Steady state creep of a composite material with short fibres

The shear within a matrix volume is assumed to be an important process during the creep of composite material reinforced with short rigid fibres. The rate of elongation of such a composite with certain fibre distributions can be estimated. The agreement with a few experimental data is reasonably good.List of main symbols V _f volume fraction of fibres in composite - aspect ratio of a fibre - L length of a fibre - h transverse size of a fibre - h interfibre spacing - m, _m , _m constants for creep for a matrix material - n, _f, _f constants of creep for a fibre material _{f m} - v rate of relative motion of two fibres - _* ultimate strength of a fibre - ^* the first critical value of aspect ratio - ^** the second critical value of aspect ratio This work was carried out when the author was a guest worker at the National Physical Laboratory, Teddington, Middlesex, UK.     

Interplay of Nuclear Magnetism and Superconductivity

The ratio of nuclear saturation magnetization and superconducting critical field, ₀ M _sat / B _S0*, classifies the strength of mutual influence of nuclear magnetism and superconductivity. In order to investigate the interplay of both phenomena for the three distinct cases 1, 1, and 1 we have measured the ac susceptibility of Al, of the intermetallic compound AuIn ₂ , and of the metal hydride TiH _2.07 at ultralow temperatures, 17 K T 1 K, as function of static field 0 B 15 mT. For Al, the interplay enables an absolute measurement of the nuclear magnetization. For AuIn ₂ , we get a steep decrease of B _S (T) and a broadening of the superconducting transition in its nuclear ferromagnetic phase. Surprisingly, the nuclear ferromagnetic state coexists with type-I superconductivity in AuIn ₂. The metal hydride TiH _2.07 , which is under present investigation, is a good candidate to show reentrant superconductivity.     

Collinearity between the Shapley value and the egalitarian division rules for cooperative games

For each cooperativen-person gamev and eachh{1, 2, ,n}, letv _h be the average worth of coalitions of sizeh andv _h ⁱ the average worth of coalitions of sizeh which do not contain playeriN. The paper introduces the notion of a proportional average worth game (or PAW-game), i.e., the zero-normalized gamev for which there exist numbersc _h such thatv _h –v _h ⁱ =c _h (v _n–1–v _n ^–1/i ) for allh{2, 3, ,n–1}, andiN. The notion of average worth is used to prove a formula for the Shapley value of a PAW-game. It is shown that the Shapley value, the value representing the center of the imputation set, the egalitarian non-separable contribution value and the egalitarian non-average contribution value of a PAW-game are collinear. The class of PAW-games contains strictly the class ofk-coalitional games possessing the collinearity property discussed by Driessen and Funaki (1991). Finally, it is illustrated that the unanimity games and the landlord games are PAW-games.     

Structural and optical studies on ortho-hydroxy acetophenone azine thin films

The bulk material and deposited thin films of ortho-hydroxy acetophenone azine (o-HAcPhAz) were identified by X-ray diffraction (XRD) to be single phase polycrystalline of the monoclinic structure. The unit cell lattice constants were determined to be a = 1.578 nm, b = 1.394 nm and c = 0.64 nm, as well as its plane angles as = 90°, = 123.8° and = 90°. FTIR spectra of the bulk and thin films of the compound under investigation were assigned in the wave number range 4000–500 cm^–1. It was revealed that they were similar to each other. The optical constants (the refractive index, n, and the extinction coefficient, k) of the compound thin films were determined from the measured transmittance, T, and reflectance, R, at normal incidence of light in the spectral range 200–2100 nm. The plot of the absorption coefficient () versus h, gave three intense bands and a shoulder which were designated as A (232.3 nm), B (299.5 nm) and C (440.6 nm, 404.8 nm, sh). The observed A and B bands were attributed to * transitions, while the C-bands were attributed to * (n). The optical high frequency dielectric constant (₁, ₂) as well as the real and imaginary parts of the optical conductivity (₁, ₂) were determined. The plots of both ₁, ₂, ₁ and ₂ versus h reveal the same obtained optical transitions. Also, the relationships between both of surface, volume and surface/volume energy losses against h gave the same optical transtions.     

Creep behaviour of polyethylene and polypropylene

Tensile creep tests and stress reduction studies during creep have been carried out for polyethylene and polypropylene. The results obtained suggest that a consistent approach for the presentation of creep data for these polymeric materials can be obtained since the creep curves at 293K for polyethylene and polypropylene over a wide stress range can be superimposed by describing the variation of creep strain,, with time,t, as= ₀ + _p [1 – exp (–K t)] + t, where ₀ is the initial strain on loading, _p is the primary creep strain, is the secondary creep rate, andK is a constant.     

Phase decomposition in extruded Zn-Al based alloy

Ageing characteristics of an extruded eutectoid Zn-Al based alloy were investigated using X-ray diffraction and scanning electron microscopy techniques. The extruded alloy consisted of Al rich phase and Zn rich _E and phases. The original cast eutectoid Zn-Al alloy was extruded at 250 °C. Both supersaturated _s and _s phase decomposed during extrusion and appeared as fine and coarse lamellar structures. The _E and phases particles formed in the original interdendritic region. It was found that two Zn rich phases _E and decomposed sequentially during ageing at 170, 140 °C. The decomposition of the _E phase occurred as a discontinuous precipitation in the early stage of ageing and the decomposition of the phase took place in a four phase transformation: + T + in the prolonged ageing. Two typical morphologies of the decomposition of the Zn rich phases _E and were distinctive in back-scattered scanning electron microscopy.     

Thermoelastic waves in a thin plate

Summary In the present work we deal with the propagation of thermoelastic waves in a thin plate occupying the Cartesian space (x ₁[–, +],x ₂[–, +],x ₃[–, +]). The analysis is based on the generalized theory of thermoelasticity proposed by Lord and Shulman modified for plane stress problems. A mathematical analysis is presented to study the wave motion characteristics of the plate and the proposed analysis is applied for the special cases of very short and very long waves.     

Dielectric relaxation in glassy Se80?xTe20Gex

Dielectric relaxation studies have been made in glassy Se_80–xTe₂₀Ge_x alloys where 0 x 20. The measurements of dielectric constant () and dielectric loss () are made in the audio frequency range (1 kHz to 10 kHz) at various temperatures from 30°C to 150°C. The results indicate that the dielectric dispersion occurs in the above frequency and temperature range. An analysis of the results shows that the dielectric losses are dipolar in nature and can be understood in terms of hopping of charge carriers over a potential barrier.     

AC electrical conductivity of electron beam evaporated Cu-GeO2 thin cermet films

AC electrical properties of 410 nm think 30 at.wt% Cu-70 at.wt% GeO₂ thin films are reported for the frequency range 10⁴ to 10⁶ Hz and temperature range 150 to 425 K. The loss tangent (tan ) and the dielectric loss (/₀) are found to show striking minima around a cut-off frequency 10⁵ Hz. In the lower frequency range (10⁵ Hz), ₁() ^s T ⁿ is obeyed with s (0 to 0.51) increasing as a function of temperature and n (0.10 to 0.14) showing a very weak temperature dependence. In the higher frequency region (10⁵ Hz), ₁() and /₀ increase sharply leading to the quadratic behavior of ₁() with s equal to 2. These processes are discussed by analyzing an equivalent circuit which shows that at lower frequencies, the effects of series resistance in leads and contacts can be neglected, while at higher frequencies such effect give rise to spurious ² dependance for the conductance. A weakly activated AC conductivity and a frequency exponent s that increases with increasing temperature suggest that the low frequency behavior originates from carrier migration by tunneling process.     

Effective Łojasiewicz inequalities in semialgebraic geometry

The main result of this paper can be stated as follows: letV ⁿ be a compact semialgebraic set given by a boolean combination of inequalities involving only polynomials whose number and degrees are bounded by someD > 1. LetF, G[X₁,, X_n] be polynomials with degF, degG D inducing onV continuous semialgebraic functionsf, g:VR. Assume that the zeros off are contained in the zeros ofg. Then the following effective ojasiewicz inequality is true: there exists an universal constantc ₁ and a positive constantc ₂ (depending onV, f,g) such that for allxV. This result is generalized to arbitrary given compact semialgebraic setsV and arbitrary continuous functionsf,g:V . An effective global ojasiewicz inequality on the minimal distance of solutions of polynomial inequalities systems and an effective Finiteness Theorem (with admissible complexity bounds) for open and closed semialgebraic sets are derived.