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.     

The age hardening effect in Ti-6 Al-4 V due to ω and α precipitation in the β grains

The structure at room temperature of a quenched TA6V titanium alloy has been investigated. This structure is + or + according to the treatment temperature; it is always metastable. During ageing the grains decomposed by the reaction + + +; this decomposition was accompanied by a large increase of the 0.2% yield stress. No structural modification was observed in. The and phase of TA6V were separately investigated in the form of single-phase alloys. The hardness of was insensitive to ageing, while was considerably hardened by and; we deduced that the strengthening of the minor phase during ageing is mainly responsible for the hardening of TA6V.     

Distribution of α-AlFeSi and β-AlFeSi particles in surface layer of AA6063 alloy billets after heat treatment

We developed the EPMA mapping method of small -AlFeSi(Al_8.3Fe₂Si) and -AlFeSi(Al_8.9Fe₂Si₂) particles in the billets of Al-Mg-Si alloys such as AA6063 alloys. To discriminate between -AlFeSi and -AlFeSi particles we used the relative X-ray intensities of Fe/Si ratio, the I _Fe/I _Si ratio, instead of the Fe/Si mass ratio. To obtain the I _Fe/I _Si ratio, we used a Monte Carlo method. In this study, using this method the mapping of -AlFeSi and -AlFeSi particles in the surface layer of AA6063 billets after the heat treatment (for 2 h at 580°C) was done. Namely, the distribution of -AlFeSi and -AlFeSi particles of zones from the billet surface to a depth of 800 m was measured. Results showed the zone from the surface to a depth of 200 m was occupied mainly by -AlFeSi particles and the zone from a depth of 200 m toward the center was occupied mainly by -AlFeSi particles. From these results, it was found that if we remove zones from the surface to a depth of 200 m, we can remove the majority of the -AlFeSi particles, and thus improve the quality of anodizing performance of Al-Mg-Si alloys extrusions.     

Standard Gibbs' energies of formation of BaCuO2, Y2Cu2O5 and Y2BaCuO5

The Gibbs' energies of formation of BaCuO₂, Y₂Cu₂O₅ and Y₂BaCuO₅ from component oxides have been measured using solid state galvanic cells incorporating CaF₂ as the solid electrolyte under pure oxygen at a pressure of 1.01×10⁵ Pa BaO + CuO BaCuO₂ G _f,ox ^o (± 0.3) (kJ mol^–1)=–63.4–0.0525T(K) Y₂O₃ + 2CuO Y₂Cu₂O₂ G _f,ox ^o (± 0.3) (kJ mol^–1)=18.47–0.0219T(K) Y₂O₃ + BaO + CuO Y₂BaCuO₅ G _f,ox ^o (± 0.7) (kJ mol^–1)=–72.5–0.0793T(K) Because the superconducting compound YBa₂Cu₃O_7– coexists with any two of the phases CuO, BaCuO₂ and Y₂BaCuO₅, the data on BaCuO₂ and Y₂BaCuO₅ obtained in this study provide the basis for the evaluation of the Gibbs' energy of formation of the 1-2-3 compound at high temperatures.     

γ ? α2 Phase transformation in fractured high temperature stress rupture Ti-48Al-2Nb(at.%)

The ₂ phase transformation in fractured high temperature stress rupture Ti-48Al-2Nb(at.%) alloy has been studied by analytical electron microscopy. ₂ and phases were found at grain boundaries. ₂ layers that suspended in layers and interfacial ledge higher than 2d ₍₁₁₁₎ at /₂ interfaces were observed in the lamellar grains. These facts indicated that ₂ phase transformation and dynamic recrystallization have occurred during high temperature stress rupture deformation. It can be concluded that deformation induced ₂ phase transformation and dynamic recrystallization resulted in the presence of particles at grain boundaries. A structural and compositional transition area between deformation-induced ₂(or ) and its adjacently original (or ₂) phases was found by HREM and EDS and is suggested as a way to transform between and ₂ phase during high temperature stress rupture deformation. The transition area was formed by slide of partial dislocations on close-packed planes and diffusion of atoms.     

The Interplay of Electronic and Nuclear Magnetism in PtFe x at Milli-, Micro-, and Nanokelvin Temperatures

We have measured ac susceptibility, nuclear magnetic resonance, and nuclear heat capacity of two PtFe _x samples with concentrations of magnetic impurities x = 11 ppm and 41 ppm at magnetic fields (0 ± 0.05) mTB248 mT. The susceptibility data have been measured at temperatures of 0.3 KT100 mK, no hint for nuclear magnetic ordering could be detected to a temperature of 0.3 K. The nuclear heat capacity data taken at 1.4 KT10 mK show enhanced values which scale with x at low polarization. This effect is described by a model assuming an internal magnetic field caused by the impurities. No indication for nuclear magnetic ordering could be detected to 1.4 K. The nuclear magnetic resonance experiments have been performed on these samples at 0.8 KT0.5 mK and 2.5 mTB22.8 mT as well as on three other samples with x = 5, 10, 31 ppm in a different setup at 40 KT0.5 mK and at 5.4 mTB200 mT. Spin-lattice and effective spin-spin relaxation times ₁and ₂ ^* of ¹⁹⁵ Pt strongly depend on x and on the external magnetic field. No temperature dependence of ₁and ₂ ^* could be detected and the NMR data, too, give no hint for nuclear magnetic ordering to 0.8 K.     

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.     

Microstructures of titanium-aluminides produced by laser surface alloying

The microstructures of Ti-Al layers (from 43–80 at %Al) produced by laser surface alloying of titanium substrate with a powder feed technique have been investigated. The laser processing parameters were; 1.8 kW laser power, 3 mm beam diameter, 7 mm s^–1 traverse speed, and values of powder flow rates of aluminium ranging from 0.07–0.11 g s^–1. The microstructures were dendrites of ₂ and interdendritic regions of ₂+ in the Ti-43 at %Al alloy; dendrites of either ₂ or ₂+ with interdendritic in the Ti-50 at %Al alloy; dendrites of ₂+ with interdendritic in the Ti-55 at %Al alloy; single phase in the Ti-60 at %Al alloy and TiAl₃ dendrites and Al solid solution in the interdendritic regions in the Ti-80 at %Al alloy. The microstructures were fine and comparable to those produced by other methods of rapid solidification processing. The microstructures of the Ti-50 and Ti-55 at %Al alloys were in agreement with the existence of the peritectic reactions:L + andL + , in the Ti-Al system.     

The influence of ageing on the stability of β-γ/γ′ derived microstructures in Ni-Al-Cr-(Co) alloys

Multiphase Ni-Al-(Fe)-(Cr)-(Co)-based intermetallics with (B2)- (A1)/(L1₂), - or - microstructures can exhibit significant room-temperature tensile ductility. In the case of Ni-Al-Cr-based alloys, microstructural development is complicated by the precipitation of -Cr, which can supplant the -phase during ageing of three-phase -/ microstructures. An investigation of the stability, during ageing, of cast Ni-Al-Cr-(Co) alloys with microstructures derived from -/ is reported. In the as-cast condition, the materials investigated consisted of a dendritic matrix containing L1₀ type martensite and interdendritic /. Extensive intra- and interdendritic -Cr precipitation was also observed. The stability during ageing of the interdendritic / microstructure is also considered and transformation of the L1₀ martensite is examined.     

Evidence for collective excitations in superconducting tin whiskers

Based on the assumption that a phase-slip center in a clean quasi-one-dimensional superconductor excites a collective oscillation, the time-averaged value of the electrochemical potential of quasiparticles is calculated. At larger distances from the phase-slip center, swings below (or above) the electrochemical potential _p of the Cooper pairs. This makes it possible to understand the unexpected results of previous measurements.     

Complex microstructural changes in as-cast eutectoid Zn-Al alloy

Phase transformations and microstructural changes of an as-cast eutectoid Zn-Al alloy (ZnAl₂₂Cu₂) were investigated during isothermal holding. The typical dendritic structures consisted of _s phase as a core with the edge of decomposed _s phase and decomposed _s in the interdendritic regions. A series of complex phase transformations was observed. Both decompositions of _s and _s were determined at an early stage of ageing and a four-phase transformation, _f+T+, was observed at the boundaries of _f phase and the phase, instead of clearly observed at the boundaries of phase, in a solution-treated Zn-Al alloy during prolonged ageing.     

Radiofrequency size-effect measurements of the electron scattering frequency in cadmium

Precise parallel- and tilted-field radiofrequency size-effect measurements of the temperature dependence of the electron scattering frequency v(T) have been made on symmetric orbits on the first-, second-, and third-band Fermi surface sheets in samples with normals 11\-20 and 10\-10. The limiting point measurements on the third-band lens near 0001 provide the clearest evidence for a T ² contribution to v(T) that is the right order of magnitude for electron-electron scattering in cadmium. In parallel field measurements on orbits on the first and second bands (including a broken orbit) we find v(T) T ² + T ³. On these orbits the values for are 5–20 times larger than for the limiting point and other orbits on the third band. The temperature dependence of v(T\> 2 K) on extremal, limiting point, and open orbits on the second- and third-band Fermi surface sheets can be well accounted for by a simple plane wave model for electron-phonon intersheet scattering. This contribution to v(T) turns on approximately as exp (–T _t /T) above T _t /10, where T _t is the minimum gap temperature on the orbit for intersheet scattering by quasi-transversely polarized phonons. The fitted gap temperatures as well as the other parameters of the plane wave model agree well with the known dimensions of the Fermi surface of cadmium. While clear evidence is lacking, we note that this intersheet scattering model can also be used to explain the large T ² coefficients obtained for the first- and second-band orbits, where, in fact, one has gap temperatures T _t smaller than 1 K.Supported by the Fonds National Suisse de la Recherche Scientifique.     

Phase decomposition of liquid-quenched β-type Ti-Cr alloys

Phase decomposition behaviour of liquid-quenched (bcc) type Ti-Cr alloys was investigated by means of transmission electron microscopy and hardness measurements. It was found that decomposition of to ₁ (Ti-rich, bcc) + ₂ (Ti-lean, bcc) takes place in the intermediate composition range of the Ti-Cr system. This experimental result proves the theoretical prediction made by Menon and Aaronson, but the observed ₁ + ₂ two-phase field expands towards higher temperatures than the predicted binodal line. The coherent ₁ + ₂ two-phase state exhibits the so-called 100 modulated structure and it was concluded that the formation of such a structure is a result of spinodal decomposition of the -phase. We obtained time-temperature-transformation (TTT) diagrams of -type Ti-30, 40 and 50 at % Cr alloys. A typical sequence of structural change is coherent ₁ + ₂ incoherent ₁ + ₂ incoherent ₁ + ₂ + grain boundary precipitates stable state of + TiCr₂ or + TiCr₂. Not all the states in the above sequence appear, depending on alloy composition, liquid-quenching rate and ageing temperature.     

Higher approximations for supersonic flow past slowly oscillating bodies of revolution

Summary Supersonic flow past slowly oscillating pointed bodies of revolution is studied. Starting from the complete nonlinear potential equation an elementary linearized solution is discussed and it is shown how this solution together with the method of matched asymptotic expansions can be used to derive an elementary second-order slender body theory. This approach is further demonstrated for the oscillating cone and its range of validity is evaluated by comparison with other theoretical methods.

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Zusammenfassung Es wird die Überschallströmung um langsam schwingende spitze Rotationskörper untersucht. Ausgehend von der vollständigen nichtlinearen Potentialgleichung wird zuerst eine elementare linearisierte Lösung besprochen und gezeigt, wie diese Lösung im Verein mit der Method of matched asymptotic expansions zur Herleitung einer elementaren Schlankkörpertheorie zweiter Ordnung verwendet werden kann. Die Theorie wird am Beispiel des schwingenden Kegels näher erläutert und mit anderen Methoden verglichen.

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Symbols a Velocity of sound - c _N Normal force coefficient - Damping coefficient - F _(x) Dipole distribution - k Reduced frequency - M Mach number - R (x) Meridian profile - t Time - x, r, Cylindrical coordinates - - Ratio of specific heats - Amplitude of oscillation - Thickness ratio - Perturbation potential - Zero angle of attack potential - æ - Velocity potential - Out-of-phase potential - - In-phase potential - - Source coordinate With 4 Figures     

Spin hydrodynamic equations with external disturbances and suitable Green's functions for superfluid3He-B. New onsager relations

The spin hydrodynamic equations for superfluid³He-B have been obtained for the case of external, time-dependent fields. On the basis of a microscopic approach, expressions are found for additional terms in equations containing these fields. Considering the linear response of the system to the switching on of external fields, formulas are found for suitable Green's functions (magnetization-magnetization, rotation-rotation, magnetization-rotation, rotation-magnetization). The rotation-rotation Green's function has the 1/q ² singularity characteristic of superfluid systems. Connections between Green's functions lead to relations among kinetic coefficients v, ₁, and ₂. It is also shown that there is a conserved quantityQ ^(B) = div v _s ^(B) that describes sources or magnetic type charges (monopoles) of the superfluid velocity v _s ^(B) . Comparison with the phenomenological approach suggests thatQ ^(B) is proportional to a pseudoscalar giving the projection of the spin density onto the vector describing the axis of rotation.     

Study of the zero-field magnetic ordering, charge fluctuation and trapping in the oxo-bridged heterometallic acetylacetonate complex Fe3YO6R3[Y11(C5O2H7)33]; (R = C5H7)

The Mössbauer, magnetic susceptibility and EXAFS data for the oxo-bridged heterometallic acetylacetonate Fe₃YO₆R₃[Y₁₁(C₅O₂H₇)₃₃] (R = C₅H₇) are analyzed in terms of a bound-to-free model describing the transition from the state of delocalized valence, denoted Fe_deloc ^(3–)+, in the magnetically disordered paramagnetic complex at 300 K to the states of localized valence, denoted Fe_loc ²⁺ and Fe_loc ³⁺, in the magnetically ordered complex at 4.2 and 77 K.     

Thermodynamics of the quasiequilibrial growth of crazes

By comparing the morphology and physical properties (averaged over the scale of 1 to 10m) of a crazed and uncrazed polymer, it can be concluded that crazing is a new phase development in the initially homogeneous material. The present study is based on recent work on the general thermodynamic explanation of the development of a damaged layer of material. The treatment generalizes the model of a crack-cut in mechanics. The complete system of equations for the quasiequilibrial craze growth follows from the conditions of local and global phase equilibrium, mechanical equilibrium and a kinematic condition. Constitutive equations of craze growth-equations are proposed that are between the geometric characteristics of a craze and generalized forces. It is shown that these forces, conjugated with the geometric characteristics of a craze, can be expressed through the known path independent integrals (J, L, M,). The criterion of craze growth is developed from the condition of global phase equilibrium. F Helmholtz's free energy - G Gibb's free energy (thermodynamic potential) - f density ofF - g density ofG - T absolute temperature - S density of entropy - strain tensor - components of - stress tensor - components of - _y stress along the boundary of an active zone (yield stress) - _b stress along the boundary of an inert zone - applied stress - value of at the moment of craze initiation - K stress intensity factor - C tensor of elastic moduli - C ^–1 tensor of compliance - internal tensorial product - V volume occupied by sample - V ₁ volume occupied by original material - V ₂ volume occupied by crazed material - V boundary ofV - (V) vector-function localized on V - (x) characteristic function of an area - (x) variation of(x) - (x) a finite function - tensor of alternation - components of the boundary displacement vector - l components of the vector of translation - n components of the normal to a boundary - _k components of the vector of rotation - e symmetric tensor of deviatoric deformation of an active zone - expansion of an active zone - J ⁽ⁱ⁾ ,L _k ⁽ⁱ⁾ ,M ⁽ⁱ⁾,N ⁽ⁱ⁾ partial derivatives ofG ⁽ⁱ⁾ with respect tol , _k, ande , respectively - [ ] jump of the parameter inside the brackets - thickness of a craze - 2l length of a craze - 2b length of an active zone - l _c distance between the geometrical centres of the active zone and the craze - ^* craze thickness on the boundary of an active and the inert zone - l ^* craze parameter (length dimension) - A craze parameter (dimensionless) - ^* extension of craze material     

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.     

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

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

Localized spin fluctuations

Scaling arguments and renormalization group techniques are used in the Anderson model Hamiltonian for the nonmagnetic limit of a magnetic impurity. The range of validity of the theory is limited toU/ 1, where the electron-electron collisions can already compete strongly with the electron-hole collisions. A parquet approximation is developed; it gives for the static susceptibility in the symmetric case = ()^–1 exp (+U/). There are some hints that the exchange force might play a crucial role in the formation of localized magnetic moment. These considerations are consistent with the electron-hole symmetry in the symmetric Anderson model.