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     

Thermal conductivity of hydrocarbons in the naphthene group under high pressures

The thermal conductivity of hydrocarbons in the naphthene group has been experimentally determined. An equation is now proposed for calculating the thermal conductivity over the given temperature and pressure ranges.Notation thermal conductivity - ₂₀ and ₃₀ values of the thermal conductivity at 20 and 30°C, respectively - t₀,P₀ thermal conductivity at t₀, p₀ - _t p thermal conductivity at temperature t and under pressure P - change in thermal conductivity - P pressure - P_melt melting pressure - P₀ atmospheric pressure - t₀ 20°C temperature - T, t temperature - T_cr critical temperature - temperature coefficient of thermal conductivity - ₂₀ temperature coefficient of density - density - ₂₀ density at 20°C - _cr critical density - M molar mass - =T/T_cr referred temperature - v specific volume - v₀ specific volume at 20°C - v change in specific volume - _{3 0} a coefficient - B (t) a function of the temperature - S a quadratic functional - W_i, weight of the i-th experimental point - _i error of the i-th experimental value of thermal conductivity - B _{y, =0.6} value of B (t) at T = 0.6T_cr - B = B (t)/B_{, =0.6} referred value of coefficient B (t) Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 491–499, September, 1981.     

Breakup of an anomolously viscous liquid film in a centrifugal force field

An equation is obtained for the breakup radius with consideration of tipping moments and Laplacian pressure forces acting on the liquid ridge at the critical point.Notation K, n rhenological constants - density - surface tension - r current cup radius - R maximum cup radius - r_c critical radius for film breakup - ¯r=¯r=r/R dimensionless current radius - ¯r_c=r_c/R dimensionless critical radius - ₀, _c actual and critical film thicknesses - current thickness - R_r ridge radius - h₀ ridge height - h current ridge height - ₀ limiting wetting angle - current angle of tangent to ridge surface - angle between axis of rotation and tangent to cup surface - angular velocity of rotation - q volume liquid flow rate - v₁ and v meridional and tangential velocities - =4vv _lm/r,=4v_m/r dimensionless velocities - M moments of surface and centrifugal forces - M_v moment from velocity head - p_r pressure within ridge - P_vm pressure from velocity head - p_m, p_pm pressures from centrifugal force components tangent and normal to cup surface - deviation range of breakup radius from calculated value - ¯r_max, ¯r_min limiting deviations of breakup radius - _c angle of tangent to curve _c/°₀=f(¯r) at critical point - t random oscillation of ratio _c/_c Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 51–56, July, 1980.     

A finite volume technique to simulate the flow of a viscoelastic fluid

Hydrodynamically developing flow of Oldroyd B fluid in the planar die entrance region has been investigated numerically using SIMPLER algorithm in a non-uniform staggered grid system. It has been shown that for constant values of the Reynolds number, the entrance length increases as the Weissenberg number increases. For small Reynolds number flows the center line velocity distribution exhibit overshoot near the inlet, which seems to be related to the occurrence of numerical breakdown at small values of the limiting Weissenberg number than those for large Reynolds number flows. The distributions of the first normal stress difference display clearly the development of the flow characteristics from extensional flow to shear flow.List of symbols D rate of strain tensor - L slit halfheight - P pressure, indeterminate part of the Cauchy stress tensor - R the Reynolds number - t time - U average velocity in the slit - u velocity vector - u,v velocity components - W the Weissenberg number based on the difference between stress relaxation time and retardation time - W ₁ the Weissenberg number based on stress relaxation time - x,y rectangular Cartesian coordinates - ratio of retardation time to stress relaxation time - zero-shear-rate viscosity, ₁ + ₂ - ₁ non-Newtonian contribution to - ₂ Newtonian contribution to - ₁ stress relaxation time - ₂ retardation time - density - (, , ) xx, yy and xy components of ₁, respectively - determinate part of the Cauchy stress tensor - ₁ non-Newtonian contribution to - ₂ Newtonian contribution to      

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     

Response of differently axially excited spinning liquid columns

Summary A solidly rotating finite liquid column consisting of frictionless liquid is subjected to various axial excitation modes. The response of the free liquid surface displacement and velocity distribution has been determined in the elliptic (>2₀) and hyperbolic range (<2₀). Differences of the various cases are presented.List of symbols a radius of liquid bridge - h length of liquid bridge - I ₀,I ₁ modified Besselfunctions - J ₀,J ₁ Besselfunctions - p liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution in rotating liquid - axial excitation amplitude - elliptic case (>2₀) - hyperbolic case (<2₀) - liquid density - surface tension - liquid surface displacement - _n damping factor - phase angle - acceleration potential - ₀ rotational speed - , ₁,₂ axial forcing frequency - natural frequency of rotating system - _0n natural frequency of harmonic axial response     

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     

Dependence of the contact heat conductivity of granular systems on the external load

An examination has been made of the dependence of the contact heat conductivity of granular systems on the external load. The calculation formulas proposed for contact heat conduction are applicable over a wide range of materials.Notation s_a area of actual contact of two particles in a granular material - _c conductivity of the contact between two particles - h_r height of a micro-roughness - _s thermal conductivity of the material of the particles - d=2r particle diameter - _c contact thermal conductivity of the granular material - p porosity of the system - S_a1, S_a2 area of contact of two particles in the freely poured state and under the action of a load - f thermal conductivity of the granular system in the freely poured state - () portion of the thermal conductivity of a granular material that depends on the external load - relative area of contact - s_n nominal area of contact of the two particles - external specific load - E modulus of elasticity of the particle material - E₀ effective modulus of elasticity of the granular material - k₁, k₂, k₃, k_m, k_b empirical coefficients     

Heat transfer of a semitransparent plate under conditions of a regular regime of the second kind

The kinetics of the cooling of a plane semitransparent layer under conditions of a regular regime of the second kind is analyzed.Notation time - T temperature - T_e temperature of the surrounding medium (the ambient temperature) - T° initial temperature of the layer - h_e coefficient of convective heat exchange - x coordinate - coefficient of absorption of the substance - n index of refraction - B(, T) surface density of radiation of a black body - C bulk specific heat - K thermal conductivity - wavelength of the radiation - _t range of wavelengths in which the material is partially transparent - _op range of wavelengths in which the material is opaque - degree of blackness of the surfaces in the range of _op - R() coefficient of reflection from the inner surfaces of the layer - ⁺ intensity of the rays consisting of acute angles with the inner normal to the surface x = 0 - ^– intensity of rays in the opposite direction - q thermal flux - angle measured from the inner normal to the surface x = 0 Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 541–546, September, 1981.     

Spin-Wave Instabilities in Spin-Echo Experiments

The importance of Castaing instabilities in –t– spin-echo experiments in spin-polarized normal Fermi fluids is investigated. For small tip angles and very large values of the spin rotation parameter M, a previous stability analysis is extended to account for angular relaxation, an effect which tends to reduce the growth of unstable modes. The results are compared with computer simulations and are applied to currently planned experiments at NHMFL.     

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.     

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.     

Evolution of transient thermal processes in layer counterflow apparatuses and heat exchangers

Results are given of an analytic investigation of transient processes inside counterflow apparatuses and heat exchangers with temperature disturbance in one of the heat carriers at the entry to the apparatus.Notation =(t–t₀)/(T₀–t₀),=(T–t₀)/(T₀ s-t₀) relative temperatures - t, T temperatures of material and gas respectively - t₀, T₀ same for the initial state - Z=[ _Vm₁/c(1–w/w_g)] [–(y₀–y)/w_g] dimensionless time - m₁=1/(1+Bi/) solidity coefficient - B₁=( _FR/) Biot number - _{F V} heat-exchange coefficients referred to 1 m² surface and 1 m³ layer - R depth of heat penetration in a portion - portion heat conductivity coefficient - shape coefficient (=0 for a plate,=1 for a cylinder,=2 for a sphere) - c, C_g heat capacities of material and gas respectively - , _g volumetric masses - w, W_g flow velocities of material and gas - y distance from the point of entry to the heating heat carrier - y₀ heat-exchanger length - Y= _Vm₁y/W_gC_{g g} dimensionless coordinate - m=cw/C_g– _gW_g water equivalent ratio Deceased.Translated from Inzhenerno-Fizicheskii Zhurnal, vol. 20, No. 5, pp. 832–840, May, 1971.     

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     

Laminar flow of a viscous incompressible liquid over the surface of solids of revolution

The laminar flow of a viscous incompressible liquid over the surface of stationary solids of revolution is examined for the case of circular inflow of the stream.Notation v₁, v velocity projections - density of the liquid - kinematic viscosity coefficient of liquid - R radius of curvature of surface of the body in the flow - thickness of boundary layer - u₀ rate of inflow of stream - r current radius - Q total flow rate - r₀ radius of contact line (circle) - ₀ thickness of layer at contact line - h thickness of layer - r_c radius of stream - r_min radius at which layer thickness is minimal - h_min minimum thickness of layer - 2 angle at apex of conical packing - current angle - , t, parameters of the ellipse - r_s conjugate line radius of plane circular torus Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 57–63, July, 1980.     

Calculated evaluations of the threshold characteristics for ferritic-pearlitic steels

On the basis of modern physical concepts of the process of formation of the prefailure zone and rules of the change in microcleavage resistance during deformation within the limits of the deformation theory of plasticity relationships of the threshold criteria of fracture to the standard mechanical properties _t, _0.2, and _K were obtained analytically. It was shown that the resistance to crack advance in ferritic-pearlitic steels is determined by the strain hardening exponent. A method of analytical determination of the constant relating the two basic threshold characteristics K_th and _th was developed.Translated from Problemy Prochnosti, No. 4, pp. 50–56, April, 1992.     

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.     

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.     

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.     

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.