _L - m _min minimum on them- curve corresponding to _L - crosshead speed during the tensile test - the strain of the entire stretching process (has same significance as ordinarily adopted ) - _F total elongation at fracture chosen for the present work - _I intermediate strains including _I1, _I2, _I3, ..., _I(i–1), _Ii , _I(i+1), ..., chosen for the present work - _L limit strain separatingm- curves into sections - _O (=0) starting strain - strain rate - flow stress     

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.     

Relationship between the energy supply parameters and the physicochemical l characteristics of polymer compositions during drying and thermal processing

The effect of the type of energy supply on the formation of temperature and concentration fields in the thermal processing of polymer compositions is considered.Notation T₀, T initial and current temperature of the coating - T_m temperature of the air - =(T-T_o)/(T_m-T₀) dimensionless temperature of the coating - a thermal diffusivity - A absorption power of the coating - D diffusion coefficient - thermal conductivity - c thermal capacity - density - _k convective heat transfer coefficient - i number of moles of reacting groups per unit volume of polymer - K₀ factor in front of the exponential - R gas constant - u concentration - Q thermal effect of the reaction - q_n density of the incident radiant flux - =x/ dimensionless coordinate over the thickness of the coating - Ki=Aq_n /(T_m-T₀) Kirpichev criterion characterizing the thermal effect of the reaction - Ki_p=Qi/c (T_m-T₀) analog of the Predvoditelev criterion, characterizing the rate of occurrence of a chemical excess in the system - Bu= Bouguer criterion - Lu=D/a Lykov number - Fo=a/² Fourier number - Bi= _k Biot number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 26–33, July, 1980.     

Stability of the nonequilibrium state of a superconductor irradiated by an electromagnetic field

Irradiation of a superconductor by an electromagnetic field with a frequency ₀ larger than twice the energy gap (order parameter) decreases the order parameter . We obtain the quasiparticle distribution function n and the dependence of the order parameter on the power of the electromagnetic field P by solving numerically the kinetic equations for n and in the steady state. We take ₀/₀ = 2.1, 8, and 20, where ₀ is the equilibrium value of the order parameter at T = 0 K. In the examples considered the dependence of on the pumping power P becomes double-valued above a critical power. We allow phonons also to be out of thermal equilibrium. To discuss the stability of the steady state thus obtained, we derive kinetic equations for small deviations of the quasiparticle distribution function and the order parameter from the steady state n and by means of the nonequilibrium Green's function theory. Assuming n, exp(i kr – t), (k) is computed using n _s/, where n _sis the steadystate quasiparticle distribution function for arbitrary . It is concluded in general that the steady state on the upper branch ( > _{c 2}) is stable with respect to both spatially homogeneous and inhomogeneous fluctuations, and the lower branch ( > _{c 2}) is unstable; _{c 2}is the value where the upper and lower branches of (P) coalesce.This work is partly supported by a Grant-in-Aid for Special Project Research from the Ministry of Education, Science and Culture of Japan.     

Dependence of helium II viscosity properties on oscillation frequency

The causes of a discrepancy in the results of measurements of He II viscosity below T 1.6 k obtained with different measurement methods are investigated. It is shown that to obtain correct results in oscillation experiments, the condition _ph should obtain, where is the depth of viscous wave penetration and _ph is the phonon free path length. Results of viscosity measurements at different ratios /_ph (by a wire viscometer) are presented. It is shown that for the condition _ph, the results obtained are in good agreement with the results of Andronikashvili (in which /_ph > 100). If the mentioned relation is not satisfied, then, as the value of the ratio /_ph is decreased, the value measured for the viscosity is increasingly lower than the results of Andronikashvili.     

Temperature and randomness dependence of the pair-breaking parameter in superconducting aluminum films

Magnetoconductance and excess conductance due to superconducting fluctuations in aluminum films are measured in order to study the temperature dependence of the pair-breaking parameter at temperatures nearT _c . The parameter _M is estimated from the relation =/8k _B T_in, where _in is the inelastic scattering time deduced from the analysis of the magnetoconductance. The parameter _F is determined by fitting theories to data on the excess conductance at zero magnetic field. It is shown that: (1) For films with a wide range of the sheet resistanceR , 12R 200 /, the temperature dependence of _M nearT _c agrees well with the theory of Brenig et al. (2) For clean films withR 100 /, the value of _F analyzed with theories including the correction term to the Maki-Thompson contribution shows almost the same temperature dependence as _M . In a film withR 200 /, however, a discrepancy between _M and _F remains.On leave from College of General Education, Kyushu University, Ropponmatsu, Fukuoka, Japan.     

Variation of the Kondo temperature with the nature and concentration of the solute metal

From the available data on the physical properties of dilute magnetic alloys, Daybell and Steyert obtain V-shaped semilog plots ofT _K vs. N (whereT _K is the Kondo temperature andN is the serial number of the magnetic solute in the 3d series). This requires a large variation in the rather small exchange interaction parameterJ, while the Kondos–d exchange model is based on a smallJE _F (whereE _F is the Fermi energy). Taking the ordinary scattering into account,T _K =T _F exp((1– cos ²)/(JD cos²)), whereJ<0, 1, is the phase shift for ordinary scattering, andD is the density of states of one spin direction per atom. It has been shown by us recently, from the concentration dependences of the Kondo slopes and the extremum values of the thermoelectric power of dilute magnetic alloys, that 0<d shells, and 3/4<< for those having less-than-half filled 3d shells. We show, on this basis, that the range of variation ofJ is now reduced to more acceptable values, as the solute metal traverses the 3d series. Again, based on our inference that increases with the increase of the solute concentrationc, we show that an increase of the more-than-half filled solute concentration decreasesT _K , while the increase of the less-than-half filled solute concentration increasesT _K . The fact that the increase of cobalt content in copper or gold favors magnetism while the increase of vanadium content in gold favors nonmagnetism is understandable on this basis.     

Dielectric properties of LiF single crystals

The dielectric constant,, loss, tan, and a.C. Conductivity, , of high quality single crystals of LiF have been measured in the frequency range 10² to 10⁵ Hz and in the temperature range 30 to 400° C. of LiF at 30° C is 8.3 and is frequency independent; tan was below detection level (tan<0.0001). increases slowly with temperature up to about 150° C (frequency independent region) beyond which it rises rapidly, being frequency dependent with larger values at lower frequencies. A similar behaviour is exhibited by tan . The activation energy for conduction in the high temperature region is calculated to be 0.93 eV from log against 1/T graphs. Log () against 1/T plots (where is the difference between the dielectric constant at any temperature and the value at room temperature, 30° C) yields an activation energy value of 1.0 eV in the high temperature region. This activation energy is found to be independent of frequency. This agreement between the two activation energy values, one for the a.c. conductivity and the other for the increase with temperature. This suggests that the same charge carriers are responsible for the two processes in the high temperature region.     

Dielectric properties of synthetic quartz crystals

The dielectric constant (K) and loss (tan), and hence the conductivity), of high-quality synthetic quartz crystals have been measured with the electric field parallel (or perpendicular) to the optical axis (c-axis). These measurements are carried out in the frequency region 102 to 10⁷ Hz and in the temperature range 30 to 400° C. Values ofK at 30° C areE c 4.58 andE c 4.36, and these are frequency independent; tan), values are quite low,E c having larger values at 10² Hz compared toE c. The temperature variation ofK at different frequencies exhibits two regions: (i) a slow increase up to about 280° C which is frequency independent, and (ii) a fast increase beyond 280° C which is frequency dependent,K having larger values at lower frequencies; similar behaviour is exhibited by tan. Log), against 1/T plots show the usual extrinsic and intrinsic regions. The values for activation energy for conduction in the intrinsic region are calculated to be 0.85 and 1.0 eV, respectively, forE c andE c. An attempt is made to understand these results.     

Bounding-surface plasticity: Stress space versus strain space

Summary A bounding-surface plasticity model is formulated in stress space in a general enough manner to accommodate a considerable range of hardening mechanisms. Conditions are then established under which this formulation can be made equivalent to its strain-space analogue. Special cases of the hardening law are discussed next, followed by a new criterion to ensure nesting. Finally, correlations with experimental data are investigated.Notation (a) centre of the stress-space (strain-space) loading surface; i.e., backstress (backstrain) - ^* (a ^*) centre of the stress-space (strain-space) bounding surface - (a ) target toward which the centre of the stress-space (strain-space) loading surface moves under purely image-point hardening - (b) parameter to describe how close the loading surface is to nesting with the bounding surface in stress (strain) space; see (H10) - (c) elastic compliance (stiffness) tensor - (d) parameter to describe how close the stress (strain) lies to its image point on the bounding surface; see (H10) - (D) generalised plastic modulus (plastic compliance); see (1) - function expressing the dependence of the generalised plastic modulus on (plastic complianceD ond) - ^* (D ^*) analogue to (D) for the bounding surface - function expressing the dependence of ^* on (D ^* ond) - () strain (stress) - ' (') deviatoric strain (stress) - ^P ( ^R ) plastic strain (stress relaxation); see Fig. 1 - () image point on the bounding surface corresponding to the current strain (stress) - _iso (f _iso) at the point of invoking consistency, the fraction of local loading-surface motion arising from a change of radius; i.e., fraction of isotropic hardening in the stress-space theory - _kin (f _kin) at the point of invoking consistency, the fraction of local loading-surface motion arising from a change in the backstress (backstrain); i.e., fraction of kinematic hardening in the stress-space theory - _nor (f _nor) at the point of invoking consistency, the fraction of backstress (backstrain) motion directed toward the image stress (strain); i.e., the image-point fraction of the kinematic hardening in the stress-space theory - _ima (f _ima) at the point of invoking consistency, the fraction of backstress (backstrain) motion directed toward the image stress (strain); i.e., the image-point fraction of the kinematic hardening in the stress-space theory - function relating _iso to , , and (f _iso tob,d, andl) - function relating _kin to , , and (f _kin onb,d, andl) - function relating _nor to , , and (f _nor onb,d, andl) - function relating _ima to , , and (f _ima onb,d, andl) - the fraction of outwardly normal bounding-surface motion at the Mróz image point which arises from a change of radius - the fraction of outwardly normal bounding-surface motion at the Mróz image point which arises from a change in the centre - function relating _iso ^* to (f _iso ^* tod) - function relating _kin ^* to (f _kin ^* tod) - (l) parameter to describe the full extent of plastic loading up to the present, giving the arc length of plastic strain (stress relaxation) trajectory; see (H10) - function relating the direction for image-point translation of the loading surface to various other tensorial directions associated with the current state; see (H5). With 6 Figures     

Effect of resonant impurity scattering on collective mode peaks in the ultrasound attenuation of heavy fermion superconductors

We have calculated the attenuation of longitudinal ultrasound due to real order parameter fluctuations in impure polar and planarp-wave superconductors. The quasiparticle self-energy and the corresponding vertex corrections have been included in thet-matrix approximation for arbitrary scattering rate =1/2_N and all scattering phase shifts _N (0 _N/2). We obtain sound attenuation peaks belowT _c whose heights, positions, and shapes depend on ₀ (sound frequency), (₀), _N, and (coupling strength due to particle-hole asymmetry). The peaks become much more distinct and sharper for _N =/2 (resonant scattering by impurities) than for _N=0 (Born approximation). By choosing , _N, and suitably, qualitative agreement between calculated and observed peaks in UBe₁₃ and UPt₃ can be achieved.     

Swelling parameter of polypropylene used in household appliances

Samples of unfilled copolymer polypropylene were immersed in various solvents and the equilibrium swelling was recorded. Two-dimensional solubility maps of the Hildebrand parameter, , versus hydrogen bonding parameter, _c, and _h versus _v for polypropylene were plotted. Using the calculated percentage swell values and the solubility maps, the and _h values for detergent were postulated. No changes in the polypropylene backbone were revealed by mid- or far-infrared spectra, showing that the polypropylene polymer, when subjected to a number of different solvents, had not altered substantially.     

The effect of Ag additions on the microstructure of aluminium–lithium alloys

Minor quantities of Ag have been added to Al–Li–Cu–Mg–Zr alloys. Their microstructure has been studied by means of optical metallography, transmission electron microscopy and X-ray diffraction. In the high Li, low Cu : Mg ratio alloys the main phases found were , , S and T₁, while fewer T₂ and Al₇Cu₂Fe precipitates were also observed. The addition of up to 0.5 wt% Ag diminishes the and T₁ precipitates size. This is attributed to a small increase of Li solubility in the matrix. In the low Li, high Cu : Mg ratio alloy the addition of 0.2 wt % Ag resulted in the precipitation of phase simultaneously with , , S and T₁ phases. Due to the low Li concentration an unusual growth of the / precipitates at the expense of the precipitates was also observed.