The elastically equivalent softening zone size for an elastic-softening material: II. A simple piece-wise softening law

The paper determines the elastically equivalent softening zone size R_E for an elastic-softening material when there is a semi-infinite crack in a remotely loaded infinite solid; the parameter R_E plays a central role in size effect expressions that are used to correlate the maximum loads that can be sustained by solids having different dimensions. The stress (p) versus displacement (v) softening law considered is that for which P = p_c for oc and P = ; qp_c = p_* for λδ_c< v <δ_c. Particular attention is focussed on the case where the parameters λ and q are both small. Such a softening law simulates the softening behaviour of plain concrete, where there is an initially rapid softening to a low stress value at a small displacement, followed by a long tail that is associated with a low stress. The paper shows that the behaviour of a material with such a softening law can be conveniently analysed by assuming that there is a non-zero stress intensity (K_IC) at the crack tip followed by a constant stress p_* within the softening zone; , where E_o is the reduced modulus and G_{I = λpcδc} is the contribution to the specific fracture energy arising from the initially rapid softening region. Analysis of a specific model demonstrates the viability of this approach by showing that there is consistency with the proposed size effect expressions based on R_E.     

Inference of critical cod from Charpy V test result

Correlation between the Charpy absorbed energy and critical COD is investigated to obtain a useful method for estimating critical COD from Charpy V data. The round bar tension test, Charpy V-notch test and static 3-point bend test with fatigue notched specimen are carried out using mild steel, 785 MPa grade high strength steel and A5083 aluminum alloy. Correlation is found between W'_c/σ_Y and δ_c as well as between EW'_c/σ_Y² and Eδ_c/σ_Y, where W'_c is the Charpy absorbed energy obtained by considering temperature difference between the Charpy transition temperature and COD transition temperature. The symbols σ_Y, δ_c and E are yield strength, critical COD and Young's modulus, respectively. The correlations are established for various kinds of metals and over a wide temperature range including not only upper shelf range but also the transition range.     

Critical parameters for HFC134a, HFC32 and HFC125

The vapour-liquid coexistence curves near the critical point for HFC134a (CF₃CH₂F: 1,1,1,2-tetrafluoroethane), HFC32 (CH₂F₂: difluoromethane) and HFC125 (CHF₂CF₃: pentafluoroethane) have been measured by visual observation of the meniscus disappearance. Three sets of 17 experimental results for the saturated liquid or vapour densities for HFC134a, HFC32 and HFC125 have been obtained in the reduced temperature range T/T_c > 0.96 and in the reduced density range 0.4 < ρ/ρ_c < 1.7. From these measurements, the critical temperature and the critical density for these HFCs have been determined in consideration of the meniscus disappearance level as well as the intensity of the critical opalescence. The critical pressure has been calculated by the extrapolation of the vapour-pressure correlation. The uncertainties of the critical temperature, critical density and critical pressure are estimated to be within ± 10 mK, ± 5 kg m⁻³ and ± 9 kPa, respectively.     

A new diagram for evaluating the relationship between convective and evaporative heat transfer during the cooling of carcasses

During the cooling of a carcass, both its heat losses by convection and by evaporation are governed by the convective heat transfer coefficient c. While both phenomena occur at the same temperature difference δ_w between the surface of the carcass and the cold air, the quantity of heat flux of the former part becomes _cδ_w, and the latter part becomes the product of _c multiplied by an equivalent temperature difference δ_D which is a function of the vapour pressure differences between the wet surface and the cold air. The ratio δ_D/δ_w can be established from the diagram and the heat loss by convection and by evaporation can be calculated for any given value of _c. Consequently, the anticipated theoretical weight loss of the carcass can be calculated.     

Evaluation of neutron thermalization parameters and benchmark reactor calculations using a synthetic scattering function for molecular gases

Using a synthetic incoherent scattering function which describes the interaction of neutrons with molecular gases we provide analytical expressions for zero- and first-order scattering kernels, σ₀(E₀ → E), σ₁(E₀ → E), and total cross section σ₀(E₀). Based on these quantities, we have performed calculations of thermalization parameters and transport coefficients for H₂O, D₂O, C₆H₆ and (CH₂)_n at room temperature. Comparison of such values with available experimental data and other calculations is satisfactory. We also generated nuclear data libraries for H₂O with 47 thermal groups at 300 K and performed some benchmark calculations (²³⁵U, ²³⁹Pu, PWR cell and typical APWR cell); the resulting reactivities are compared with experimental data and ENDF/B-IV calculations.     

CdGeAs2晶体的热膨胀行为研究

采用WinTA 100热膨胀仪研究了四方黄铜矿CdGeAs₂晶体在320~620 K温度范围内的热膨胀行为, 探索了CdGeAs₂晶体热膨胀各向异性的物理机制。测定晶体a轴和c轴方向的热膨胀系数α_a和α_c发现, α_a>>α_c>0, 表现出强烈的各向异性热膨胀特性。利用最小二乘法, 拟合出CdGeAs₂晶体的晶格常数(a, c)与温度(T)的函数关系式, 与文献报道值吻合。分别计算出不同温度下的四方畸变因子δ=2-c/a, Cd-As 键长(l_Cd-As)和 Ge-As 键长(l_Ge-As)以及相应的热膨胀系数α_Cd-As和α_Ge-As。结果表明, a、c、δ、l_Cd-As、l_Ge-As和α_Cd-As均随着温度的升高而增大, c/a和α_Ge-As则随着温度的升高而减小。当T=360 K时,α_Cd-As是α_Ge-As的6.36倍, 是造成CdGeAs₂晶体强烈热膨胀各向异性的主要原因。     

Fracture-resistant ultralloys for space-power applications: Normal-spectral-emissivity and electron-emission studies of tungsten, rhenium, hafnium-carbide alloys at elevated temperatures

A series in this journal on high-temperature properties of “fracture-resistant ultralloys for space-power systems” preceded the present paper: the antecedent publications covered tungsten(W), rhenium(Re) alloys with and without thoria(ThO₂) (W, 23Re; W, 27Re; W, 30Re and W, 30Re, 1ThO₂). This paper reports radiative and thermionic effects of hafnium carbide(HfC) and Re variation in W alloys: normal spectral emissivity(ε_λ) is used in pyrometry to determine the true temperature of a surface. Effective work function (φ_e) is an important consideration in the selection of the electrode materials for high-temperature thermionic energy converters in space-power applications. The _0.535μ, ε_0.65μ and φ_e trends of W, Re, 0.35HfC with 5–20% Re were measured in the range of 1700–2500K. The results indicate that ε_λ decreases with increasing temperatures and Re contents. The presence of HfC produced higher ε_λ values than those of sintered materials with comparable W,Re alloy contents. The results also indicate that φ_e increases with rhenium contents. This can be explained as growth of the potential barrier at the metal, vacuum boundary associated with a volume effect—the decrease in the lattice constant of W.     

Magnetic and electrical characterization of heavily boron-doped diamond

For a heavily boron-doped diamond (BDD) film, temperature variations of the electrical conductivity σ and magnetic susceptibility χ are reported. The room temperature σ 143 (Ω-cm)⁻¹ corresponds to a carrier concentration 10³ ppm, and its temperature variation yields an activation energy E_a 28 meV from 140 to 300 K and E_a0.88 meV from 40 to 80 K. It is argued that larger boron doping leads to lower magnitudes of E_a. The χ vs. T data (1.8–350 K) fits the Curie–Weiss law, with the concentration of paramagnetic species 120 ppm and a diamagnetic susceptibility −0.4×10⁻⁶ emu/g Oe. The results obtained from the measurements of σ and χ are discussed and compared.     

Charge carrier transport in Cu(COOH)2 organic molecular single crystal

The temperature dependences of the d.c. electrical conductivity (σ) and thermoelectric power (TEP) of low-dimensional Cu(COOH)₂ single crystal have been studied. The electrical conductivity is highly anisotropic (σ_‡/σ = 3.0 × 10²) and the crystal undergoes a Peierls transition at 208 K and two polymorphous phase transitions, namely → β and β → at 327 and 377 K respectively. The conductivity in this crystal is found to be mainly due to a non-adiabatic hopping mechanism. TEP measurements carried out at various temperatures show that the conductivity is due to the mobility of holes.     

The Dislocation Structure of a Single-Crystal γ + γ′ Two-Phase Alloy After Tensile Deformation

The dislocation structures of an industrial single-crystal γ + γ′ two-phase alloy DD3 after tensile deformation from room temperature to 1273K were studied by transmission electron microscopy. The strength of this alloy decreased with an increase in the temperature, and showed a strength peak at 1033K. At room temperature, the dislocations shearing the γ′ particles were found to be 1/3<112> partial dislocations on the dodecahedral slip system <112>{111}. Some dislocation pairs on the cubic <110>{100} system that blocked the glide of dislocations were found at a medium temperature of 873K. As a result, dislocation bands were formed. Shearing of γ′ particles by 1/3<112> partial dislocations on the dodecahedral slip system <112>{111} was also found at this temperature. At the peak temperature of 1033K, because of the strong interaction between dislocations on the {111} and {100} planes, the extent of dislocation bands with high dislocation densities was extensive. The 1/3<112> partial dislocations on the dodecahedral slip system <112>{111} also existed. When the temperature reached the high temperature of 1133K, the range of dislocation bands was limited. The γ′ particles were sheared by <110> dislocation pairs on the octagonal <110>{111} system and the cubic <110>{100} system. At 1273K, the regular hexagonal dislocation networks were formed in the γ matrix and at the γ/γ′ interface. The Burgers vectors of the network were found to be b₁ = 1/2[110], b₂ = 1/2[1–10], b₃ = [100], and the last one was formed by the reaction of b₁ + b₂ → b₃. Dislocations shearing the γ′ particles were found to be <110> dislocation pairs on the octagonal system <110>{111} and cubic slip system <110>{100} at 1273K.     

AC Conductivity and Dielectric Response of Polycrystalline and Amorphous C70

The AC conductivity and dielectric constant of polycrystalline and amorphous C₇₀ samples were measured in the 75-300 K temperature range and in the 100 Hz to 1 MHz frequency range. For polycrystalline samples, we observe effects caused by O₂ intercalation due to prolonged exposure to ambient air. The conductivity σ of these samples around 300 K depends on the measuring frequency ν as a σ ∼ νⁿ with n ≈ 0.88, implying a strong reduction of DC conductivity to less than 10^-12 S/cm. The dielectric constant of polycrystalline samples shows an anomaly at 285 K which is interpreted as due to the transition from its intermediate rhombohedral phase into its monoclinic low-temperature phase. In contrast with the polycrystalline samples, the amorphous C₇₀ samples prepared by sublimation do not contain interstitial 0₂, their conductivity at 300 K is of about 10^-6 S/cm, is independent of frequency, and is well described by the hopping mechanism (Davis-Mott T^1/4 law) in the 200-300 K range. All evidence of phase transitions disappears in the amorphous samples.     

Effect of ferroic domain pattern changes on the Raman spectra of some ferroic crystals

The influence of changes in the pattern of ferroic domain structure on the Raman spectra of β-LiNH₄SO₄ and (NH₄)₃H(SO₄)₂ single crystals were studied. It was shown that the Raman spectra of β-LiNH₄SO₄ passed from the ferroelastic phase differ from those of “as-grown” crystal and those of the crystal, which was in the paraelectric phase. Significant changes could be observed in the Raman bands related to triply degenerated ν₃ and ν₄ vibrations of the SO₄ tetrahedron. Detailed temperature studies of the Raman spectra of β-LiNH₄SO₄ close to the paraelectric–ferroelectric phase transition, exhibit anomaly of some internal vibrations of SO₄ in the temperature range where a regular large-scale structure is observed. Different types of evolution of the ferroelastic domain structure and temperature behaviour of the donor and acceptor vibrations were shown while heating and cooling the (NH₄)₃H(SO₄)₂ crystal. Different values of temperature hysteresis were found in temperature studies of the ferroelastic domain structure (ΔT_S  3–5 K) and in Raman spectra studies (ΔT_S  12 K). No changes were observed in the pattern of ferroelastic domain structure at the temperature T_II–III  265 K, at which C2/c → P2/n structural phase transition takes place. On the other hand, at T_III–IV  135 K additional domains with W′-type of domain wall orientation were found.     

Moving singularity creep crack growth analysis with the (ΔT)c and C integrals

The physical meaning of (ΔT)_c and its applicability to creep crack growth are reviewed. Numerical evaluation of(ΔT)_c and C^* is discussed with results being given for compact specimen and strip geometries. A moving crack-tip singularity, creep crack growth simulation procedure is described and demonstrated. The results of several crack growth simulation analyses indicate that creep crack growth in 304 stainless steel occurs under essentially steady-state conditions. Based on this result, a simple methodology for predicting creep crack growth behavior is summarized.     

Enhanced piezoelectric properties of potassium niobate single crystals with fine engineered domain configurations

Potassium niobate (KNbO₃) single crystals were grown by a top seed solution growth (TSSG) method. At first, the electric field was applied along [0 0 1]_c (cubic notification system) direction of KNbO₃ crystals to induce the engineered domain configurations into KNbO₃ crystals. Prior to domain engineering, the piezoelectric properties of [0 0 1]_c oriented KNbO₃ single-domain crystals were measured. These measured values were completely consistent with the calculated apparent d₃₁ and d₃₂. Finally, the engineered domain configurations were induced into KNbO₃ crystals. As a result, piezoelectric properties increased with decreasing domain sizes of the engineered domain configuration.     

Optical constants of polycrystalline CuGaTe2 films

Thin films of CuGaTe₂ with thicknesses in the range, 0.1–1.0 μm were deposited on Corning 7059 glass substrates by flash evaporation. The substrate temperatures, T_s, were maintained in the range 373–623 K. The transmittance of the films was recorded in the wavelength range 900–2500 nm. The dependence of the optical band gap, E_g, on substrate temperature showed that the value of E_g varied from 1.21 eV to 1.24 eV. The variation of refractive index and extinction coefficient with photon energy was studied from which the material properties such as the limiting value of dielectric constant, ε_∞, plasma frequency, ω_p, and hole effective mass, m_h^*, were evaluated as ε_∞ = 7.59, ω_p = 1.47 × 10¹⁴ and m_h^* = 1.25 m₀.     

Temperature dependence of the growth of gallium oxide on CoGa(100)

The oxidation of a CoGa(100) surface at high temperatures has been studied by scanning tunnelling microscopy (STM) and auger electron spectroscopy (AES). When CoGa(100) is oxidised at a sufficiently high temperature (>600 K), an ordered Ga₂O₃ film is formed. The stability of the film depends on the sample temperature and partial oxygen pressure of the ambient gas. At negligible oxygen pressure (<10⁻¹¹ mbar) the oxide is stable up to 850 K. At an oxygen pressure of 10⁻⁶ mbar the oxide is stable up to 930 K and some of the oxide remains present up to 970 K. The oxide film is found to be very uniform. The thickness of the film is constant and independent of the oxidation temperature (600 K<T<930 K), oxygen pressure (<10⁻⁶ mbar), and exposure (10⁻⁴–10⁻² mbar.s≈10²–10⁴ L). We find a clear improvement of the order of the oxide film surface with increasing oxidation temperature. In STM images, a domain structure of the oxide film is observed. The size of the domains increases by a factor of 5–10 when the oxidation temperature is increased from 700 to 900 K.     

Comparative study on chemical stability of dielectric oxide films under HF wet and vapor etching for radiofrequency microelectromechanical system application

HF wet and vapor etching of dielectric oxide films, which were prepared by thermal atomic layer deposition (ALD) and plasma-enhanced ALD (PEALD), are examined for radiofrequency microelectromechanical system (RF MEMS) application. The chemical stability of oxide films was increased in the order of ALD–Al₂O₃ < PEALD–ZrO₂ < PEALD–TiO₂ ≈ ALD–Ta₂O₅ under wet etching in 6:1 buffered HF aqueous solution, but in a different order of Ta₂O₅ < ZrO₂ < TiO₂ ≈ Al₂O₃ under anhydrous HF/CH₃OH vapor etching at 4 kPa. The unstable films were uniformly and completely etched under the wet etching, while transformed to have increased thickness or non-uniformly etched with thicker residue under the vapor etching. Al₂O₃ and TiO₂ (Ta₂O₅ and TiO₂) can be used for RF MEMS capacitive switch fabricated by using HF vapor (wet) etching of sacrificial SiO₂.     

Raman Spectroscopy of the Charge Transfer Complex (TTF)x C60 Br8

We report Raman studies on powder samples of the charge transfer complex (TTF)_x C₆₀Br₈ at room temperature. The phonons show considerable softening with respect to the frequencies observed in the Raman spectrum of solid C₆₀ Brg. The strongest mode at 1464 cm^-1 in C₆₀Br₈ is red shifted to a doublet with peaks at 1414 and 1421 cm^-1, implying an average phonon softening Δω of -47 cm^-1. A comparison with the phonon softening of the corresponding A_g(2) mode in alkali-doped C₆₀ (Δω ~ - 36 cm^-1 for A₆C₆₀, A = K, Rb or Cs) suggests that 8 electrons are transferred per C₆₀Br₈ molecule in the charge transfer complex. The mode at 503 cm_--1 in C₆₀Br₈ is shifted upwards, similar to that in A₆ C₆₀ compounds.     

On the buckling of a column in an elastic medium

One deals with the buckling of a cantilever column in an elastic medium by the aid of the differential eqns (2), (2′) with bilocal conditions (3), (3′). Introducing the conventional load (4), one considers the three cases P_cr < P₀, P_cr = P₀ and P_cr > P₀ and one determines the corresponding characteristics eqns (8″), (12), (15″). The reduced critical load P_cr/P₎ and the reduced critical length l_cr/l are listed in a table and plotted into diagrams for various values of an adimensional magnitude bl. One obtains also the asymptotic formulae (16), (16′).     

Crack growth resistance characterized by the strain energy density function

Stable ductile fracture of a typical metal alloy is found to be governed by the condition dS/da = const., i.e. the rate change of the strain energy density S with crack length 2a (or a) remained constant. Since fracture and/or yielding are load rate dependent, the incremental theory of plasticity is employed for analyzing crack growth where unloading in the material near the crack can take place. Attention is focused on the energy per unit volume, dW/dV, stored along the prospective path of crack growth. The nearest neighbor continuum element must necessarily be at a finite distance r from the crack front. This leads to the general relation dW/dV = S/R. The critical value (dW/dV)_c representing the area under the uniaxial true stress and strain curve is assumed to correspond with failure of material elements. If yielding and unloading occurred locally, a certain amount of irrecoverable energy will not be available for dissipation during macrocracking. Hence, the threshold energy density must be modified to read as (dW/dV)_c^* < (dW/dV)_c. The quantity (dW/dV)_c may be regarded as the crack growth resistance whose magnitude decreases with increasing distance from the crack tip at which point yielding is most intensified.

The results are displayed graphically and shown that the condition dS/da = const. provides a rational means of collating and interpreting ductile fracture data.