Internal material damping of polymer matrix composites under off-axis loading

The objective of this paper is to determine theoretically the material damping of short fibre-reinforced polymer matrix composites. The major damping mechanism in such composites is the viscoelastic behaviour of the polymer matrix. The analysis was carried out by developing a finite-element program which is capable of evaluating the stress and strain distribution of short fibre composites under axial loading (see Fig. 1a). Using the concept of balance of force we can express the modulusE _x along the loading direction as a function of the mechanical properties of the fibre and matrix materials, fibre aspect ratio,l/d, loading angle,, and fibre volume fraction,V _f. Then we apply the elastic-viscoelastic correspondence principle to replace all the mechanical properties of the composite, fibre and matrix materials such asE _x,E _f,E _m,G _m, by the corresponding complex moduli such asE _x +iE _x , andE _f +iE _f . After separation of the real and imaginary parts, we can expressE _' ^x/t' andE _x ^t" as functions of the fibre aspect ratio,l/d, loading angle,, stiffness ratio,E _f/E _m, fibre volume fraction,V _f, and damping properties of the fibre and matrix materials such as _f and _m. Numerical results of the composite storage modulus,E _x , loss modulus,E _x , and loss factor (damping), _C, are plotted as functions of parameters such asl/d,,V _f, and are discussed in terms of variations ofl/d,, andE _f/E _m, in detail. It is observed that for a given composite, there exist optimum values ofl/d and at whichE _x and _c are maximized. The results of this paper can be used to optimize the performance of composite structures.Nomenclature A _c,A _f,A _m cross-sectional area of composite, fibre and matrix, respectively - d fibre diameter - E _L longitudinal modulus of composite (along the fibre direction) (see Fig. 1a) - E _T transverse modulus of composite (see Fig. 1a) - E _x modulus of composite along thex-direction (see Fig. 1b) - E _f tensile modulus of fibre - E _m tensile modulus of matrix - G _m shear modulus of matrix - G _LT in-plane shear modulus of composite (see Fig. 1a) - l fibre length - m tip to tip distance between fibres - i (–1)^1/2 - R one-half of centre-to-centre fibre spacing - V _f fibre volume fraction - x distance along fibre from end of fibre - defined in Equation 22 - defined in Equation 3 - ^* defined in Equation 19 - _L extensional (longitudinal strain) of composite - _f, _m extensional (longitudinal strain) of fibre and matrix, respectively - _c, _f, _m extensional loss factor of composite, fibre and matrix respectively - G _m shear loss factor of matrix - angle between fibre and thex-direction - ¯ _c, ¯ _f, ¯ _m average longitudinal stress in composite, fibre and matrix, respectively - longitudinal stress in fibre - shear stress at fibre-matrix interface - defined in Equation 23     

Incommensurate Dynamical Properties of Optimally Doped YBa2Cu3O6.9

The resonance and incommensurate peaks in optimally doped high-T _c superconductor YBa₂Cu₃O_6.9 are observed by means of TOF neutron scattering technique. Obtained overall dynamical properties in a wide Q-E space show distinct incommensurate structure around antiferromagnetic (AF) zone center (, ). The incommensurability of =0.1 at 36 meV corresponds to the previous triple-axis neutron measurement. Variation of temperature dependence suggests the spectral weight of antiferromagnetic fluctuation observed around 25 meV at (, ) shifts to resonance peak position below T _c. Moreover obtained results with E _i=80 meV neutron energy indicate new feature of dynamical incommensurate structure at higher frequency region up to 53 meV.     

On the dispersion of gases under the action of the medium

Some general regularities of dispersion of a gas emerging from a nozzle submerged in a liquid are considered. A condition for establishment of the so-called maximum dispersion state is formulated.Notation ₀ coefficient of surface tension at the liquidgas boundary - contact angle of wetting of the nozzle material surface by the liquid - p_at atmospheric pressure - p air pressure - density of the liquid - g gravitational acceleration - h height of the liquid column - ₁, and _g dynamic viscosity coefficients of the liquid and gas, respectively - R and r radii of the bubble and nozzle, respectively - Q and F dimensionless criteria - , , , , and undetermined coefficients - ratio of the circumference of a circle to its diameter     

Structure of unidimensional temperature stresses

Using the structural approach, the temperature stresses are examined in a semiinfinite rod, insulated on the lateral faces and rigidly fixed at the end. A comparative analysis is made for three heat-transfer models.Notation k(t) heat flux relaxation function - (t) internal energy relaxation function - T rod temperature - ambient temperature - t time - x coordinate along the rod - _xx(x, t) stress - u(x, t) displacement - (x, t) deformation - c₀=(E/)^1/2 speed of sound in the rod under isothermal conditions - E elasticity modulus - density of the material - _t coefficient of thermal expansion - thermal-conductivity coefficient - a thermal-diffusivity coefficient - b thermal-activity coefficient - c_q=(a/_r)^1/2 velocity of heat propagation - _r heat flux relaxation time - (t) unique Heaviside function Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 5, pp. 912–921, November, 1977.     

Localized single-particle excitations and the density of states for superconducting composites

The problem of localized single-particle excitations and the density of states (DOS) for an inhomogeneous system consisting of a spherical superconductor (with radius a and order parameter ₁) embedded in another superconductor (order parameter ₂) of infinite size is considered. With the assumption of constant values of ₁ and ₂, the Bogoliubov equations are solved for general values of l (the orbital angular momentum quantum number). For a fixed value of ₁/₂ and different values of ₂/E _F, the dependence of the excitation energy (l=0)/₂ on the particle sizek _F a is shown (k _F is the Fermi wave vector andE _F is the Fermi energy). Fork _F a=300, 450, and 800 and a fixed value of ₂/E _F, the variations in the DOS by changing ₁/₂ are also shown.     

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.     

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.     

Some electrical characteristics of lithium and yttrium sialons

Some electrical properties of hot-pressed lithium sialons, Li _x/8Si_6–3x/4Al_5x/8O _x N_8–x havingx<5 and an yttrium sialon were measured between 291 and 775 K; the former consisted essentially of a single crystalline phase whereas the latter contained 98% glassy phase. For lithium sialons, the charging and discharging current followed al(t) t ^–nlaw withn=0.8 at room temperature. The d.c. conductivities were about 10^–13 ohm^–1 cm^–1 at 291 K and rose to 5×10^–7 ohm^–1 cm^–1 at 775 K. At high temperatures electrode polarization effects were observed in d.c. measurements. The variation of the conductivity over the frequency range 200 Hz to 9.3 GHz followed the () ⁿ law. The data also fitted the Universal dielectric law,() ^n–1 well, and approximately fitted the Kramers-Kronig relation()/()– =cot (n/2) withn decreasing from 0.95 at 291 K to 0.4 at 775 K. The temperature variations of conductivities did not fit linearly in Arrhenius plots. Very similar behaviour was observed for yttrium sialon except that no electrode polarization was observed. The results have been compared with those obtained previously for pure sialon; the most striking feature revealed being that _d.c. for lithium sialon can be at least 10³ times higher than that of pure sialon. Interpretation of the data in terms of hopping conduction suggests that very similar processes are involved in all three classes of sialon.     

Distribution characteristics of mechanical properties and correlation between the respective properties on S35C carbon steel

Mechanical properties of tensile strength, , upper yield stress, _SU, lower yield stress, _SL elongation, , area reduction, , Vickers hardness, H _v, and impact absorbed energy, E, were examined using 50 specimens of S35C carbon steel, which were machined from two bars supplied from the same charged and heat-treated material. Distribution characteristics of these properties are discussed, and the correlation between each pair of them is investigated from a statistical viewpoint. The main conclusions obtained are summarized as follows; distribution characteristics of _B, _SL, , , H _v and E are well approximated by a normal distribution, but those of asu are not approximated as well by this type of distribution. In the latter case, a Weibull distribution is preferable to represent the distribution pattern. No significant correlation was observed between each pair of the above mechanical properties. Consequently, individual properties have the inherent distribution characteristics independent of the other properties.     

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.     

Generalization of the temperature-strain characteristics for polyvinyl chloride under tension

A universal temperature-time characteristic of the stress-strain relation has been derived for polyvinyl chloride under uniaxial tension.Notation P true stress - strain - l ₀ initial length of specimen - l length of specimen at any instant of time - total elongation factor - _p=max elongation factor at maximum stress on P () curve - v elongation rate - strain rate - t time - T absolute temperature - E_t relaxation modulus - H relaxation spectrum - relaxation time - T_S reference temperature, °K - a _T reference temperature coefficient Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 6, pp. 1031–1035, June, 1972.     

Analysis of the tensile properties and fractography of as-cast and heat treated 359-SiC-20p composite

An experimental study of the heat treatment of 359-SiC 20p composite and its base alloy was made to determine the strength-ductility characteristics under varying conditions of heat treatment. Microstructural observations revealed that addition of the SiC_p reinforcement to the base alloy produced a more uniform and refined interdendritic microstructure compared to the latter. The tensile data obtained was analysed in terms of the theoretical models existing in the composite literature. Ultimate tensile strength (UTS)-log elongation relationships were obtained to test the applicability of the quality index parameter,Q, to the present composite. From this analysis, it was found that all data points in the ageing temperature range 140–210 °C could be represented by a single line (cf. two lines in the case of 359 alloy), indicating the important fact that the tensile properties of this composite can be predicted/determined over the entire temperature range. The presence of the SiC particles was seen to accelerate the Mg₂Si precipitation kinetics, but not to alter it. Fracture mechanisms were determined from both the fracture surfaces and their longitudinal sections beneath the fracture surface, employing both optical and scanning electron microscopy.Nomenclature a Particle diameter - b Burger's vector - b _ii Numerical constant relating P _ii ^E _m andP ₃₃ ^A - E _c Young's modulus of the composite - E _m Young's modulus of the matrix - E _p Young's modulus of SiC particles - El Elongation (%) - f _p SiC volume fraction - P ₃₃ ^A Applied stress - P _ii ^E Long range back stress developed by elastic misfit - P _m ^F Change in matrix flow stress - <P _ii ^P >_m Back stresses due to plastic deformation - P _c ^ps Proof strain of a composite - q _ii Plastic misfit - Q Quality index - R Statistical correlation coefficient - RE Rockwell E hardness value - S SiC particle aspect ratio - S _c Critical aspect ratio for the SiC particles - UTS Ultimate tensile strength of the alloy or composite - YS Yield strength of the alloy or composite - Critical misfit strain - Constant, 1.25 for aluminum alloys - Plastic strain - ^ps Plastic strain at whichP _c ^ps is required - Work hardening rate at a given plastic strain - Work hardening rate as a function of total strain - Shear modulus - Dislocation density - _c ^O Yield stress of the composite - _CTE Increase in yield stress due to coefficient of thermal expansion (CTE) - _m ^O Yield stress of the matrix - _p Particle strength - _i Interfacial shear strength     

Response of a spinning liquid column to pitch excitation

Summary The response of a solidly rotating liquid bridge consisting of inviscid liquid is determined for pitch excitation about its undisturbed center of mass. Free liquid surface displacement and velocity distribution has been determined in the elliptic (>2₀) and hyperbolic (<2₀) excitation frequency range.List of symbols a radius of liquid column - h length of column - I ₁ modified Besselfunction of first kind and first order - J ₁ Besselfunction of first kind and first order - r, ,z cylindrical coordinates - t time - u, v, w velocity distribution in radial-, circumferential-and axial direction resp. - mass density of liquid - free surface displacement - velocity potential - ₀ rotational excitation angle - ₀ velocity of spin - forcing frequency - _1n natural frequency - surface tension - acceleration potential - for elliptic range >2₀ - for hyperbolic range >2₀     

Effects of carbon content on microstructures and magnetic properties of annealed or solution treated Fe-Cr-Ni-C alloys

The correlations between microstructures and magnetic properties were studied in four Fe-17.5 mass%Cr-2.0 mass%Ni-Xmass%C (X = 0.3–0.6) alloys. Each alloy consisted of ferromagnetic and M₂₃C₆ carbide phases by step-annealing at 1053 K and 848 K. The number of the M₂₃C₆ carbide particles increased with the carbon content, and this microstructural variation caused a deterioration of the soft magnetic properties. On the other hand, the alloy with 0.3 mass% carbon content consisted of ferromagnetic and paramagnetic retained structures after solution treatment at 1473 K. The amount of the stable structure increased with the carbon content, while the amount of the structure decreased. This microstructural variation caused a decrease in the relative permeability, _r, and the stabilization of the paramagnetic property to low temperatures below room temperature. The temperature stability of the _r values was closely related to the martensite start temperature, M _s. From an equation for the estimation of M _s from the chemical compositions of the phase, the M _s's of the alloys with 0.3, 0.4, 0.5 and 0.6 mass%C were estimated to be 326, 289, 241 and 216 K respectively. These values were consistent with the M _s's expected from the microstructures and temperature dependences of the _r values.     

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.     

Crystallization kinetics in glassy Ge20Se80−x In x alloys

Crystallization kinetics is studied in glassy Ge₂₀Se_80–xIn_x (0 x 20) using isothermal annealing at temperatures between the glass transition and melting. D.c. conductivity is taken as a parameter to estimate the extent of crystallization (). The activation energy of crystallization (E) and the order parameter (n) are calculated by fitting the values of in the Avrami equations of isothermal crystallization. The results indicate that E is highly composition-dependent, which is explained in terms of the stable phases in the Ge-Se-In system.     

An extension of the theory of oscillating cup viscometers

The theory of the fluid motion in the interior of an oscillating or rotating cup is reexamined. The quantity of interest in viscometry is the torque exerted by the fluis on the sides and rims of the cup. In this paper expressions for the torque are obtained for geometries for which the cup height approaches a fluid boundary layer thickness. Interest in such geometries is due to viscosity measurements made in mixtures in the critical region where cups of small height are used in order to minimize gravity effects.Nomenclature D() Torque on the cup, Eq. (5) - E() Truncation error term, Eq. (24) - h Internal half-height of a filled cup or the height of the liquid in a partially filled cup - I Moment of inertia of cup and suspension system - I Moment of inertia of fluid inside cup - I _n Modified Bessel function of order n - J _{i, n} Defined in Eq. (13) - R Radius of the cup - S _n Defined in Eq. (7) - S _n Defined in Eq. (10) - x Variable 2 ₀/ - z Variable 2 ₀^1/2 - () Angular displacement of the cup - Boundary layer thickness - Logrithmic decrement - Laplace transform variable - ₀ Dimensionless height h/ - Frequency ratio / ₀ - Kinematic viscosity - ₀ Dimensionless radius R/ - Density of liquid - Dimensionless time ₀ t - Phase angle of oscillation - Angular frequency of oscillation with liquid present in cup - ₀ Angular frequency of oscillation in a vacuum     

o′-β′ sialon ceramics

Powders of Si₃N₄, Al₂O₃ and SiO₂ were mixed with Y₂O₃ as sintering aid and hot-pressed to form o- sialon. During sintering, the o phase preferentially precipitated in the temperature region of 1550 to 1600 °C, and the phase precipitated at temperatures of 1700 °C and above. The resultant microstructure consisted of dual phases of o and . The mechanical properties of o- sialon were improved with increasing amount of the phase. When SiO₂ required for the formation of the o phase was all included in the grain boundary phase, o- sialon exhibited a three-point bending strength as much as 1400 MPa. The oxidation resistance of o- sialon is expected to improve due to the presence of the o phase, but actually was not so good due to the presence of the grain-boundary glassy phase and impurities.     

The critical curve in an antiferromagnetic superconductor with nonmagnetic impurities

The critical curve of a transition of the second kind in an antiferromagnetic superconductor (AFS) with nonmagnetic impurities has been studied. The AFS is described by using the mean-field model given by Nass, Levin, and Grest and assuming a one-dimensional electron band. We find that the points on the critical curve satisfy the thermodynamic stability condition for 0₁/₀5.04 and 0.49H_Q/₀1.64.Here ₁ is the inverse lifetime of a conduction electron for nonmagnetic impurity scattering,H _Q is the antiferromagnetic molecular field, ₀ is the zero-temperature order parameter of a superconductor in the absence ofH _Q and impurities. Further, ₁ and H_Q denote the values of these quantities for points on the critical curve. For ₁/₀>5.04 and H_Q/₀>1.64, the phase transition from the superconducting to the normal state is always of the second kind. Some thermal properties of the system near the critical curve have also been investigated and we find that these depends dramatically on the impurity concentration.