Environmental stress cracking of glassy polymers and solubility parameters

The use of solubility parameters to predict critical stress ( _c ^* ) or strains (_c) for environmental cracking/crazing in several glassy polymers (e.g. PMMA, PPO, PS, PVC, PSF and PC) is re-examined. It is shown that the enthalpic component ( _H ) of the Flory-Huggins semi-interaction parameter () does not always give a good correlation between _c and _H even though solvent molar volume and polymer-solvent molecular interactions have already been considered. Re-analysis of available experimental data using Gent's theory shows that there is a general trend for _c ^* (or _c) to increase with . These results, therefore, support Gent's proposed mechanism of environmental stress crazing/cracking. It is finally concluded that unless a definite relationship can be established between _c or _c ^* with _H it is not possible to predicta priori _c or _c ^* , given the empirical solubility parameters of a solvent. Unfortunately, there are not many such relationships as discovered in this paper.     

Thermal boundary resistance in superfluid4He nearT λ

New measurements of the boundary resistivity in superfluid⁴He (2ppb³He) nearT are reported as a function of ¦¦ ( =T/T (Q) — 1) and of heat flux Q in a cell with parallel polished copper surfaces. Here we call T(Q) the temperature where the superfluid state abruptly disappears. In this design, the sidewall gaps between the copper pieces and the stainless steel spacer were eliminated. In contrast to several previous experiments but in agreement with those of Li and Lip a, no largeQ-dependent boundary resistivity anomaly was detected. However, as ¦¦ 0 the small weakly divergent resistivity was observed and its dependence onQ over the experimental range 1 <Q < 80 W/cm² was found to be very small. These new results are compared with previous experiments and predictions. An explanation of the previously observed anomalous transport phenomena is presented in terms of a heat flow through the sidewall gaps in these cells, and its limitation by a critical flow value _c. This phenomenological model can be fit satisfactorily to the observations. In the appendix we calculate _c from mutual friction.     

Environmental stress cracking behaviour of urethane methacrylate based resins

Two kinds of cross-linked urethane methacrylate resins have been investigated using three-point bend tests to determine their environmental stress cracking (ESC) behaviour in a range of liquids (water, sodium hydroxide, ethylene glycol, acetonitrile, acetic acid, acetone, tetrahydrofuran, toluene, 3,5,5-trimethylhexanol and petrol). The resins were found to undergo ESC in organic liquids only, and the critical strains, _c, and critical stresses, _c, have been related to the solubility parameters, , of the liquid environments. The most severe ESC was observed in solvents with –19–20 MPa^1/2, corresponding to minimum points in the plots of _c and _c against . Generally, the resin with the higher cross-link density had a greater resistance to ESC, but the effect of liquid diffusion complicated the situation and was found to play an important role in the ESC behaviour of these materials. The results confirmed that liquid diffusion into the resins lowered the critical strain (and stress), leading to earlier failure. In the case of the lower cross-link density resin, very fast diffusion was found to cause softening. However, it was noted that liquid diffusion can also blunt crazes and cracks.     

Longitudinal dielectric function and collective surface oscillations in superconductors

The electrodynamic approach to the problem of collective oscillations in superconductors is considered. The kinetic equation for quasiparticles is used to find the longitudinal dielectric function ₁ (, k) of a pure superconductor at ( is the collision frequency). With the help of the evaluated ₁ (, k) the existence of collective oscillations localized near the boundary of the superconductor is investigated.     

High-field electrical conduction in m Hgl2

The electrical and dielectric properties of illuminated Hgl₂ were studied at room temperature under various a.c.-signal amplitudes in the frequency range 1 Hz to 10 kHz. Below 40 H, We real part of the dielectric constant, ,was found to vag slightly with voltege for low electric fields (E < 10³V cm^–1, above which it showed a steady increase with the applied voltage. At higher frequencies, no voltage dependence of (or the geometrical capacitance) of the crystal was observed. On the other hand, the imaginary part of the dielectric constant, or the a.c. conductivity, (=_o) was found to decrease considerably with the applied voltage forE < 10³V cm^–1 at all frequencies. For higher fields (E > 10³V cm^–1), exp [C(E/)^1/2], whereC is e constant. Above 40 Hz, this variation was in good agreement with the behaviour of the bulk, resistance of the crystal. Such behaviour is discussed in the view of Richardnon-Schottky and Poole-Frenkel conduction mechanisms, which seem to be operative in Hgl₂ at room temperature.     

A model for determining the strength of materials with heat-resistant coatings

A simplified mechanical model of a section of a heat-resistant coating (HRC) as a round plate with an immovable center having radial tangential stresses is presented. It is a natural consequence of a normal density distribution of the probability function for the shear strength and for the local compliance. Stresses and the strength conditions are determined for the two-dimensional case. Also determined is the relationship of to an external thermal load _cE_c for the one-dimensional case. It was shown that with increase in the value of _cE_c significant additional (previously unknown) stresses develops in the HRC due to the specifies of the model. Using this model a qualitative explanation of the known experimental data can be given.Translated from Problemy Prochnosti, No. 3, pp. 50–55, March, 1993.     

Theory of motional inhibition of interlayer quantum tunneling in thin 3He films

An attempt is made to interpret NMR data on ³He films for coverages just over one monolayer in terms of motion due to the quantum exchange of particles between layers. A summary of the relevant data and of various possible relaxation mechanisms is given and it is found that a portion of the data seems amenable to an interlayer exchange interpretation. The detailed theory of this process requires the use of the exchange operator concept and a Kubo-theory treatment of the effect of second-layer motion on the exchange process. It is shown that the bare interlayer exchange process characterized by constant J ₁₂ is slowed by second-layer translational motion so that the effective exchange parameter becomes \~J ₁₂ J ₁₂ ²/₂, where ₂ is a second-layer single-particle translational energy. In order to fit the NMR data it is found that ₂ must be evaluated in the classical limit rather than the degenerate Fermi limit, and that \~J ₁₂ J ₁₁, the exchange energy within the first-layer solid. These conditions require a helium second-layer effective mass of m ^* 5m and J ₁₂600J ₁₁, which are anomously large values for these parameters. The relation of this analysis to the problem of surface ferromagnetization in bulk ³He is also discussed briefly.     

Transport properties of helium near the liquid-vapor critical point. II. Thermal conductivity of a3He-4He mixture

Measurements of the thermal conductivity are reported for an 80%³He-20%⁴He mixture above the critical point along several isotherms and near-critical isochores, using the same techniques and apparatus described for a study of³He. Using again the assumption that the observed conductivity can be decomposed into a sum of a regular and a singular contribution _reg and _sing, it is shown that along two near-critical isochores, _sing diverges. In particular, along the isochore showing the largest at the phase transition, the divergence is nearly the same as for³He and can be roughly characterized by a simple power law (T-T_c)^– with 0.58. This observation is contrary to predictions that foresee _sing0 asT _c is approached. The relaxation times characterizing the attainment of steady state conditions after switching the heat flux on and off show a similar behaviour as a function of reduced temperature as do those for pure³He. This result might indicate a substantial coupling between concentration and entropy diffusion. In the Appendix, the correlation length for³He nearT _c is calculated from heat conductivity, viscosity, and specific heat data.Work supported by Grant DMR 8024056 of the National Science Foundation.     

The dielectric properties of aluminium nitride substrates for microelectronics packaging

The dielectric behaviour of sintered polycrystalline aluminium nitride substrates has been examined over the frequency range 500 Hz to 10 MHz and correlated with composition and microstructure. For pure, white AlN at 20 ° C both the permittivity () and dielectric loss () are frequency independent giving = 9.2±0.05 and tan = (2.1±0.1) × 10^–3. The permittivity is less than for pure alumina substrates ( = 10.2) but tan compares favourably, with that (1.4 × 10^–3) of alumina, which though used more widely has a thermal conductivity some eight times less than that of AlN. The addition of impurities, particularly iron, to give opaque black AlN causes large, frequency dependent increases in ; at 500 Hz the loss is seven times that of pure white AlN and is two times greater above 100 kHz. The temperature coefficient of permittivity [( – 1)( + 2)]^–1 [/T]_p between –180 and +180 ° C for pure white AlN is 1.05×10^–5 K^–1 which is similar to the value of 9×10^–6 K^–1 for pure Al₂O₃. For impure black AlN the coefficient below 20 ° C is the same but above 20 ° C there is a rapid, non-linear increase of with temperature. Below 180 ° C for pure white AlN and 20 ° C for impure black AlN the values of temperature coefficient are frequency independent at least up to 200 kHz.     

Study of dielectric and electrical properties of mortar in the early hydration period at microwave frequencies

The dielectric constant, , and electrical conductivity, , of mortars with various sand-cement ratios,s/c, were measured for the first 30 h hydration using microwave techniques in the frequency range 8.2–12.4 GHz. The and of the mortars were found to increase linearly with increasing water-solid ratiow/(s + c), but decrease with increasings/c. It was found that as long as thes/c values were the same, the rate of changes in and of the mortars were the same. It appears that thes/c is the key factor controlling the rates of changes in dielectric and electrical parameters of cement hydration in mortar. The relationship between compressive strength and dielectric and electrical properties of mortars was also discussed.     

Optical and photoelectric properties of Cd<Subscript>1 - <Emphasis Type="Italic">x</Emphasis></Subscript>Zn<Subscript>x</Subscript>As<Subscript>2</Subscript> single crystals

The optical absorption, photoconductivity, and short-circuit photocurrent spectra of structurally perfect Cd_{1 - x} Zn_xAs₂ (x = 0.03, 0.05, 0.06) single crystals are studied for the first time near the intrinsic edge in the range 80–300 K. The results demonstrate that the intrinsic edge in the solid solutions is due to indirect transitions involving the formation of excitons for both the E c and E c polarizations. The indirect gaps _g ⁱ of the solid solutions are determined. In the range 80–300 K, the data for x = 0–0.06 and both polarizations are well fitted by _g ⁱ (x) = _g ⁱ (0) + 0.0866x + 2.35x ². The introduction of 6 mol % ZnAs₂ into CdAs₂ increases its _g ⁱ by 14 meV.Translated from Neorganicheskie Materialy, Vol. 41, No. 3, 2005, pp. 268–272.Original Russian Text Copyright © 2005 by Morozova, Marenkin, Mikhailov, Koshelev.This revised version was published online in April 2005 with a corrected cover date.This revised version was published online in April 2005 with a corrected cover date.     

Application of a new iterative method for elastic-plastic stress analysis

A new iterative method for elastic-plastic stress analysis based on a new approximation of the constitutive equations is proposed and compared with standard methods on the accuracy and the computational time in a test problem. The proposed method appears to be better than the conventional methods on the accuracy and comparable with others on the computational time. Also the present method is applied to a crack problem and the results are compared with experimental ones. The agreement of both results are satisfactory.List of symbols u = (u ₁, u ₂) displacements u ^(H) = u ⁽ⁿ⁺¹⁾ - u ⁽ⁿ⁾ u _k ⁽ⁿ⁾ = u _(k ^{(n + 1)} - u ⁽ⁿ⁾ (n, k = 0, 1, 2, ...) - = ₁₁, ₂₂, ₁₂) stresses - = (₁₁, ₂₂, ₁₂) strains - = (₁₁, ₂₂, ₁₂) center of yield surface - D elastic coeffficient matrix, C = D ^–1 - von Mises yield function. The initial yielding is given by f() = _Y - f {f/} - ^* transposed f - H hardening parameter (assumed to be a positive constant for kinematic hardening problems) - time derivative of - [K] total elastic stiffness matrix - T traction vector - = [B] relation between nodal displacements and strains     

Problem of measuring the thermophysical characteristics of thin resistive and dielectric films

We consider the theoretical and experimental possibilities of determining a complex of thermophysical characteristics of thin films on a substrate, on the basis of a nonstationary method with boundary conditions of the fourth kind.Notation time - x coordinate perpendicular to the film surface - ₂, ₀, ₁ coefficients of thermal activity (=/a) of the substrate, the film, and the secpnd body - T₀₀ initial temperature of the film-substrate system - T₁₀ initial temperature of the second body - =T₁₀ – T₀₀ T ₀ ⁰ temperature at the boundary after contact as 0 - T ₀ ^t8 temperature at the boundary after contact as Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 1, pp. 98–101, January, 1982.     

Electrical resistivity in ferromagnetic NiCu alloys near the Curie point

Direct measurements of the temperature derivative of the electrical resistivity d/dT have been made on several ferromagnetic NiCu alloys with high Cu content (20, 30, 40, 50.4 at %). For Ni₈₀Cu₂₀ and Ni₇₀Cu₃₀ the results closely resemble the general pattern found in pure ferromagnets: d/dT - b – a ln ¦¦, for 10^–3 ¦¦ 10^–1, with a and b constants and = (T/T _c )– 1. In Ni₆₀Cu₄₀ the rounding off of the magnetic transition is already so pronounced that a similar analysis is hardly significant. In the Ni_49.6Cu_50.4 sample negative values of d/dT were confirmed above ~165 K. The possible theoretical implications of the results are briefly discussed.Work supported by Instituto de Alta Cultura, Portugal (Project PF1).     

Thermal transport properties in helium near the superfluid transition. I.4He in the normal phase

The thermal conductivity and the associated relaxation time to reach steady-state conditions are reported for the normal phase of several very dilute mixtures of³He in⁴He (X<4 × 10^–6) at saturated vapor pressure near T. The measurements were made over the reduced temperature range 2.5 × 10^–6<<2×10^–1, where (T–T)/T, and are representative for pure⁴He. The spacing between the cell plates was 0.147 cm. The systematic uncertainty in the conductivity data is estimated to increase from 2% for =0.2 to 4% for =3 × 10^–6. The random scatter due to finite temperature resolution increases to 7% at the smallest . The data are in agreement within the combined uncertainty with recent ones by Tam and Ahlers (cell F, spacing 0.20 cm) and with previous ones in this laboratory taken with a different plate spacing. The thermal diffusivity coefficientD _T = / C _p obtained from is found to agree within better than 15% with the calculated one using data for , the density , and the specific heatC _p . Measurements of the effective boundary resistivityR _b in the superfluid phase are described.R _b is found to depend on the thermal history of the cell when cycled up to 77 K and above. Also,R _b shows the beginning of an anomalous increase for ¦¦10^–4. The possible reasons for this anomaly are discussed, and their impact on the analysis of conductivity data in the normal phase is appraised.     

The surface of liquid 4He,based on the idea that π i<j f(r ij) describes a droplet

We argue that the wave function f(r _ij) describes the ground state of a droplet of liquid ⁴ He. With this wave function, expressions for the surface energy and the surface tension of liquid ⁴ He at T = 0 are derived. Choosing particular f(r) and density profile, and the simplest pair correlation function, we plot the variation of and with surface thickness t. For slow variation of density at the surface, becomes proportional to t. The surface thickness is found to be about 4 ». The inclusion of phonon zero-point motion correlations in the wave function leads (at T = 0) to a –R ² log R term in the energy of a droplet of radius R, implying a logarithmic divergence in both and . At T > 0 the phonon correlations give a log T dependence of and and a negative bulk specific heat. Suggestions as to the reason for these problems are explored, but no definite conclusions are reached.     

Theory of thermohyperelasticity for near-incompressible elastomers

Summary Elastomers are often used in hot and confining environments in which thermomechanical properties are important. It appears that published constitutive models for elastomers are mostly limited to isothermal conditions. In this study, athermohyperelastic constitutive model for near-incompressible elastomers is formulated in terms of the Helmholtz free energy density . Shear and volume aspects of the deformation are decoupled. Thermomechanical coupling occurs mostly as thermal expansion. Criteria for thermodynamic stability are derived in compact form. As illustration, a particular expression for is presented which represents the thermomechanical counterpart of the conventional two-term incompressible Mooney-Rivlin model. It is used to analyze several adiabatic problems in a rubber rod.List of symbols A _i matrices appearing inD - c _e, _e, c _e specific heat at constant strain - C Cauchy strain tensor - C _R reduced Cauchy strain tensor - C ₁,C ₂ coefficients of Mooney-Rivlin model - c vectorial counterpart ofC: VEC (C) - c ₂ vectorial counterpart ofC ²: VEC (C ²) - D isothermal tangent stiffness matrix - e vectorial counterpart of : VEC () - deviatoric Lagrangian strain tensor - e _R reduced deviatoric Lagrangian strain tensor - e volume strain - e _T reduced volume strain - f thermal expansion function,=[1+(T–T ₀)/3]^–1 - F, F _T deformation gradient tensor - F _R reduced deformation gradient tensor - H Hessian matrix for the Gibbs free energy density - H related toH - I ₁,I ₂,I ₃ invariants ofC - I _1R,I _2R,I _3R invariants ofC _R - I, I ₉ identity matrix - i vectorial counterpart ofI: VEC (I) - J determinant ofF - J _R determinant ofF _R - J _T determinant ofF _T - J ₁,J ₂ invariants of /J _{R 2} ³ - J _1R,J _2R invariants of _R /R _J ^2/3 - k thermal conductivity coefficient - K ₁,K ₂,K ₃ invariants of /J ^2/3 - K _1R,K _2R,K _3R invariants ofe _R/J^2/3 - p hydrostatic pressure - s vectorial counterpart of stress : VEC () - s isotropic stress - T (absolute) temperature - T ₀ reference temperature - conventional (isothermal) strain energy density (per unit volume) - volumetric thermal expansion coefficient - thermal expansion vector - strain, Lagrangian strain - entropy density - isothermal bulk modulus - Lagrange multiplier - _i extension ratio - shear modulus - stability coefficient - mass density - stress, 2nd Piola-Kirchhoff stress - _i principal stress - Cauchy stress - _d deviatoric Cauchy stress - , _{M C T 0} Helmholtz free energy density - _i /I _i - _ij ²/I _i I _j - Gibbs free energy density - (.) variational operator - VEC (.) vectorization operator - operator for Kronecker product     

Investigation of microstructure of molybdenum—copper black electrodeposited coatings with reference to solar selectivity

Optical and microstructural properties of electrodeposited molybdenum-copper (Mo-Cu) black coatings have been studied with reference to their selectivity in absorption of solar radiation. Such coatings were found to have a solar absorptance, , about 0.87 and low thermal emittance, , such that the selectivity, /, was 3.6. Electrodeposited molybdenum-black coatings generally have selectivity /3. The oxidation state of molybdenum in (Mo-Cu) black coatings as determined by X-ray photoelectron spectroscopy is about + 5 (which is fairly close to that of Mo₄O₁₁). Large numbers of irregular particles were found on the surface of molybdenum-copper black coatings. There is evidence that the particles contain copper oxide.     

Optimization of the designs of small-size helium cryostats

Using a computer program that simulates thermophysical processes occurring in small helium cryostats, the surface emissivities of actual cryostats are verified. The efficiency of the heat transfer from the walls of the reservoir suspension tube to the helium vapors is determined. The program makes it possible to optimize the designs of cryostats according to the specific conditions of their use.Notation Stefan-Boltzmann, constant - _bg, _ho, _sh, _res, _det emissivities of the background surrounding the cryostat, housing surface of the cryostat, radiation shield, helium reservoir, and radiation detector - T _bg,T _ho,T _sh,T _res temperatures of the background, cryostat housing, shield, and reservoir - _re1, _re2, _re3 reduced emissivities of the shield, housing, and reservoir - F _sh,F _ho,F _res surface areas of shield, housing, and reservoir - F ₁,F ₂,F ₃ areas of the entrance window in the cryostat housing, of the filter on the radiation shield, and of the inlet hole of the matching optics - ₁, ₂ emissivities of the filter and entrance window - ₁ solid angle at which the background radiation is absorbed by optical filter - ₂ solid angle at which radiation is transferred by matching optics to the radiation detector - ₁, ₂, ₃ transmission of radiation by way of the entrance window, filter, and matching optics - S cross-sectional area of the helium reservoir suspension tube - (T) temperature dependence of the thermal conductivity of the tube material - n ₁,n ₂,n ₃ number of mechanical couplings between the housing and the shield, electric wires, and mechanical couplings between the shield and reservoir - S ₁,S ₂,S ₃ cross-sectional areas of the mechanical coupling between the housing and shield, of the electric wire, and of the mechanical coupling between the shield and reservoir - l ₁,l ₂,l ₃,l ₄ lengths of mechanical couplings and electric wires over the body-shield and the shield-reservoir portions - ₁(T), ₂(T), ₃(T) temperature dependences of the thermal conductivities of the materials of mechanical couplings between the housing and shield, of electric wires, and mechanical couplings between the shield and reservoir - specific resistance of the material of electric wires - I working electric current - d inner diameter of the helium reservoir suspension tube - L ₁,L ₂,L ₃ lengths of the portions of the tube in the first, second, and third zones participating in heat exchange with helium vapors - U ₁,U ₂,U ₃ coefficients of heat conduction from the tube walls to helium vapors in the first, second, and third zones - T ₁, T ₂, T ₃ temperature differences in the corresponding zones of the tube - G ₁ weighted quantity of nitrogen evaporated per unit time - r ₁ latent heat of nitrogen vapor generation - G weighted quantity of helium evaporated per unit time - r latent heat of helium vapor generation - T _h temperature of helium vapors - c _p heat capacity of gaseous helium - G weighted quantity of helium evaporated per unit time due to heat supply only along the helium reservoir suspension tube All-Russian Scientific Center S. I. Vavilov State Optical Institute, St. Petersburg, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 5, pp. 760–766, September–October, 1995.     

Effect of intermittent polishing on low-cycle fatigue of pure aluminium

Low-cycle fatigue tests of aluminium were interrupted in order to remove surface roughening and superficial cracks produced by prior loading. Depending on the frequency of intermittent polishing and the strain level considerable increases in endurance life were observed.Nomenclature _t total strain range - _p plastic strain range - _e elastic strain range - N _p the number of cycles at which the intermittent polishing is carried out (single-step tests) - N _mp the number of cycles at which the last intermittent polishing action is performed in addition to preceding ones in every 50 cycles (multi-step tests) - N _pf the endurance life in the case of intermittent polishing (single- or multi-step tests) - N _f the endurance life without intermittent polishing