A model with length scales for composites with periodic structure. Steady state heat conduction problem

A new high-order model for analysing distribution of temperature in periodic composites is proposed. The original scalar elliptic problem with Y-periodic coefficients (Y is a cube) is replaced with a vectorial elliptic problem of constant coefficients. The unknown fields are: the averaged distribution of temperature and the vector field which stands for perturbation of the temperature within the cells of periodicity. The recovery of temperature in the original composite is given by the approximation: 0(x)=0(x) +h ^a (x/) _a (x) analogous with the first terms of the two-scale asymptotic expansion known from the homogenization theory. The functions h are defined as approximations of the solutions to the basic cell problems. In contrast to the two-scale expansion the expression for satisfies the boundary condition.     

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.     

Notch tip stress distribution in strain hardening materials

Using the results of elastic-plastic stress analyses for notched bars, it is shown that a modified form of slip-line field solution can satisfactorily explain the variation of longitudinal stress ahead of notch tips in strain hardening materials.

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Résumé En utilisant les résultats d'analyses de contrainte élastoplastique dans le cas de barres entaillées, on montre qu'il est possible d'utiliser une forme simplifiée de solution du champ des lignes de glissement pour expliquer de façon satisfaisante la variation des contraintes longitudinales en avant d'extrémités d'entaille dans des matériaux susceptibles d'un écrouissage.

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Nomenclature _yy longitudinal tensile stress in the notch tip plastic zone - _xx transverse stress in the x-direction - _zz transverse stress in the z-direction - k yield stress in shear - ₀ yield stress in tension - ₀ ^* strain hardened yield stress (flow stress) - _{0/* c} flow stress at notch tip - _total total strain _pl plastic strain _l principal strain - _{1 c} maximum principal strain at notch tip - _1pl plastic strain in they-direction - _{1 cp1} E_{1 pl} at notch tip - _eff effective plastic strain - _{c eff eff} at notch tip - ₀ yield strainC Stress decay constant in the notch tip region - /e_pl linear strain hardening rate - n strain hardening exponent in power hardening law - 2 flank angle of notch - distance from notch tip - p notch tip radius - k _I applied stress intensity for Mode I loading - E Young's modulus - V _c crack tip opening displacement     

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     

Indications that the yield point at constant strain rate and the inception of tertiary creep are manifestations of the same failure criterion using the universal viscoelastic model

In a preceding publication this author introduced a new universal viscoelastic model to describe a definitive relationship between constant strain rate, creep and stress relaxation analysis for viscoelastic polymeric compounds. Since creep failure criterion for this model had not been addressed in detail in previous publications, selected creep failure criterion for this model were addressed in this study.The first manifestation of the yield stress failure criterion as applied to creep was elucidated at the intersection of the yield stress relaxation curve and the creep stress vs time curve. A second way to apply yield point failure criterion to creep failure was through the identification of a specific creep time associated with the limiting strain to yield, . The creep strain at occurs at the very end of the straight line portion of secondary creep and is also the strain at which tertiary creep appears to be initiated, _itc = .As the strain increases from the inception of tertiary creep, _itc, eventually a strain is reached where a calculation option using this model would require a step back in time to go to the next differential element of strain. Since going back in time is currently impossible, only a huge jump in strain obtained by another calculation option for the next element of time would be realistic. Since this critical creep strain, _CC, is slightly greater than the inception of tertiary creep, if failure did not occur at the inception of tertiary creep then it would almost surely be expected to fail catastrophically at this condition.The near equivalency of the critical creep strain criterion and the yield strain criterion was found to be much more probable the lower the value of efficiency of yield energy dissipation such that 0 < n .4.     

Singularity parametersε andκ for interface cracks in transversely isotropic piezoelectric bimaterials

Two parameters, and (Suo et al., 1992), are of key importance in fracture mechanics of piezoelectric material interfaces. In this paper, it is shown, for any transversely isotropic piezoelectric (TIP) bimaterial, that one of the two parameters and always vanishes but the other one remains non-zero. Physically, it means that the non-oscillating crack-tip generalized stress field singularity exists for some TIP bimaterials (with vanishing ). Consequently, TIP bimaterials can be classified into two classes: one with vanishing performed crack tip generalized stress field oscillating singularity and the other one with vanishing is independent from the oscillating singularity. Some numerical results for and are given too.     

On the resonance of acoustic waves in slightly deformed and slowly moving slabs

The stability is studied of acoustic waves generated by a time harmonic force in slabs described by: 0z1±g(x, y). By using a recently developed method, the exact solution of the Dirichlet problem is found for =0. It is shown that the solution is unstable against values of the frequency: =n,n. This is in agreement with the result already known in the literature, but found by other means. In a slightly deformed slab, 0<1, it is shown that stabilization of the resonant wave occurs at a time of order ^–. This is valid if the upper boundary is a concave surface. In case of a slab with slowly moving upper boundary, only the growth rate of the amplitude of the resonant wave is reduced. This holds for a non-oscillating motion of the upper boundary. In the case of an oscillating motion a further resonance is produced.     

An Improved Transient Calorimetric Technique for Measuring the Total Hemispherical Emittance of Nonconducting Materials (Emittance Evaluation of Glass Sheets)

For measurements of the total hemispherical emittance _h of nonconducting materials, a problem of the thermal gradient produced in a sample specimen arises. An improved transient calorimetric technique to reduce the thermal gradient is proposed in this study. Glass sheets (borosilicate), semi-transparent for radiation, are selected as the nonconducting test material. The _h values of the glass sheets for various thicknesses are measured, and their results are presented as functions of thickness and temperature. The thermal gradients in the specimens are calculated by a three-dimensional analysis, and the corner effect due to them on the measured _h is estimated. It is shown that the proposed technique is useful for measuring the emittance _h of nonconducting materials.     

A dilatometric method to measure the thermal diffusivity of nonmetallic liquids

A new method to measure the thermal diffusivity of liquids is presented. It requires determination of the time dependence of the thermal expansion of the liquid when it is subjected to a heat source at the top of the cell containing the liquid. The high accuracy of the method (about 3%) is due to an essential reduction of convective currents and also to the absence of temperature detectors, which generally introduce unwanted perturbations on the thermal Field.Nomenclature Thermal conductivity - c Specific heat - Density - c = specific heat x density - h Newton coefficient - Thermal diffusivity - T, 0 Temperature - tV Electric signal - Calibration coefficient - _exp, _th Volume change of the liquid     

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     

Dielectric properties of chemically vapour-deposited Si3N4

The dielectric properties of chemically vapour-deposited (CVD) amorphous and crystalline Si₃N₄ were measured in the temperature range from room temperature to 800° C. The a.c. conductivity ( _a.c.) of the amorphous CVD-Si₃N₄ was found to be less than that of the crystalline CVD-Si₃N₄ below 500° C, but became greater than that of the crystalline CVD-Si₃N₄ over 500° C due to the contribution of d.c. conductivity ( _d.c.). The measured loss factor () and dielectric constant () of the amorphous CVD-Si₃N₄ are smaller than those of the crystalline CVD-Si₃N₄ in all of the temperature and frequency ranges examined. The relationships of ^n-1, (- ) ^n-1 and/(- ) = cot (n/2) (were observed for the amorphous and crystalline specimens, where is angular frequency andn is a constant. The values ofn of amorphous and crystalline CVD-Si₃N₄ were 0.8 to 0.9 and 0.6 to 0.8, respectively. These results may indicate that the a.c. conduction observed for both of the above specimens is caused by hopping carriers. The values of loss tangent (tan) increased with increasing temperature. The relationship of log (tan) T was observed. The value of tan for the amorphous CVD-Si₃N₄ was smaller than that of the crystalline CVD-Si₃N₄.     

Investigation of the creep and micropolar creep of various materials under static and dynamic loads

Creep is investigated under a uniform stress state with allowance for the micropolar creep of the following materials: lignostone (T=293°K), steel ON2M (T=773° K), and an AIMgSi aluminum alloy (T= 293° K) understate and cyclic tension, i.e., atA = ^a/^m = 0, 0.25, and 0.5. It is established that for lignostone, the microstrains I₁₁ are two orders lower than 2₁₂ in torsion, and the values of 2l₁₂ are only a half order lower than ₁₁ in tension. The creep strain of lignostone is described using nonlinear theory of viscoelasticity. For alloys and metals under static creep, the value of I_ij is two or three orders lower than _ij A qualitative change in microipolar creep occurs in the case of dynamic loading: whenA = 0.5,the ratio of values of fatigue creep rate 21₁₂/₁₂ = 0.2.A subject investigated in 1990 with funding provided by the Ministry of National Education.Translated from Problemy Prochnosti, No. 12, pp. 18–23, December, 1993.     

Effects of Bonding Configuration and Structural Perfection on the Properties of Doped NaNbO -Based Solid Solutions

The effects of bonding configuration (electronegativity) and doping-produced vacancies on the properties of doped NaNbO₃-based solid solutions were studied. The results demonstrate that there is an average electronegativity of the elements involved above which the uniform distortion parameter increases and the relative dielectric permittivity ^T ₃₃/₀decreases with increasing electronegativity, as is common in other solid-solution systems. Below this value, both and ^T ₃₃/₀vary in the opposite way. An explanation for the anomalous behavior of is proposed.     

A boundary layer theory for the end problem of a circular cylinder

Summary This paper discusses the nature of an approximate solution for the hollow circular cylinder whose fixed ends are given a uniform relative axial displacement and whose cylindrical surfaces are free from traction. We shall take the solution of this problem to be given by a super-position of the following two problems: problem I considers a finite length cylinder whose ends are given a relative axial displacement, but are no longer fixed; problem II removes the radial displacement at the end of the cylinder obtained in problem I.Nomenclature a mid-surface radius of cylinder - c half-height of cylinder - E, in-plane elastic moduli - E_t, _t, G_t transverse elastic moduli - _z, , _r axial, circumferential, and normal strain - _rz transverse shear strain - h cylinder thickness - _z, , _r axial, circumferential, and normal stress - _rz transverse shear stress - z, r axial and radial coordinates - u_z, u_r axial and normal displacements     

The dielectric properties of glass-ceramic-on-metal substrates for microelectronics packaging

The dielectric properties of some glass-ceramic-on-metal substrates have been determined over the frequency range 500 Hz to 5 MHz using a.c. bridge techniques. The substrates consisted of cordierite-based glass-ceramics screen printed on molybdenum. For glass layers of thickness greater than 100 m both the permittivity, and the dielectric loss, , are frequency independent over this frequency range at room temperature giving the value of =6.5 and tan =8×10^–3; the room-temperature data are consistent with the universal law of dielectric response. The variation of permittivity with temperature has also been examined and, below 120 °C, the temperature coefficient [(–1) (+2)]^–1 (/T)_p, was found to be 1.3×10^–5 K^–1. The results are compared with those previously reported for Al₂O₃ and AIN substrates.     

Effect of Gamma Irradiation on the Piezoelectric Properties of K2Sr4Nb10O30–K6Li4Nb10O30 Solid Solutions

The effect of gamma irradiation on the dielectric ( ₃₃/₀, tan) and piezoelectric (d ₃₁, g ₃₁, K _p, Q _m) properties of ₂Sr₄Nb₁₀O₃₀–K₆Li₄Nb₁₀O₃₀ solid solutions (tetragonal tungsten bronze structure) was studied as a function of K₆Li₄Nb₁₀O₃₀ content. The results demonstrate that increasing the gamma dose to 9 × 10⁵ Gy reduces ₃₃/₀ and tan. With increasing Li⁺ content (filling of triangular channels), d ₃₁, g ₃₁, K _p, and Q _m increase. The results are interpreted in terms of the generation of stable defects and effective redistribution of the energy of gamma radiation over the ceramic sample.     

Low-temperature plasticity observations of superconducting Pb-Sb alloys

Plasticity of quenched and aged Pb-Sb alloys of various Sb concentrations and the _ns value of the creep strain jump at transition to the superconducting state have been studied. It is shown that the jump value for the quenched state is in inverse proportion to the hardening coefficient. In the aged alloy the _ns value decreases with the impurity concentration increasing, and at 3 at. % of Sb it becomes equal to zero. The results obtained are compared with Natsik's theory considering thermally activated unpinning of dislocations from obstacles, which is more probable in the superconducting state. The comparison demonstrates a good qualitative agreement of theory with experiment.     

A Method for Calculating Thermal Radiation Properties of Multilayer Films from Optical Constants

A calculation method for the incident angle dependence of the solar absorptance _S and the temperature dependence of the total hemispherical emittance _H of multilayer films is proposed. The method is based on calculation of _S and _H from optical constants in the wavelength region from 0.25 to 100 m for thin polymer films and deposited metal. In this paper we provide values of _S in the incident angle region from 0 to 90° and _H in the temperature range from 173.15 to 373.15 K for two-layer samples of aluminum-deposited polyimide film. The results obtained for _S and _H by the present method are compared with experimental results measured by both spectroscopic and calorimetric methods. The calculated results of _S and _H agree well with the experimental results.     

Coaxial variable-length resonator for determining the electromagnetic parameters of materials at normal and higher temperatures

Conclusions It is possible by means of the above resonator, according to our analysis and in the absence of air gaps between the sample and the line, to evaluate the real components and of permeability and permittivity respectively in the range of 2 to 100 with an error between ±3% and ±10% in the temperature range from room temperature to +400°C, and the imaginary components and (for tan and tan in the range of 0.001 to 2) with an error of 7 to 20% over the same temperature range.     

The dielectric behaviour of single-crystal MgO,Fe/MgO and Cr/MgO

The dielectric constants and loss factors,, for pure single-crystal MgO and for Fe-and Cr-doped crystals have been measured at frequencies, , from 500 Hz to 500 kHz at room temperature. For pure MgO at 1 kHz the values of and the loss tangent, tan , (9.62 and 2.16×10^–3, respectively) agree well with the data of Von Hippel; the conductivity, , varies as ⁿ withn=0.98±0.02. In Fe-doped crystals increases with Fe-concentration (at any given frequency); for a crystal doped with 12800 ppm Fe, was about four times the value for pure MgO. At all concentrations the variation of log with log was linear andn=0.98±0.02. A decrease in with increasing Fe-concentration was also observed. A similar, although less pronounced, behaviour was found in Cr-doped crystals. The effects are discussed in terms of hopping mechanisms.