Heat conduction in a multilayer composite wedge

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

Boundary layer similarity flow driven by power-law shear

Summary Similarity solution of the Prandtl boundary layer equations describing wallbounded flows and symmetric free-shear flows driven by rotational velocitiesU(y)=y are determined for a range of exponents and amplitudes . Asymptotic analysis of the equations shows that for <–1 no similarity solutions with proper algebraic decay exist. For wall-bounded flow, exact solutions found at =–1/2 and =1 correspond to an Airy function wall jet and uniform planar Couette flow. Numerical integration of the governing similarity equation reveals singular behaviour for wall-bounded flows as ₀ = –2/3, and no solutions are found in the range –1<–2/3. For >–2/3 the shear stressf(0) parameter is determined as a function of and . Symmetric free-shear flow solutions become singular as ₀ = –1/2 and no solutions are found in the range –1<–1/2. For >–1/2 the centerline velocityf(0) is determined as a function of and . An asymptotic analysis of the singular behavior of these two problems as ₀, given in a separate Appendix, shows excellent comparison with the numerical results. Similarity solutions at the critical values ₀ have exponential decay in the far field and correspond to the Glauert wall jet for wall-bounded flow and to the Schlichting/Bickley planar jet for symmetric free-shear flow.     

High-frequency dielectric properties of Mg-Al-Si,Ca-Al-Si and Y-Al-Si oxynitride glasses

Recently developed coaxial line techniques [1] have been used to determine, at room temperature, the values of the real () and imaginary (') parts of the dielectric constants for some Mg-Al-Si, Ca-Al-Si and Y-Al-Si oxynitride glasses over the frequency range 500 MHz to 5 GHz. The frequency dependencies of and ' are consistent with the universal law of dielectric response in that (-_t8)^(n–1) and '^(n–1) for all glass compositions; the high experimental value of the exponent (n=1.0±0.1) suggests the limiting form of lattice loss [2] situation. In this frequency range, as previously reported [3] at longer wavelengths, the addition of nitrogen increases the dielectric constant, (); in both the oxide and oxynitride glasses is also influenced by the cation, being increased with cation type in the order magnesium, yttrium, calcium as at lower frequencies.     

The martensitic transformation in cold-worked Fe-Mn alloys studied by Mössbauer spectroscopy

The effect of cold-working on 16, 23 and 30 at% Mn iron-manganese alloys (C<0.05 at%) has been examined using Mössbauer spectroscopy and X-ray diffractometry. The induced martensitic transformation , depends on the composition and on the initial structure. It is found that the transformation in presence of the phase occurs only at high deformations.     

Stability and work hardening of an Fe-12Cr-23Mn austenitic steel

The effect of pre-strain on the strain-induced martensitic transformation of an Fe-12Cr-23Mn austenitic steel has been investigated through transmission electron microscopy and X-ray analysis. Pre-strain was performed either at room temperature or at 200° C. Final strain was carried out at liquid-nitrogen temperature. The phase was shown to form on {1 1 1} planes of the austenite matrix predominantly by overlapping of stacking faults. The martensite transformation sequence was . Nucleation of the phase mainly occurred at intersections of bands. Austenite stability was shown to increase by pre-strain at 25° C or 200° C. Pre-strain at 200° C has a greater effect on austenite stability than does pre-strain at 25° C. The mechanism was discussed in terms of martensite transformation rate and various substructures introduced during straining. Work hardening was shown to depend on the degree of pre-strain and final strain. The correlation between work hardening and substructures introduced during straining was examined.     

A scaled equation of state for real fluids in the critical region

A scaled equation of state is proposed for real fluids in the critical region which incorporates asymmetry with respect to the critical isochore. In the range of reduced densities 0.65(/ _c)1.4 and for reduced temperatures (T/T _c)1.2, the equation represents P-V-T data for steam within the experimental accuracy.     

Suppression of Anomalous Allotropic Transformations at High Pressures

Anomalous allotropic transformations accompanied by a reduction in the density of the substance can be suppressed by applying a high pressure equal to the ratio of the heat of transition to the difference in the volumes of the phases involved. The estimated pressures necessary to suppress the (ZrO₂), (Fe), and (Sn) phase transitions are 4.34, 3.00, and 0.495 GPa, respectively.     

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

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

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     

The morphology of α′ martensite in a two-phase (α+γ) Fe-Cr-Ni stainless steel

Both lath-shaped and martensites are induced by tensile deformation within of a two-phase ( + ) Fe-Cr-Ni stainless steel, forms from the through the at an intersection of two crystals. These are observed both when is surrounded by and when borders . The amount of strain at which both and nucleate, increases with test temperatures in the range –196 to 50° C. Adjacent laths are either twin-related, or 5, 9, 15 or 19° off the twin relationship, as found by analysing electron diffraction patterns.     

Inhomogeneous shear flows of linear polymers

Solutions of a system of equations of nonlinear viscoelastic fluid motion describing inhomogeneous shear flows of linear polymers are indicated.Notation _ij stress tensor - p pressure - F_i mass force vector - _ij Kronecker delta - coefficient of shear viscosity - relaxation time - _ij inner parameter - _ij=vi/x_j velocity gradient tensor - ₀ initial value of the shear viscosity coefficient - ₀ initial value of the relaxation time - D dimensionless first invariant of the additional stress tensor - A, B, C constants of integration - f(D) universal function characterizing the material - r, , z cylindrical coordinates - u=v_z axial component of the velocity vector - v=v circumferential component of the velocity vector - ₁, ₂ first and second differences of the normal stress - Q volume mass flow rate - R radius of a circular tube - R₁, R₂ radii of the inner and outer cylinders, respectively - M moment per unit length Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 449–456, September, 1981.     

Bifurcation of crack pattern in arrays of two-dimensional cracks

Theoretical calculations based on simple arrays of two-dimensional cracks demonstrate that bifurcation of crack growth patterns may exist. The approximation used involves the dipole asymptotic or pseudo-traction method to estimate the local stress intensity factor. This leads to a crack interaction parametrized by the crack length/spacing ratio =a/h. For parallel and edge crack arrays under far field tension, uniform crack growth patterns (all cracks having same size) yield to nonuniform crack growth patterns (bifurcation) if is larger than a critical value _cr. However, no such bifurcation is found for a collinear crack array under tension. For parallel and edge crack arrays, respectively, the value of _cr decreases monotonically from (2/9)^1/2 and (2/15.096)^1/2 for arrays of 2 cracks, to (2/3)^1/2/ and (2/5.032)^1/2/ for infinite arrays of cracks. The critical parameter _cr is calculated numerically for arrays of up to 100 cracks, whilst discrete Fourier transform is used to obtain _cr for infinite crack arrays. For infinite parallel crack arrays under uniaxial compression, a simple shear-induced tensile crack model is formulated and compared to the modified Griffith theory. Based upon the model, _cr can be evaluated numerically depending on (the frictional coefficient) and c ₀/a (c ₀ and a are the sizes of the shear crack and tensile crack, respectively). As an iterative method is used, no closed form solution is presented. However, the numerical calculations do indicate that _cr decreases with the increase of both and c ₀/a.     

An exact calculation of Price's law for the law of Lotka

Price's law asserts — in its simpliest version — that authors produce half of the papers made by the total ofN authors. More generally: the topN (0<<1) authors produce a fraction (0<<1) of the papers made by the total ofN authors and the Price's law says that . In this paper — using Lotka's law — we prove a mathematical relationship of in function of and the parameter (the mean number of papers per author) and investigate when . More-over our reasoning uses the theory of the 80/20 rule as developed in: L. EGGHE, On the 80/20-rule,Scientometrics, 10 (1986) 55–68, thereby also showing the relation betwwen the 80/20-rules (being an arithmetical form of measuring elitarism) and Price's law (being a geometric form of measuring elitarism).     

Effect of magnesium content on the stress exponent and effective stress in the steady state creep of Al-Mg alloys

The stress exponent of steady state creep,n, and the internal ( _i) and effective stresses ( _e) have been determined using the strain transient dip test for a series of polycrystalline Al-Mg alloys creep tested at 300° C and compared with previously published data. The internal or dislocation back stress, _i, varied with applied stress,, but was insensitive to magnesium content of the alloy, being represented by the empirical equation _i=1.084 ^1.802. Such an applied stress dependence of _i can be explained by using an equation for _i of the form _i (dislocation density)^1/2 and published values for the stress dependence of dislocation density. Values of the friction stress, _f, derived using the equation _e/=(1–c) (1– _f/), indicate that _f is not dependent on the magnesium content. A constant value of _f can best be rationalized by postulating that the creep dislocation structure is relatively insensitive to the magnesium content of the alloy.On leave from Engineering Materials Department, University of Windsor, Windsor, Ontario N9B 3P4, Canada.     

Hydraulic characteristics and vapor content in a channel with boiling of a liquid underheated up to the saturation temperature

A method is proposed for calculating the hydraulic characteristic and vapor content in a channel with underheated boiling.Notation H heated length of channel - d_t thermal diameter - d_h hydraulic diameter - _t thermal perimeter - _h hydraulic perimeter - s through cross section - N power of channel - q heat flux - G weight flow rate - W velocity - coefficient of heat transfer - t, T temperatures - t temperature difference - i enthalpy - P pressure - P pressure drop - x weight vapor content - volumetric vapor content - C_p heat capacity - r heat of vaporization - coefficient of thermal conductivity - coefficient of surface tension - liquid density - vapor density - g acceleration of gravity - _o coefficient of friction of liquid against the channel wall - shear stress - density of two-phase medium averaged over a channel cross section - dynamic viscosity Indices s on saturation line - en at channel entrance - l liquid - v vapor - w wall Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 784–792, November, 1979.     

Dielectric properties of thin solid films formed on silicon

We report on the measurement of the frequency-dependent complex permittivity, ()=()-i(), over the frequency range, 30 MHz to 6 GHz, of silicon wafers and of thin dielectric films formed on silicon. Measurements, as a function of temperature and time treatments, were obtained by means of an HP Network Analyzer and dielectric probe and the resulting ()and()plots for the silicon wafers are shown to have a Debye-type [1] profile, thereby indicating that the associated polarization mechanism is of the orientational variety.     

Wide-band phase-metering frequency transducers with fixed frequency heterodynes

Conclusions It has already been pointed out [3] that the PMFTs with a repeated sequential transformation of frequency in ISSs and restoration of the heterodyne frequency contain a minimum number of transducers (two WBFSs) and provide, only for the condition that <, an adequately small error due to an incomplete suppression of the image frequencies (₁₂) in the WBFSs.Over a wider frequency range (), i.e., at any frequency with the exception of=, the PMFTs operate with the same small errors due to an incomplete suppression of the WBFS image frequencies (₁₂), provided that the ISS contains two WBFSs and an SM, or three WBFSs, and that the reference-signal shaping channel consists of a frequency doubler and k₁=k₂=1.Certain PMFTs which contain an FST at one of the heterodyne outputs [5] (k₂>k₁=1) have even a. wider band. Thus, the PMFTs corresponding to combinations of their component transducers shown in the lines 2, 5, 8, and 11 of Table 1 operate, for any relationship of the frequencies ₁ and k₂, with adequately small errors due to an incomplete supression of the image frequency (₁₂) in the WBFSs.The above error, with the remaining conditions being the same, is minimal (¹²³) in the PMFTs which consist of three WBFSs and have transducer combinations shown in the lines 1 and 3 of Table 1.Bearing in mind that WBFSs can now be made with an image frequency suppression factor of the order of 5·10^–3, the error under consideration of such PMFTs can be of the order of 10^–7 rad or 5·10^–5 degrees, i.e., it can be small as compared with other modern phase-metering devices' error components (due to coupling between channels, presence of higher signal harmonic components, etc).Translated from Izmeritel'naya Tekhnika, No. 1, pp. 21–25, January, 1974.     

Experimental investigation of the effects of stress rate and stress level on fracture in polystyrene

The effects of stress rate and stress level on fatigue crack propagation in compression-moulded single-edge notched specimens (0.25 mm in thickness) of polystyrene are reported. Values of the stress rate are obtained from the formula = 2v(_max – _max),, wherev is the frequency and _max, _min are the maximum and minimum stresses of the fatigue cycle. Different levels of are achieved by changing the frequency while keeping _max, _min at fixed values. The effect of the stress level is investigated by keeping and _min constant and varying _max andv. The results show that when the kinetic data are plotted as l/t against the energy release rateG ₁, a relatively small effect of the stress rate is observed. If the same data are treated as l/N againstG ₁, a decrease in l/N with test frequency is seen. The increase in the level of _max results in a higher crack speed. The critical crack length is found to be practically the same for all stress-rate experiments. A decrease in the critical crack length is observed with the increase in stress level. Analysis of craze distribution around the crack path shows that the extent of crazing decreases with the increase in stress rate and increases with the increase in stress level. For all experimental conditions, the ratio of the second moment to the square root of the fourth moment of the histograms of craze density along directions normal to the crack path is found to be constant throughout the slow phase of crack propagation. This result supports a self-similarity hypothesis of damage evolution proposed in the crack layer model.     

Nucleation and growth of β′magnesium sialons and their composition limits

Previous reports on the solubility of magnesium in -sialons have been conflicting. The present work shows conclusively that crystalline magnesium sialons with the silicon nitride structure do exist. They are formed by crystallization of magnesium sialon glasses at low temperatures. -magnesium sialon crystals nucleate on -sialon nuclei which are themselves formed by precipitation from Mg-Si-Al-O-N liquids at high temperatures. The current results suggest that -magnesium sialons exist only over a limited composition range within the 3M/4X plane of the Mg-Si-Al-O-N system, which is indicative of some form of ordering within the structure. Although the compositions investigated in the present study are unstable with respect to forsterite above about 1000° C, the possibility of producing -magnesium sialons which are stable at much higher temperatures cannot be fully discounted at present.     

Phase transformations in permanent-mould-cast aluminium bronze

The phases obtained in aluminium bronze (Cu-10Al-4Fe) cast into a permanent mould were investigated. The parameters examined were the pre-heating temperature of the mould and the graphite coating thickness. The phases and ₂ were detected as well as the metastable phases and . The intermetallics of the system Fe-Al were obtained in various stoichiometric compositions. The different cooling rates of the casting resulted in two mechanisms of transformation to grains out of the unstable phase, one being nucleation and growth producing needle-shaped grains, the other exhibiting a massive transformation to spherical grains. These two mechanisms determine the changes in the size of the a grains as result of changes in the cooling rate in its various ranges.