High frequency dielectric properties of MgO,Fe/MgO and Cr/MgO

The study of the dielectric constant and loss in pure single-crystal MgO and in Fe- and Cr-doped crystals, the low frequency results of which have been reported [1], has now been extended to cover frequencies from 500 Hz to 9 GHz. Measurements were made on the same specimens, at room temperature, using bridge, cavity, slotted-line and cavity-resonator techniques. Over the whole frequency range, a good fit is obtained to the Universal Laws of dielectric response: _ac ⁿ and (–) ^n–1 with n=0.98±0.02 for both pure and doped MgO. At any point in this frequency range the addition of iron or chromium increases and decreases , the changes being more pronounced with iron. These effects are discussed in terms of hopping mechanisms.     

Interfacial debonding and fibre pull-out stresses

Based on a theoretical model developed previously by the authors in Part II of this series for a single fibre pull-out test, a methodology for the evaluation of interfacial properties of fibre-matrix composites is presented to determine the interfacial fracture toughness G _c, the friction coefficient , the radial residual clamping stress q _o and the critical bonded fibre length z _max. An important parameter, the stress drop , which is defined as the difference between the maximum debond stress _d ^* and the initial frictional pull-out stress _fr, is introduced to characterize the interfacial debonding and fibre pull-out behaviour. The maximum logarithmic stress drop, In(), is obtained when the embedded fibre length L is equal to the critical bonded fibre length z _max. The slope of the In()-L curve for L bigger than z _max is found to be a constant that is related to the interfacial friction coefficient . The effect of fibre anisotropy on fibre debonding and fibre pull-out is also included in this analysis. Published experimental data for several fibre-matrix composites are chosen to evaluate their interfacial properties by using the present methodology.On leave at the Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong.     

The influence of antimony-additions on the creep behaviour of a 25wt% Cr-20wt% Ni austenitic stainless steel

The effect of antimony on the creep behaviour (dislocation creep) of a 25 wt% Cr-20 wt% Ni stainless steel with ~ 0.005 wt% C was studied with a view to assessing the segregation effect. The antimony content of the steel was varied up to 4000 ppm. The test temperature range was 1153 to 1193 K, the stress range, 9.8 to 49.0 MPa, and the grain-size range, 40 to 600m. The steady state creep rate, , decreases with increasing antimony content, especially in the range of intermediate grain sizes (100 to 300m). Stress drop tests were performed in the secondary creep stages and the results indicate that antimony causes dislocations in the substructure to be immobile, probably by segregating to them, reducing the driving stress for creep.Nomenclature _a Creep stress in a constant load creep test without stress-drop - _A Initial applied stress in stress-drop tests - Stress decrement - ( _A-) Applied stress after a stress decrement, - t _i Incubation time after stress drop (by the positive creep) - _C Strain-arrest stress - _i Internal stress - _{s s}-component (= _i- _c) - Steady state creep rate (average value) in a constant load creep test - Strain rate at time,t, in a constant load creep test - New steady state creep rate (average value) after stress drop from _A to ( _A-) - Strain rate at time,t, after stress drop.     

Experimental study of the boundary between single-phase convection and boiling in underheated cryogenic liquids

The effect of pressure and underheating on the position of the boundary between heat-transfer regimes in liquid helium and hydrogen is investigated.Notation q heat flux - p pressure - =T_s–T underheating - T_s saturation temperature - T temperature of liquid - T=T_wa – T T_s=T_wa – T_s - T_wa temperature of heat-emitting surface - A,a, B, b, C constants - m, n indices - Nu Nusselt number - Ra Rayleigh number - thermal conductivity - coefficient of cubical expansion - kinematic viscosity - g acceleration - standard deviation Indices 01 conditions of convection-boiling transition - 02 conditions of boiling-convection transition Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 1, pp. 5–11, January, 1982.     

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.     

Vibrational properties of wood along the grain

The dynamic Young's modulus (E_L) and loss tangent (tan _L ) along the grain, dynamic shear modulus (G_L) and loss tangent (tan _S) in the vertical section, and density () of a hundred spruce wood specimens used for the soundboards of musical instruments were determined. The relative acoustic conversion efficiency ( ) and a ratio reflecting the anisotropy of wood (, (E_L/G_L)(tan _S/tan _L)) were defined in order to evaluate the acoustic quality of wood along the grain. There was a positive correlation between and , and the variation in was larger than that in . It seemed logical to evaluate the acoustic quality of spruce wood by a measure of . By using a cell wall model, those acoustic factors were expressed with the physical properties of the cell wall constituents. This model predicted that the essential requirement for an excellent soundboard is smaller fibril angle of the cell wall, which yields higher and higher . On the other hand, the effects of chemical treatments on the and of wood were clarified experimentally and analyzed theoretically. It was suggested that the and of wood cannot be improved at the same time by chemical treatment.     

Pyramidal yield criteria for epoxides

The tensile, compressive and shear yield strengths of two epoxides were measured under superposed hydrostatic pressure extending to 300 MN m^–2. For both materials, the ratio of the moduli of the tensile, _T, to compressive, _C, yield stress at atmospheric pressure was approximately 34, as has been reported previously for a number of thermoplastics. The ₂= ₃ envelope in stress space was plotted according to these two-parameter ( _C and _T) yield criteria: conical, paraboloidal and pyramidal; the best correlation was with the last. The experimental tensile and compressive data for tests under pressure, however, fit slightly better two straight lines which are consistent with a three-parameter single hexagonal pyramidal yield surface. For plane stress and shear under pressure yield envelopes of these surfaces, the correlation with experimental data is again best for the pyramidal criteria, except for biaxial or triaxial tension when these resins are brittle. The third independent parameter employed in the pyramidal criterion was the equi-biaxial compressive yield stress, determined by tensile experiments under appropriate superposed hydrostatic pressure; alternatively plane strain compressive yield stress, _PC, may be used.     

Charged defects-controlled conductivity in Ge-ln-Se glasses

The variation of the d.c. electrical conductivity, , with composition and temperature was investigated for glasses of the Ge-In-Se system. The results indicate a decrease in the activation energy for electrical conductivity, E, and an increase in on introduction of indium into Ge-Se glasses. The changes in E and with composition (selenium content in the glasses) are identical for the Ge_x In₅ Se_95–x and Ge_x In₈Se_92–x families. The results have been traced to the conduction controlled by charged defects in these chalcogenide glasses. The changes in E and have been explained by a shift in the Fermi level, being brought by the introduction of indium.     

On the maximum reduced upper critical magnetic field in Eliashberg theory

Consideration of the functional derivative of the zero-temperature reduced upper critical magnetic fieldh _c2(0) with electron-phonon spectral density ² F() suggests that its value can be maximized, for a given areaA under ² F(), with the choice of a delta-function spectral density. We show thath _c2(0) is then independent ofA and that it increases steadily as the Einstein frequency _E of the delta function is lowered. We argue that there is a local maximum inh _c2(0) at _E=0. The value at maximum is very sensitive to impurity content and increases sharply from a clean-limit value of 1.5 atT _c /_E=1.33 to more than 3.45 in the dirty limit.     

Energy loss distribution of charged particles in thin absorbers

Conclusions 1. For thin absorbers, the Landau theory incorporating certain above-listed corrections is a general-purpose one and is in good agreement with experiment both for heavy and light charged particles 0.01. 2. For intermediate layers (0.01 1 and 1), exact solutions are provided by the Vavilov theory [11]. 3. The numerical-analytic method of plotting the energy loss distribution function proposed in [13] is suitable for very thin ( 0.01) absorbers.Translated from Izmeritel'naya Tekhnika, No. 3, pp. 60–62, March, 1970.     

Optimal design of a thick-walled pipeline cross-section against creep rupture

Summary Cylinder under combined loadings (pressure, bending, axial force) is subject to non-linear creep described by Norton-Odqvist creep law. In view of bending a circularly-symmetric cross-section is no longer optimal in this case. Hence we optimize the shape of the cross-section; minimal area being the design objective under the constraint of creep rupture. Kachanov-Sdobyrev hypothesis of brittle creep rupture is applied. The solution is based on the perturbation method (expansions into double series of small parameters), adjusted to optimization problems.Notation A cross-sectional area - C, , creep rupture constants - K, n, _C , _C creep constants - F dimensionless creep modulus - M bending moment - N axial force - a(),b() internal and external radii of the cross-section - j creep modulus - p internal pressure - r, ,z cylindrical coordinates - s _r ,s ,s _z ,t _r dimensionless stresses - t _R time to rupture - stress function - , () dimensionless internal and external radii - _e effective strain rate - _kl strain rates - rate of curvature - rate of elongation of the central axis - dimensionless radius - _e effective stress - _I maximal principal stress - _S Sdobyrev's reduced stress - _r , , _z , _r components of the stress tensor - measure of material continuity - measure of deterioration With 7 Figures     

The tensile strength and ductility of continuous fibre composites

The plastic instability approach has been applied to the tensile behaviour of a continuous fibre composite. It is shown that the combination of two components with different strengths and degrees of work-hardening produces a new material with a new degree of work-hardening, which may be determined by the present analysis. Expressions for the elongation at rupture and the strength of a composite have been obtained and the results of the calculation are compared with some experimental data.List of symbols V _f volume fraction of fibres in composite - , , true strain of fibre, matrix and composite - s true stress - , , nominal stress on fibre, matrix and composite - _*, _*, _* critical stress of fibre, matrix and composite (ultimate tensile strength) - _*, _* critical strain of separate fibre and matrix - _* critical strain of composite - Q external load - A cross-sectional area - A ₀ initial value of area     

Convection in a shallow laterally heated cavity with conducting boundaries

Shallow cavity flows driven by horizontal temperature gradients are analysed over a range of Rayleigh numbersR and Prandtl numbers , whereR is comparable in size to the aspect ratioL(1). Eigenvalue calculations show the existence of a critical Prandtl number R > R _c (), below which the parallel core-flow structure is destroyed for Rayleigh numbersR>R _c(). For other Rayleigh numbers and Prandtl numbers the horizontal scale of influence of the end walls of the cavity is determined.     

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     

Deformation of a carbon-epoxy composite under hydrostatic pressure

This paper describes the behaviour of a carbon-fibre reinforced epoxy composite when deformed in compression under high hydrostatic confining pressures. The composite consisted of 36% by volume of continuous fibres of Modmur Type II embedded in Epikote 828 epoxy resin. When deformed under pressures of less than 100 MPa the composite failed by longitudinal splitting, but splitting was suppressed at higher pressures (up to 500 MPa) and failure was by kinking. The failure strength of the composite increased rapidly with increasing confining pressure, though the elastic modulus remained constant. This suggests that the pressure effects were introduced by fracture processes. Microscopical examination of the kinked structures showed that the carbon fibres in the kink bands were broken into many fairly uniform short lengths. A model for kinking in the composite is suggested which involves the buckling and fracture of the carbon fibres.List of symbols d diameter of fibre - E _f elastic modulus of fibre - E _m elastic modulus of epoxy - G _m shear modulus of epoxy - k radius of gyration of fibre section - l length of buckle in fibre - P confining pressure (= ₂ = ₃) - R radius of bent fibre - V _f volume fraction of fibres in composite - _t, _c bending strains in fibres - angle between the plane of fracture and ₁ - ₁ principal stress - ₃ confining pressure - _c strength of composite - _f strength of fibre in buckling mode - _n normal stress on a fracture plane - _m strength of epoxy matrix - shear stress - tangent slope of Mohr envelope - slope of pressure versus strength curves in Figs. 3 and 4.     

On internal stress and activation volume in polymers

The two-site model is developed for the analysis of stress relaxation data. It is shown that the product of d In (– )/d and (- _i) is constant where is the applied stress, _i is the (deformation-induced) internal stress and = d/dt. The quantity d In ( )/d is often presented in the literature as the (experimental) activation volume, and there are many examples in which the above relationship with (- _i) holds true. This is in apparent contradiction to the arguments that lead to the association of the quantity d In (– )/d with the activation volume, since these normally start with the premise that the activation volume is independent of stress. In the modified theory presented here the source of this anomaly is apparent. Similar anomalies arise in the estimation of activation volume from creep or constant strain rate tests and these are also examined from the standpoint of the site model theory. In the derivation presented here full account is taken of the site population distribution and this is the major difference compared to most other analyses. The predicted behaviour is identical to that obtained with the standard linear solid. Consideration is also given to the orientation-dependence of stress-aided activation.     

Surface tension of helium at the superfluid critical end-point

The singularity in the vapor-liquid interfacial tension, (T), of helium at the transition to superfluidity is analyzed theoretically. The universal amplitude ratio R ⁺ =K₊( ₀ ⁺ )^d–1/k _B T , where K₊ and K_– are the amplitudes of the |T–T|^µ singularity in , with =1.34 ₃ , is known from recent work to first order in =4–d for the general n-vector model in d dimensions. Extrapolation to d=3 for n=2 indicates R ⁺ =0.05–0.08, which is shown to be consistent with the experimental data. Further analysis of the experiments establishes that the universal ratio Q=K₊/K _– exceeds 0.35, and is consistent with the recent prediction Q0.9; this demonstrates the inadequacies of earlier theoretical treatments. The existence in the observed surface tension of an anomalous, negative contribution of unknown origin at a few millikelvin beneath T is stressed.     

Application of a new iterative method for elastic-plastic stress analysis

A new iterative method for elastic-plastic stress analysis based on a new approximation of the constitutive equations is proposed and compared with standard methods on the accuracy and the computational time in a test problem. The proposed method appears to be better than the conventional methods on the accuracy and comparable with others on the computational time. Also the present method is applied to a crack problem and the results are compared with experimental ones. The agreement of both results are satisfactory.List of symbols u = (u ₁, u ₂) displacements u ^(H) = u ⁽ⁿ⁺¹⁾ - u ⁽ⁿ⁾ u _k ⁽ⁿ⁾ = u _(k ^{(n + 1)} - u ⁽ⁿ⁾ (n, k = 0, 1, 2, ...) - = ₁₁, ₂₂, ₁₂) stresses - = (₁₁, ₂₂, ₁₂) strains - = (₁₁, ₂₂, ₁₂) center of yield surface - D elastic coeffficient matrix, C = D ^–1 - von Mises yield function. The initial yielding is given by f() = _Y - f {f/} - ^* transposed f - H hardening parameter (assumed to be a positive constant for kinematic hardening problems) - time derivative of - [K] total elastic stiffness matrix - T traction vector - = [B] relation between nodal displacements and strains     

Solution of thermal conductivity problems with boundary condition of the third kind and arbitrary coordinate and time dependence of the biot number

An analytical solution of the thermal conductivity problem with boundary conditions of the third kind and arbitrary coordinate and time dependence of the Biot number is found in the form of a converging series of quadratures.Notation , z dimensionless coordinates - dimensionless temperature - Q dimensionless volume heat-liberation density per unit time - Fo=/² Fourier number - Bi₁(, Fo)=(, Fo) · / Biot number - thermal diffusivity coefficient - plate thickness - time - (, Fo) heat-liberation coefficient - thermal conductivity coefficient - i summation index - Jo zero order Bessel function of the first kind Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 536–540, September, 1981.     

On the effects of microstress on macroscopic diffusion processes

Summary The effects of internal microstress fields are neglected in a usual simulation of the diffusion of a small solute trough solid heterogeneous media. However, when a heterogeneous material is used in a structure undergoing external mechanical loading, highly nonuniform stress fields can arise locally due to the variable microstructure. In this paper a simple quasi-Fickian model is studied which employs a spatially variable stress-dependent diffusivity,D . The structure ofD stems from an assumption that the stresses nonuniformly open and close the pores of the material microstructure, thus providing preferential sites for accumulation of the diffusing solute. When =0, the usual stress-free Fickian diffusivity,D ⁰, is recovered. Because of the highly oscillatory stress fields on the micro level, when employing numerical methods, such as the finite element or finite difference method, the distance between discretization nodes must be far smaller than the microstructural oscillations to obtain accurate simulations. This fact makes direct numerical simulations involvingD virtually impossible without computationally intensive, and complicated, special techniques. In this paper upper bounds are developed for the difference between solutions produced when usingD and alternativelyD ⁰ in the body under analysis. The general case, whenD ⁰, and consequentlyD , are spatially variable, is considered. The bounds are a function of onlyD ⁰ and and do not require any knowledge of the stress-dependent solution, and can thus be used as an a-priori check to determine whether potentially expensive computations are necessary.Dedicated to Prof. Dr. Peter Haupt on the occasion of his 60th birthday