Isochoric Heat Capacity Measurements for 2,2-Dichloro-1,1,1-Trifluoroethane (R123) at Temperatures from 167 to 341 K and 1-Chloro-1,2,2,2-Tetrafluoroethane (R124) from 94 to 341 K at Pressures to 35 MPa

Molar heat capacities at a constant volume (C _v) of 2,2-dichloro-1,1,1-trifluoroethane (R123) and 1-chloro-1,2,2,2-tetrafluoroethane (R124) were measured with an adiabatic calorimeter. Temperatures ranged from 167 K for R123 and from 94 K for R124 to 341 K, and pressures were up to 33 MPa. Measurements were conducted on the liquid in equilibrium with its vapor and on compressed liquid samples. The samples were of a high purity, verified by chemical analysis of each fluid. For the samples, calorimetric results were obtained for two-phase (C ⁽²⁾ _v), saturated liquid (C or C _x ), and single-phase (C _v) molar heat capacities. The C data were used to estimate vapor pressures for values less than 100 kPa by applying a thermodynamic relationship between the saturated liquid heat capacity and the temperature derivatives of the vapor pressure. Due to the tendency of both R123 and R124 to subcool, the triple-point temperature (T _tr) and the enthalpy of fusion ( _fus H) could not be measured. The principal sources of uncertainty are the temperature rise measurement and the change-of-volume work adjustment. The expanded uncertainty (at the 2 level) for C _v is estimated to be 0.7%, for C ⁽²⁾ _v it is 0.5%, and for C it is 0.7%.     

Molar heat capacity at constant volume of difluoromethane (R32) and pentafluoroethane (R125) from the triple-point temperature to 345 K at pressures to 35 MPa

Molar heat capacities at constant volume (C _v) of dill uoromethane (R32) and pentalluoroethane (R125) were measured with an adiabatic calorimeter. Temperatures ranged from their triple points to 345 K, and pressures up to 35 MPa. Measurements were conducted on the liquid in equilibrium with its vapor and on compressed liquid samples. The samples were of a high purity, verified by chemical analysis of each fluid. For the samples, calorimetric results were obtained for two-phase (C _v ⁽²⁾ ), saturated liquid (C orC _x ), and singlephase (C _v) molar heat capacities. TheC data were used to estimate vapor pressures for values less than 0.3 MPa by applying a thermodynamic relationship between the saturated liquid heat capacity and the temperature derivatives of the vapor pressure. The triple-point temperature (T _tr) and the enthalpy of fusion (_fus H) were also measured for each substance. The principal sources of uncertainty are the temperature rise measurement and the change-ofvolume work adjustment. The expanded uncertainty (at the two-sigma level) forC _v is estimated to be 0.7%, forC _v ⁽²⁾ it is 0.5%, and forC it is 0.7%.     

Molar Heat Capacity at Constant Volume of 1,1-Difluoroethane (R152a) and 1,1,1-Trifluoroethane (R143a) from the Triple-Point Temperature to 345 K at Pressures to 35 MPa

Molar heat capacities at constant volume (C _v) of 1,1-difluoroethane (R152a) and 1,1,1-trifluoroethane (R143a) have been measured with an adiabatic calorimeter. Temperatures ranged from their triple points to 345 K, and pressures up to 35 MPa. Measurements were conducted on the liquid in equilibrium with its vapor and on compressed liquid samples. The samples were of high purity, verified by chemical analysis of each fluid. For the samples, calorimetric results were obtained for two-phase ((C _v ⁽²⁾ ), saturated-liquid (C or C _x ^' ), and single-phase (C _v) molar heat capacities. The C data were used to estimate vapor pressures for values less than 105 kPa by applying a thermodynamic relationship between the saturated liquid heat capacity and the temperature derivatives of the vapor pressure. The triple-point temperature and the enthalpy of fusion were also measured for each substance. The principal sources of uncertainty are the temperature rise measurement and the change-of-volume work adjustment. The expanded relative uncertainty (with a coverage factor k=2 and thus a two-standard deviation estimate) for C _v is estimated to be 0.7%, for C _v ⁽²⁾ it is 0.5%, and for C it is 0.7%.     

Effect of magnesium content on the stress exponent and effective stress in the steady state creep of Al-Mg alloys

The stress exponent of steady state creep,n, and the internal ( _i) and effective stresses ( _e) have been determined using the strain transient dip test for a series of polycrystalline Al-Mg alloys creep tested at 300° C and compared with previously published data. The internal or dislocation back stress, _i, varied with applied stress,, but was insensitive to magnesium content of the alloy, being represented by the empirical equation _i=1.084 ^1.802. Such an applied stress dependence of _i can be explained by using an equation for _i of the form _i (dislocation density)^1/2 and published values for the stress dependence of dislocation density. Values of the friction stress, _f, derived using the equation _e/=(1–c) (1– _f/), indicate that _f is not dependent on the magnesium content. A constant value of _f can best be rationalized by postulating that the creep dislocation structure is relatively insensitive to the magnesium content of the alloy.On leave from Engineering Materials Department, University of Windsor, Windsor, Ontario N9B 3P4, Canada.     

Shock response of stainless steel at high temperature

Measurements of the dynamic tensile strength of HR-2 (Cr-Ni-Mn-N) stainless steel have been carried out over the initial temperature range of 300 K–1000 K at shock stress of 8 GPa, the corresponding spall strength _f and Hugoniot elastic limit _HEL are determined from the wave profiles. In the temperature range of 300 K–806 K, _f and _HEL decrease linearly with increasing temperature T, i.e., _f = 5.63-4.32 × 10^–3T, _HEL = 2.08-1.54 × 10^–3T, but when heated to 980 K, _HEL increases from 0.84 GPa at 806 K to 0.93 GPa at 980 K and _f keeps at an almost fixed value of 2.15 GPa. The TEM analysis on recovery samples identified the existence of intermatallic compound Ni₃Al and the carbide Cr₂₃C₆ in the sample of 806 K, another intermatallic compound Ni₃Ti was found in the sample of 980 K. All these products emerge along crystal boundary. While no such products were found in the samples of 300 K and 650 K.     

Frequency and temperature dependence of the millimeter wave conductivity of epitaxial YBa2Cu3O7 films

A millimeter wave spectrometer for frequencies between 100 and 350 GHz consisting of continuously tunable backward wave oscillators as sources and a quasioptical interferometer in the Mach-Zehnder configuration was used to measure the transmittivity in phase and amplitude of YBa₂Cu₃O₇ thin films on NdGaO₃ substrates. From the measured spectra we derived the real and imaginary part of the dynamic conductivity= ₁+i ₂ in the superconducting state as a function of temperature. The ₁(T) and ₂(T) values at 300 GHz were compared to corresponding values at 19 GHz determined by surface impedance measurements of the same films using a shielded dielectric resonator. Our observed frequency dependence of both ₁(T) and ₂(T) is consistent with a strong reduction of the quasiparticle scattering rate ^–1(T) with decreasing temperature belowT _c .     

Quantum statistical foundation to the fermi liquid model and Ginzburg-Landau wave function

An energy eigenvalue equation for a quasi-particle is derived, starting with the Heisenberg equation of motion for an annihilation operator. An elementary derivation of the Fermi liquid model having a sharply defined Fermi surface in thek-space is given, starting with a realistic model of a metal including the Coulomb interaction amongand between electrons and lattice-ions. The Ginzburg-Landau wave function (r), where represents the superconducting pairon (Cooper-pair) state, is shown to be connected with the one-pairon density operatorn by (r) = r¦_n ^1/2¦. A close analogy between supercurrent and laser is indicated.On sabbatical leave from Department of Physics and Astronomy, State University of New York at Buffalo, Buffalo, New York.     

Stress relaxation in hot-drawn low density polyethylene

The tensile stress relaxation behaviour of hot-drawn low density polyethylene, (LDPE), has been investigated at room temperature at various draw ratios. The drawing was performed at 85° C. The main result was an increase in relaxation rate in the draw direction, especially at low draw ratios when compared to the relaxation behaviour of the isotropic material. This is attributed to a lowering of the internal stress. The position of the relaxation curves along the log time axis was also changed as a result of the drawing, corresponding to a shift to shorter times. The activation volume, , varied with the initial effective stress ₀ ^* according to ₀ ^* 10kT, where ₀ ^* =₀ — _i, is the difference between the applied initial stress, ₀, and the internal stress _i. This result supports earlier findings relating to similarities in the stress relaxation behaviour of different solids.     

Molar Heat Capacity at Constant Volume of n-Butane at Temperatures from 141 to 342 K and at Pressures to 33 MPa

Molar heat capacities at constant volume (C _V) for normal butane are presented. Temperatures ranged from 141 to 342 K for pressures up to 33 MPa. Measurements were conducted on liquid in equilibrium with its vapor and on compressed liquid samples. The high purity of the samples was verified by chemical analysis. For the samples, calorimetric results were obtained for two-phase [C _v ⁽²⁾ ], saturated liquid (C or C _x ), and single-phase (C _V) molar heat capacities. The principal sources of uncertainty are the temperature rise measurement and the change-of-volume work adjustment. The expanded uncertainty (i.e., a coverage factor k=2 and thus a two-standard deviation estimate) for values of C _V is estimated to be 0.7%, for C _v ⁽²⁾ it is 0.5%, and for C it is 0.7%.     

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     

A note on the resistance to brittle fracture in various ceramic materials

The square of the ratio of the abraded bending strength, _d, to the unabraded bending strength, , is proposed as a measure of the resistance to crack propagation in ceramic materials. Data for various porcelains, glass-ceramics, and glasses showed that _d is essentially constant and that (_d/)² decreased rapidly with increase of the unabraded strength.     

Stress intensity factors in a fully interacting,multicracked, isotropic plate

An essential part of describing the damage state and predicting the damage growth in a multicracked plate is the accurate calculation of stress intensity factors (SIF's). Analytical derivations of these SIF's for a multicraked plate can be complex and tedious. Recent advances, however, in intelligent application of symbolic computation can overcome these difficulties and provide the means to rigorously and efficiently analyze this class of problems. Here, the symbolic algorithm required to implement the methodology for the rigorous solution of the system of singular integral equations for SIF's is presented. The special problem-oriented symbolic functions to derive the fundamental kernels are described, and the associated automatically generated FORTRAN subroutines are given. As a result, a symbolic/FORTRAN package named SYMFRAC, capable of providing accurate SIF's at each crack tip, has been developed and validated.Simple illustrative examples using SYMFRAC show the potential of the present approach for predicting the macrocrack propagation path due to existing microcracks in the vicinity of a macrocrack tip, when the influence of the microcracks' location, orientation, size, and interaction are accounted for.List of symbols offset angle between inner tips of two parallel cracks - _lr, _mz direction cosines between two local coordinate systems - _jl strain tensor - offset of notch-microcracks system with respect to Y axis - _k four roots of the characteristic equation - v Poisson's ratio - _jl ^o , _jl ^T far-field and total stress field, respectively - _XX ^o , _YY ^o , _XY ^o components of stress in global coordinate system - _j angle defining local frame orientation - , normalized real variable - (s, y) Fourier transform of Airy stress function with respect to x variable - a _j half crack length - a ₁₁, a₁₂, a₂₂ coefficients of strain-stress relationship - d normalized radial (tip) distance - f _nj auxiliary functions - k ₁, k₂ mode-I and mode-II stress intensity factors - ker _inf ^sup Fredholm kernels - p _j normal traction at crack surface - q _j shear traction at crack surface - s Fourier variable - r _j, r_kX, r_kY position vector and its components, for an origin of local frame - u, v x, y component of displacement, respectively - w weight function - x _j y_jand X, Y local and global coordinates - [A] matrix of coefficients - C' _j, C_j functions of s in Fourier space (i.e., constrants in x, y-real space) - E Young modulus - F _j(x_j, y_j) Airy stress function - G_nj(_p) discrete auxiliary function - {} loading function vector     

Convection in a shallow laterally heated cavity with conducting boundaries

Shallow cavity flows driven by horizontal temperature gradients are analysed over a range of Rayleigh numbersR and Prandtl numbers , whereR is comparable in size to the aspect ratioL(1). Eigenvalue calculations show the existence of a critical Prandtl number R > R _c (), below which the parallel core-flow structure is destroyed for Rayleigh numbersR>R _c(). For other Rayleigh numbers and Prandtl numbers the horizontal scale of influence of the end walls of the cavity is determined.     

Pyramidal yield criteria for epoxides

The tensile, compressive and shear yield strengths of two epoxides were measured under superposed hydrostatic pressure extending to 300 MN m^–2. For both materials, the ratio of the moduli of the tensile, _T, to compressive, _C, yield stress at atmospheric pressure was approximately 34, as has been reported previously for a number of thermoplastics. The ₂= ₃ envelope in stress space was plotted according to these two-parameter ( _C and _T) yield criteria: conical, paraboloidal and pyramidal; the best correlation was with the last. The experimental tensile and compressive data for tests under pressure, however, fit slightly better two straight lines which are consistent with a three-parameter single hexagonal pyramidal yield surface. For plane stress and shear under pressure yield envelopes of these surfaces, the correlation with experimental data is again best for the pyramidal criteria, except for biaxial or triaxial tension when these resins are brittle. The third independent parameter employed in the pyramidal criterion was the equi-biaxial compressive yield stress, determined by tensile experiments under appropriate superposed hydrostatic pressure; alternatively plane strain compressive yield stress, _PC, may be used.     

Electrical conductivity,thermoelectric power and dielectric constant of NiWO4

The a.c. electrical conductivity ( _ac), thermoelectric power () and dielectric constant () of antiferromagnetic NiWO₄ are presented. _ac and have been measured in the temperature range 300 to 1000 K and in the temperature range 600 to 1000 K. Conductivity data are interpreted in the light of band theory of solids. The compound obeys the exponential law of conductivity = ₀ exp (–W/kT). Activation energy has been estimated as 0.75eV. The conductivity result is summarized in the following equation =2.86 exp (–0.75 eV/kT)^–1 cm^–1 in the intrinsic region. The material is p-type below 660 K and above 950 K, and is n-type between 660 and 950 K.     

Experimental investigation of the effects of stress rate and stress level on fracture in polystyrene

The effects of stress rate and stress level on fatigue crack propagation in compression-moulded single-edge notched specimens (0.25 mm in thickness) of polystyrene are reported. Values of the stress rate are obtained from the formula = 2v(_max – _max),, wherev is the frequency and _max, _min are the maximum and minimum stresses of the fatigue cycle. Different levels of are achieved by changing the frequency while keeping _max, _min at fixed values. The effect of the stress level is investigated by keeping and _min constant and varying _max andv. The results show that when the kinetic data are plotted as l/t against the energy release rateG ₁, a relatively small effect of the stress rate is observed. If the same data are treated as l/N againstG ₁, a decrease in l/N with test frequency is seen. The increase in the level of _max results in a higher crack speed. The critical crack length is found to be practically the same for all stress-rate experiments. A decrease in the critical crack length is observed with the increase in stress level. Analysis of craze distribution around the crack path shows that the extent of crazing decreases with the increase in stress rate and increases with the increase in stress level. For all experimental conditions, the ratio of the second moment to the square root of the fourth moment of the histograms of craze density along directions normal to the crack path is found to be constant throughout the slow phase of crack propagation. This result supports a self-similarity hypothesis of damage evolution proposed in the crack layer model.     

Surface tension of helium at the superfluid critical end-point

The singularity in the vapor-liquid interfacial tension, (T), of helium at the transition to superfluidity is analyzed theoretically. The universal amplitude ratio R ⁺ =K₊( ₀ ⁺ )^d–1/k _B T , where K₊ and K_– are the amplitudes of the |T–T|^µ singularity in , with =1.34 ₃ , is known from recent work to first order in =4–d for the general n-vector model in d dimensions. Extrapolation to d=3 for n=2 indicates R ⁺ =0.05–0.08, which is shown to be consistent with the experimental data. Further analysis of the experiments establishes that the universal ratio Q=K₊/K _– exceeds 0.35, and is consistent with the recent prediction Q0.9; this demonstrates the inadequacies of earlier theoretical treatments. The existence in the observed surface tension of an anomalous, negative contribution of unknown origin at a few millikelvin beneath T is stressed.     

Microstructure and mechanical properties of metastable lath martensite wires in the Fe-Ni-Cr-Al-C system produced by melt spinning in rotating water

Metastable lath martensite ( _L ) phase wires with high strengths have been produced in the Fe-Ni-Cr-Al-C alloy system by melt spinning in rotating water. These wires have a circular cross section and a white lustre and the wire diameter is in the range of 100 to 140m. The width and length of each lath in the _L phase are as small as about 0.3 and 2m, respectively. The _y, _f and _p are about 900 and 1650 MPa and 2.0% for the _L wires. The subsequent annealing causes an increase in _p as well as _y and _f and the attained values are about 1000 and 1700 MPa and 3.0% for Fe-10Ni-10Cr-6.5 Al-1.0C wire annealed at 773 K for 1 h owing to the precipitation strengthening of a very fine unidentified carbide and to a high density of dislocations and lath boundaries in the _L phase. Further annealing causes a significant decrease in _p through decomposition of _L to+M₇C₃+M₂₃C₆. Therefore, the high strength combined with relatively good ductility for the _L wires is interpreted as due to the suppression of the phase transformation of _L to a mixed structure of+M₇C₃+M₂₃C₆ by melt quenching.     

Interfacial debonding and fibre pull-out stresses

Based on a theoretical model developed previously by the authors in Part II of this series for a single fibre pull-out test, a methodology for the evaluation of interfacial properties of fibre-matrix composites is presented to determine the interfacial fracture toughness G _c, the friction coefficient , the radial residual clamping stress q _o and the critical bonded fibre length z _max. An important parameter, the stress drop , which is defined as the difference between the maximum debond stress _d ^* and the initial frictional pull-out stress _fr, is introduced to characterize the interfacial debonding and fibre pull-out behaviour. The maximum logarithmic stress drop, In(), is obtained when the embedded fibre length L is equal to the critical bonded fibre length z _max. The slope of the In()-L curve for L bigger than z _max is found to be a constant that is related to the interfacial friction coefficient . The effect of fibre anisotropy on fibre debonding and fibre pull-out is also included in this analysis. Published experimental data for several fibre-matrix composites are chosen to evaluate their interfacial properties by using the present methodology.On leave at the Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong.     

Surface tension of liquid3He at low temperature

The thermal contribution to the surface tension of liquid³He due to the single quasiparticle motion is estimated in the low-T regime using a local approximation for the entropy. The density and temperature dependence of the effective mass is shown to play a crucial role in determining the behavior of (T). The theoretical predictions explain the anomalous behavior of (T) recently observed at low temperature by Suzuki et al.³ Predictions for the temperature dependence of the interfacial tension of liquid³He-⁴He mixtures are also given.