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.     

Microstructure refinement with forced convection in aluminium and superalloys

The cooling and average local solidification times were determined for slow solidifiation of Al-4.4 wt% Cu alloy under natural convection and under electromagnetically forced axisymmetric rotation during liquid cooling and solidification in graphite moulds. Cooling rates were measured within situ thermocouples. The conditions needed to stabilize the radial temperature gradient with rotation were established. The microstructure size decreased with increasing rotation, as did the local solidification times. The average grain and dendrite size without imposed rotation is coarser near the mould wall compared with the centre of the casting. This trend is reversed with imposed rotation. Rotation also led to a smaller spread of grain and dendrite size at any chosen height of the casting. These results are discussed in relation to existing theories, and several reasons for an improved heat transfer coefficient with rotation are presented. Forced convective solidification was then carried out for various shapes of integral investment cast Nimonic-90 alloy solidifying under modified conditions that prevented columnar grain formation. Similar results to those recorded for the aluminium case were obtained and are presented here. The major conclusion is that observations indicating a reduction of microstructure spacing during forced convection should also consider improved heat extraction at the mould-metal interface.List of symbols Gr Grashof number =gTZ ^{3 3}/ ³ - g _r acceleration in radial direction - g acceleration in direction - g _z acceleration inZ direction (gravity) - h heat transfer coefficient - k _l thermal conductivity of liquid - Nu _z Nusselt number =hZ/k _l - Pr Prandtl number =/ - Ra Rayleigh numberGr Pr - R radius of mould - Re _r Reynolds number =V ₀ R/ - T temperature - T temperature difference in radial direction - Ta Taylor number = ²4H ⁴ W ²/ ² - V velocity - W r.p.m. - thermal diffusivity - coefficient of volume expansion - viscosity - density Mr G. S. Reddy is also a post graduate student registered at the Banaras Hindu University, Varanasi, India.     

The age hardening effect in Ti-6 Al-4 V due to ω and α precipitation in the β grains

The structure at room temperature of a quenched TA6V titanium alloy has been investigated. This structure is + or + according to the treatment temperature; it is always metastable. During ageing the grains decomposed by the reaction + + +; this decomposition was accompanied by a large increase of the 0.2% yield stress. No structural modification was observed in. The and phase of TA6V were separately investigated in the form of single-phase alloys. The hardness of was insensitive to ageing, while was considerably hardened by and; we deduced that the strengthening of the minor phase during ageing is mainly responsible for the hardening of TA6V.     

Phase transformations in permanent-mould-cast aluminium bronze

The phases obtained in aluminium bronze (Cu-10Al-4Fe) cast into a permanent mould were investigated. The parameters examined were the pre-heating temperature of the mould and the graphite coating thickness. The phases and ₂ were detected as well as the metastable phases and . The intermetallics of the system Fe-Al were obtained in various stoichiometric compositions. The different cooling rates of the casting resulted in two mechanisms of transformation to grains out of the unstable phase, one being nucleation and growth producing needle-shaped grains, the other exhibiting a massive transformation to spherical grains. These two mechanisms determine the changes in the size of the a grains as result of changes in the cooling rate in its various ranges.     

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.     

The physics and mechanics of fibre-reinforced brittle matrix composites

This review compiles knowledge about the mechanical and structural performance of brittle matrix composites. The overall philosophy recognizes the need for models that allow efficient interpolation between experimental results, as the constituents and the fibre architecture are varied. This approach is necessary because empirical methods are prohibitively expensive. Moreover, the field is not yet mature, though evolving rapidly. Consequently, an attempt is made to provide a framework into which models could be inserted, and then validated by means of an efficient experimental matrix. The most comprehensive available models and the status of experimental assessments are reviewed. The phenomena given emphasis include: the stress/strain behaviour in tension and shear, the ultimate tensile strength and notch sensitivity, fatigue, stress corrosion and creep.Nomenclature a _i Parameters found in the paper by Hutchinson and Jensen [33], Table IV - a _o Length of unbridged matrix crack - a _m Fracture mirror radius - a _N Notch size - a _t Transition flaw size - b Plate dimension - b _i Parameters found in the paper by Hutchinson and Jensen [33], Table IV - c _i Parameters found in the paper by Hutchinson and Jensen [33], Table IV - d Matrix crack spacing - d _s Saturation crack spacing - f Fibre volume fraction - f _l Fibre volume fraction in the loading direction - g Function related to cracking of 90 ° plies - h Fibre pull-out length - l Sliding length - l _i Debond length - l _s Shear band length - m Shape parameter for fibre strength distribution - m _m Shape parameter for matrix flaw-size distribution - n Creep exponent - n _m Creep exponent for matrix - n _f Creep exponent for fibre - q Residual stress in matrix in axial orientation - s _ij Deviatoric stress - t Time - t _p Ply thickness - t _b Beam thickness - u Crack opening displacement (COD) - u _a COD due to applied stress - u _b COD due to bridging - v Sliding displacement - w Beam width - B Creep rheology parameter _o/ _o ⁿ - C _v Specific heat at constant strain - E Young's modulus for composite - E _o Plane strain Young's modulus for composites - Unloading modulus - E _* Young's modulus of material with matrix cracks - E _f Young's modulus of fibre - E _m Young's modulus of matrix - E _L Ply modulus in longitudinal orientation - E _T Ply modulus in transverse orientation - E _t Tangent modulus - E _s Secant modulus - G Shear modulus - G Energy release rate (ERR) - G _tip Tip ERR - G _tip ^o Tip ERR at lower bound - K Stress intensity factor (SIF) - K _b SIF caused by bridging - K _m Critical SIF for matrix - K _R Crack growth resistance - K _tip SIF at crack tip - I _o Moment of inertia - L Crack spacing in 90 ° plies - L _f Fragment length - L _g Gauge length - L _o Reference length for fibres - N Number of fatigue cycles - N _s Number of cycles at which sliding stress reaches steady-state - R Fibre radius - R R-ratio for fatigue (_max/_min) - R _c Radius of curvature - S Tensile strength of fibre - S _b Dry bundle strength of fibres - S _c Characteristic fibre strength - S _g UTS subject to global load sharing - S _o Scale factor for fibre strength - S _p Pull-out strength - S _th Threshold stress for fatigue - S _u Ultimate tensile strength (UTS) - S _* UTS in the presence of a flaw - T Temperature - T Change in temperature - t Traction function for thermomechanical fatigue (TMF) - t _b Bridging function for TMF - Linear thermal coefficient of expansion (TCE) - _f TCE of fibre - _m TCE of matrix - Shear strain - _c Shear ductility - _c Characteristic length - Hysteresis loop width - Strain - _* Strain caused by relief of residual stress upon matrix cracking - _e Elastic strain - _o Permanent strain - _o Reference strain rate for creep - Transient creep strain - _s Sliding strain - Pull-out parameter - Friction coefficient - Fatigue exponent (of order 0.1) - Beam curvature - Poisson's ratio - Orientation of interlaminar cracks - Density - Stress - _b Bridging stress - ¯_b Peak, reference stress - _e Effective stress = [(3/2)s _ijs_ij]^1/2 - _f Stress in fibre - _i Debond stress - _m Stress in matrix - _mc Matrix cracking stress - ^o Stress on 0 ° plies - _o Creep reference stress - _rr Radial stress - ^R Residual stress - _s Saturation stress - _s ^* Peak stress for traction law - Lower bound stress for tunnel cracking - ^T Misfit stress - Interface sliding stress - _f Value of sliding stress after fatigue - _o Constant component of interface sliding stress - _s In-plane shear strength - ¯_c Critical stress for interlaminar crack growth - _ss Steady-state value of after fatigue - ^R Displacement caused by matrix removal - _p Unloading strain differential - _o Reloading strain differential - Fracture energy - _i Interface debond energy - _f Fibre fracture energy - _m Matrix fracture energy - _R Fracture resistance - _s Steady-state fracture resistance - _T Transverse fracture energy - Misfit strain - _o Misfit strain at ambient temperature     

Standard Gibbs' energies of formation of BaCuO2, Y2Cu2O5 and Y2BaCuO5

The Gibbs' energies of formation of BaCuO₂, Y₂Cu₂O₅ and Y₂BaCuO₅ from component oxides have been measured using solid state galvanic cells incorporating CaF₂ as the solid electrolyte under pure oxygen at a pressure of 1.01×10⁵ Pa BaO + CuO BaCuO₂ G _f,ox ^o (± 0.3) (kJ mol^–1)=–63.4–0.0525T(K) Y₂O₃ + 2CuO Y₂Cu₂O₂ G _f,ox ^o (± 0.3) (kJ mol^–1)=18.47–0.0219T(K) Y₂O₃ + BaO + CuO Y₂BaCuO₅ G _f,ox ^o (± 0.7) (kJ mol^–1)=–72.5–0.0793T(K) Because the superconducting compound YBa₂Cu₃O_7– coexists with any two of the phases CuO, BaCuO₂ and Y₂BaCuO₅, the data on BaCuO₂ and Y₂BaCuO₅ obtained in this study provide the basis for the evaluation of the Gibbs' energy of formation of the 1-2-3 compound at high temperatures.     

An instability mechanism for the sliding motion of finite depth of bulk granular materials

Summary Field observations and experimental records indicate that the primary mode of motion of many large landslides is that ofsliding rather thanflowing. Most of shear during sliding is concentrated at the base of slides, with little or no mixing taking place away from the base. This sliding motion may generate strong pressure waves at the interface between the quasi-static deforming granular mass and the grain-inertia dominated rapid granular flow, thus inducing a Kelvin-Helmholtz type instability mechanism for large landslides. The existence of a transitional zone in granular flow is essential for the generation of this type of instability waves. A model using a finite depth of elastic sliding bulk granular materials riding on a basal granular shear flow layer is estabilished to represent the sliding motion of these large volume of bulk granular materials. The balance and the stability of this sliding system are investigated under the perturbation of internal pressure waves. The generated instability waves will force favorable phase shifts between the overburden pressure and the sliding velocity, leading to a net reduction in the total power loss due to friction. The depth of sliding mass will affect the generation of this type of instability waves. Both analytical and numerical results show that smaller depth slides can induce stronger instability waves than larger depth slides do.Notation a perturbation wave amplitude - C nondimensional instability wave speed - C _i growth rate, the imaginary part ofC - C _r wave phase speed, the real part ofC - c _p compressional wave speed in elastic medium - c _s shear wave speed in elastic medium - D nondimensional depth of sliding mass - d depth of sliding mass - G shear modulus of elastic medium - H nondimensional basal depth - h depth of basal shear zone - i - K Coulomb friction coefficient - P _xx, P_yy lateral and normal pressures in granular material, respectively - P _xy shear stress in granular material - p ₀ amplitude of perturbation pressure - p _yy perturbation pressure - r nondimensional complex wave number of instability wave - S nondimensional wave number of shear wave - t time scale - U uniform sliding velocity of a landslide inx direction - u, v velocities inx direction andy direction, respectively - u ₀ granular flow velocity in the basal shear zone - V, V _c nondimensional sliding velocity and its critical velocity, respectively - W power loss to friction - internal friction angle - , Lame's potentials, and are time-independent amplitudes of and , respectively - perturbation wave surface profile - wave number of perturbation wave, _r and _i are the real and imaginary parts of - Poisson's ratio of elastic medium - wave frequency of perturbation wave - , _g density of granular material - stress component in elastic medium - Rankine's earth pressure coefficient - -K ² - Re{}, Im{} the real and imaginary parts of complex quantity inside {}, respectively - , the divergence and the curl of perturbation wave velocities, respectively - Laplacian operator - _ij Kronecker delta; _ij =1 fori=j, _ij =0 forij - ()i, ()j, ()ij tensor - ()1, ()e in sliding mass - ()2, ()b in ground     

Brittle matrices reinforced with polyalkene films of varying elastic moduli

The inclusion of polyalkene films of different moduli in a cement-based matrix has shown the benefits to be gained, in terms of increased stress at a given strain, from the use of films of high elastic modulus. Further, the concept of load-bearing cracks is used to explain the transition region between the limit of proportionality and the bend-over point on the tensile stress-strain curve, which is found to exist with high film modulus composites. This transition region could be an important factor affecting the choice of film to be used in a commercial composite.Nomenclature E _c uncracked composite modulus - E _m matrix modulus - E _f film modulus - V _m matrix volume-fraction - V _t film volume-fraction - V _f(crit) (E _{c mu})/ _fu - A _c cross-sectional area of composite - (E _m V _m/E _fV_f) - _m matrix strain - _mu matrix cracking strain - _mu average matrix cracking strain, (#x03C3;_co)/E _c - _mc strain at end of multiple cracking - _fu ultimate fibre stress - _cu ultimate composite stress - _co average composite cracking stress (assumed at a strain of _mc/2) - S4 81 draw ratio polypropylene film - S8 181 draw ratio polypropylene film - E3H polyethylene film - LOP limit of proportionality (stress at first crack, assumed to be a departure from linearity of the tensile stress-strain curve of a perfectly straight and uniform test specimen. However, this point cannot be reliably determined from the stress-strain curve because of the clamping strains induced in warped specimens) - BOP bend-over point (stress at which the approximately horizontal portion of multiple cracking region commences. The BOP is generally higher than the LOP and is a much more reliable point to determine experimentally than the LOP)     

Natural damped frequencies and axial response of a rotating finite viscous liquid column

Summary For a finite solidly rotating cylindrical liquid column the damped natural axisymmetric frequencies have been determined. The liquid was considered incompressible and viscous. The cases of freely slipping edges and that of anchored edges have been treated. It was found that instability appears in a purely aperiodic root for the spinning liquid bridge. This is in contrast to the instability appearing in the damped oscillatory natural frequency of a nonspinning liquid column at . The spinning viscous liquid column exhibits the same instability as the frictionless liquid. It appears at for axisymmetric oscillations.List of symbols a radius of liquid column - I _m modified Bessel function of first kind and orderm - s complex frequency ( ) - r, ,z polar cylindrical coordinates - p pressure - t time - u, v, w radial-, azimuthal- and axial velocities of liquid, respectively - Weber number - h height of liquid column - dynamic viscosity of liquid - v kinematic viscosity of liquid (v=/) - density of liquid - surface tension of liquid - _r , _rz shear stress - (r, z, t) circulation - (r, z, t) streamfunction - ₀ angular velocity of liquid column about the axis of symmetry - (,t) free surface displacement     

Effect of swelling in the extrusion of an elastic liquid from a capillary

The article demonstrates that the profile of a jet extruded from a capillary can be constructed from the data of uniform stretching.Notation V₁ mean velocity of the liquid in the capillary - r₁ radius of the capillary - q flow rate - P pressure in the preinlet zone of the capillary - F₁ and F₀ extrusion force - ₁ and ₂ elastic deformations in parallel Maxwellian elements upon stretching - p, z radial and longitudinal coordinates, respectively - v_z(p) velocity of steady-state flow in the capillary - _i modulus of elasticity in the i-th Maxwellian element - swelling coefficient - t time - l length of the specimen at instant t - elastic deformation - x rate of deformation - ₀, ₁ deformation - L length from which onward the radius of the jet extruded from the capillary practically does not change - r radius of the jet - t₁ time from which onward the radius of the specimen in retardation practically does not change - d₀,l ₀ diameter and length, respectively, of the undeformed specimen - l _r length to which the extended specimen tends after removal of the load - b length of the capillary - ₁ tensile stress (for uniform stretching at t = 0, for extrusion from the capillary at z = 0) - l _H length of the stretched specimen at the instant of beginning reading of t Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 2, pp. 343–350, August, 1980.     

Thermodynamics of the quasiequilibrial growth of crazes

By comparing the morphology and physical properties (averaged over the scale of 1 to 10m) of a crazed and uncrazed polymer, it can be concluded that crazing is a new phase development in the initially homogeneous material. The present study is based on recent work on the general thermodynamic explanation of the development of a damaged layer of material. The treatment generalizes the model of a crack-cut in mechanics. The complete system of equations for the quasiequilibrial craze growth follows from the conditions of local and global phase equilibrium, mechanical equilibrium and a kinematic condition. Constitutive equations of craze growth-equations are proposed that are between the geometric characteristics of a craze and generalized forces. It is shown that these forces, conjugated with the geometric characteristics of a craze, can be expressed through the known path independent integrals (J, L, M,). The criterion of craze growth is developed from the condition of global phase equilibrium. F Helmholtz's free energy - G Gibb's free energy (thermodynamic potential) - f density ofF - g density ofG - T absolute temperature - S density of entropy - strain tensor - components of - stress tensor - components of - _y stress along the boundary of an active zone (yield stress) - _b stress along the boundary of an inert zone - applied stress - value of at the moment of craze initiation - K stress intensity factor - C tensor of elastic moduli - C ^–1 tensor of compliance - internal tensorial product - V volume occupied by sample - V ₁ volume occupied by original material - V ₂ volume occupied by crazed material - V boundary ofV - (V) vector-function localized on V - (x) characteristic function of an area - (x) variation of(x) - (x) a finite function - tensor of alternation - components of the boundary displacement vector - l components of the vector of translation - n components of the normal to a boundary - _k components of the vector of rotation - e symmetric tensor of deviatoric deformation of an active zone - expansion of an active zone - J ⁽ⁱ⁾ ,L _k ⁽ⁱ⁾ ,M ⁽ⁱ⁾,N ⁽ⁱ⁾ partial derivatives ofG ⁽ⁱ⁾ with respect tol , _k, ande , respectively - [ ] jump of the parameter inside the brackets - thickness of a craze - 2l length of a craze - 2b length of an active zone - l _c distance between the geometrical centres of the active zone and the craze - ^* craze thickness on the boundary of an active and the inert zone - l ^* craze parameter (length dimension) - A craze parameter (dimensionless) - ^* extension of craze material     

Calculating the hydraulic resistance of foam flows in tubes

Formulas are derived for calculating the hydraulic resistance factor of a foam flow for isothermal flow in a tube with allowance for compressibility, biphasality, and a change in the structure of the foam during its movement.Notation p pressure in a cross section of the tube - p total pressure drop on a section of the tube - p_fr pressure drop due to friction on a section of the tube - u mean flow rate - specific gravity - K expansion ratio - T flow temperature - R universal gas constant - G weight flow rate - weight gas flow rate - ¯d weighted mean diameter of bubble - surface tension coefficient - D tube diameter - L length of section of tube - F cross-sectional area of tube Indices liquid phase - 0 atmospheric conditions for p=9.8·10⁴ Pa Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 4, pp. 624–628, October, 1980.     

Efficiency of heating methods for polymer fibers with formation of adhesion compounds

Efficiency of contact and contactless methods of heating of a fiber polymer material upon formation of adhesion compounds between its layers is analyzed. The advisability of contact heating in the preliminary stage and contactless heating in the final stage of formation of compounds is shown.Notation e spectral density of radiation - T temperature - a spectral absorption coefficient - radiation density within the spectral region ₂–₁, and 0–, respectively - wavelength - _max wavelength of the maximum of black-body radiation - E _0– total density of black-body radiation - the Boltzmann constant - E _ef effective radiation density - E radiation density absorbed by the material - X dimensionless coordinate - r radius of the filament of the lamp - h distance from the lamp to the surface of the material - S area - P power absorbed by the portion of the material - T _m temperature of the onset of variations in the appearance, shrinking, and melting of the material - Q heat - T ₀ initial temperature of heating - c specific heat capacity of the polymer - m mass of the material being heated - time of heating toT _m - y coordinate - R thickness - T _s stabilized temperature - Fo Fourier number - thermal conductivity of the material Institute of Mechanics of Metal-Polymer Systems, Academy of Sciences of Belarus, Gomel', Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 3, May–June, 1995.     

Dielectric Dispersion in Yttrium and Erbium Formate Dihydrate Crystals

The dielectric properties of Y(HCOO)₃ · 2H₂O and Er(HCOO)₃ · 2H₂O are studied. The frequency dependences (0.01 Hz to 20 kHz) of the real () and imaginary () parts of dielectric permittivity ( = – i) are shown to follow a fractal scaling law for the dielectric response of solids. In the tan versus temperature curves, a number of maxima are revealed in a narrow temperature range. The experimental data are used to evaluate the activation energies of relaxation processes. The observed anomalies are assumed to be associated with changes in the dynamics of protons in hydrogen bonds.     

Direct and inverse heat-conduction problems for a semiinfinite rod for a partial outflow of heat through the surface

Analytical solutions of the direct and inverse problems of nonstationary heat conduction in a thin semiinfinite rod are given for the case of radiative heat fluxes at the lateral surfaces and a partial outflow of heat by convection and radiation through the end of the rod.Notation thermal diffusivity - x₁ coordinate along the length of the rod - t₁ time - t=t₁/d² dimensionless time (Fourier number) - x=X₁/d relative coordinate - T_o initial temperature - Boltzmann constant - Sk=aT_c ³d/ Stark number - Bi=d/ reduced Biot number - emissivity Translated from Inzhenero-Fizicheskii Zhurnal, Vol. 47, No. 1, pp. 148–153, July, 1984.     

Shear viscosity of the B phase of superfluid3He

The shear viscosity (T) in the Balian-Werthamer (BW) state of superfluid ³ He is calculated variationally throughout the region 0t 1(t=T/T _c) from the transport equation for Bogoliubov quasiparticles. Coherence factors are treated exactly in the calculation of the collision integral. The numerical result for =_s= _s(T)/_n(T_c) agree very well with experiment in the range 0.8t1.0. Analytic expressions = 0.577 (1–1.0008t) and =1–(23/64) [=(T)/k _B T] are obtained in the low-temperature region and in the vicinity ofT _c, respectively. From the numerical analysis it is shown that the latter equation is valid only in the temperature range 0.9997t1.0.Supported by the Research Institute for Fundamental Physics, Kyoto University.     

Interface shapes in a torsionally oscillating,layered medium of viscoelastic liquids

Summary The free surface motion of a layered medium of liquids in a gravitationally stable configuration, resting on top of a layer of mercury, driven by a torsionally oscillating, cylindrical outer wall is investigated. The non-linear problem in the unknown physical domain is expressed as a series of linear problems in the rest state by means of a domain perturbation method. The flow variables and the stress are expanded into series in terms of the amplitude of the oscillation of the cylinder. The shapes in the mean of the interfaces between layers and the flow field are determined up to second order in the perturbation parameter, the amplitude of the oscillation.Nomenclature Density - Modified pressure field - Amplitude of the oscillation - Frequency of the oscillation - Interfacial value of the surface tension - Dynamic viscosity - , , Material functions - Complex viscosity - Stream function - Position vector at timet= - ₁, ₂ The first two Rivlin-Ericksen constants - Quadratic shear relaxation modulus - ,t Time - u Velocity vector - u,v,w Velocity components - S Extra stress tensor - h Interface elevation - D Stretching tensor - G Strain history tensor - A ₁ The first Rivlin-Ericksen tensor - J Mean curvature - p Pressure - t Unit tangent vector - n Unit normal vector - G Shear relaxation modulus - X Position vector in the rest stateD ₀ - r, ,z Rest state coordinates - x Position vector in the physical spaceD - R, ,Z Physical space coordinates - r ₀ Radius of the oscillating cylinder - e _r ,e ,e _z Physical basis vectors inD ₀ - e _R ,e ,e _Z Physical basis vectors inD - Indicates the jump in the enclosed quantity across an interface With 1 FigurePresented at the Xth Canadian Congress of Applied Mechanics, The University of Western Ontario, London, Ontario, Canada, June 2–7, 1985.     

Relationship between the energy supply parameters and the physicochemical l characteristics of polymer compositions during drying and thermal processing

The effect of the type of energy supply on the formation of temperature and concentration fields in the thermal processing of polymer compositions is considered.Notation T₀, T initial and current temperature of the coating - T_m temperature of the air - =(T-T_o)/(T_m-T₀) dimensionless temperature of the coating - a thermal diffusivity - A absorption power of the coating - D diffusion coefficient - thermal conductivity - c thermal capacity - density - _k convective heat transfer coefficient - i number of moles of reacting groups per unit volume of polymer - K₀ factor in front of the exponential - R gas constant - u concentration - Q thermal effect of the reaction - q_n density of the incident radiant flux - =x/ dimensionless coordinate over the thickness of the coating - Ki=Aq_n /(T_m-T₀) Kirpichev criterion characterizing the thermal effect of the reaction - Ki_p=Qi/c (T_m-T₀) analog of the Predvoditelev criterion, characterizing the rate of occurrence of a chemical excess in the system - Bu= Bouguer criterion - Lu=D/a Lykov number - Fo=a/² Fourier number - Bi= _k Biot number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 26–33, July, 1980.     

Residual thermal stresses in the pull-out specimen: A finite element calculation

The residual thermal stress field in the pull-out specimen is calculated in the case of a high properties thermoset system (carbon-bismaleimide). The calculation is performed within the framework of the linear theory of elasticity by means of a finite element method. The specimen is modelled as a three-phase composite (holder-fibre-matrix). The meniscus which forms at the fibre entry is taken into account in order to provide a realistic stress concentration. The latter is far higher than the matrix strength. Evidence that fibre debonding propagates from the fibre end during cooling is then produced.Nomenclature T thermal load - L _e embedded length - r _f fibre radius - _c curvature radius of the meniscus (fibre entry) - r _c radial dimension of the finite element mesh - E _m,E _h matrix and holder moduli - E _A,E _T fibre axial and transverse moduli - _m, _h matrix and holder thermal expansion coefficients - _A, _T fibre axial and transverse thermal expansion coefficients - _rr, , _zz, _rz non-zero components of the residual stress field - _rr ⁱ , ^im , _zz ^im , _rz ⁱ stresses at the interface in the matrix (r=r _f + ) - _rr ⁱ , ^if , _zz ^if , _rz ⁱ stresses at the interface in the fibre (r=r _f–) - _p1 maximum principal stress - _zz ^f mean axial stress over the fibre section - _rupt ^m matrix strength - u _r ,u _z non-zero components of the displacement field