Near-tip dynamic fields for a crack advancing in a power-law elastic-plastic material: Modes I, II and III

Near-tip dynamic asymptotic stress fields of a crack advancing in an incompressible power-law elastic-plastic material are presented. It is shown that the stress- and strain-singularity are, respectively, of the order (In(R₀/r))^1/(n−1) and (In(R₀/r))^n/(n−1), where R₀ is a length parameter, r measures distance from the crack tip, and n is the power-law exponent. The angular variations of these fields are identical with those corresponding to dynamic crack growth in an elastic-perfectly-plastic material (Gao and Nemat-Nasser, 1983a,b).     

Structure quantitative map in application for AB2X4 system

Structure maps are constructed for AB₂X₄ (A = metal, B = three-valency element and X = O, S, Se, Te) system (>490 compounds). A way to improve the resolution of the maps is proposed. Crystal structure characteristic (symmetry) is represented on a quantitative scale (coordinate axe Z). The 3D structure diagram with approximating integral plane is constructed and a field of high symmetry compounds is specified with ion radii ratio R(A)/R(X) ≈ 0.60–0.85 and R(B)/R(X) ≈ 0.55–0.70.     

Second-order non-linear optical effects in Langmuir-Blodgett films

The synthesis of a new series of amphiphilic dyes of the form R¹R²NC₆H₄CH=CHC₅H₄⁺NCH₂CH₂COO^- (R¹=R²=C₆H₁₃,C₁₀H₂₁,C₁₄H₂₉ and C₁₈H₃₇) is described. These dyes have two alkyl chains per chromophore so as to facilitate fast deposition of Langmuir-Blodgett films. We report on the fabrication of monolayer films of these materials and the measurement of optical second harmonic generation in them. We deduce information about molecular tilt orientations and hyperpolarizabilities and compare the latter with previously published values of the electro-optic coefficients.     

A continuous review inventory model with a time discount

This paper presents a continuous review inventory model with a lost sales assumption. The model is unique due to the inclusion of a time discount. Whenever the supplier faces the likelihood of being out of stock, he may issue a discount to motivate customers to accept delayed deliveries and thus avoid the occurrence of lost sales. We propose a control policy with four parameters R₁, Q, R₂ and T where R₁ and Q are the normal reorder point and quantity, respectively and R₂ and T are the triggers for this time discount. During each replenishment cycle, if the on-hand inventory drops to R2 at or before T after the reorder time epoch, the time discount will be granted. A derivation as well as a solution approach for the total cost function are provided. Based on computational results, such a system with a time discount is superior to that without a time discount in terms of minimizing the total system cost. Finally, we compare the performance of the time discount and the emergency ordering approaches.     

Mid-infrared (2.5 ≤ λ ≤ 12.5 μm) optical absorption enhancement of textured silicon surfaces coated with an antireflective thin film

High-performance solar cells and optical detection devices frequently incorporate microscopic surface texturing and antireflective (AR) thin films to reduce the reflection of incident radiation and, thus, enhance optical absorption. Using conventional electrochemical and single-crystal silicon micromachining techniques, porous silicon (PS) and textured surfaces composed of randomly spaced and sized pyramids (RSSPs) were fabricated and optically characterized over the mid-infrared (2.5 ≤ λ ≤ 12.5 μm) portion of the optical spectrum. The utility of a 1.53 ± 0.03 μm thick yttrium oxide (Y₂O₃) AR thin film was also investigated in an attempt to enhance optical absorption. The optical measurements were accomplished using a 21 ° incident illumination angle (measured with respect to the sample's normal) and a Bomem® total integrating sphere to quantify the total (specular and diffuse) reflectance (R). A highly-polished, uncoated, single-crystal silicon wafer was used as a reference surface (R_ave = 0.436 with R_σ = 0.033). The performance of the uncoated PS samples revealed R_ave = 0.205 with R_σ = 0.078, and the RSSP samples manifested R_ave = 0.090 with R_σ = 0.003. The AR coating significantly improved the performance of the reference and the RSSP textured surfaces: reference sample, (R_ave = 0.251 with R_σ = 0.040; RSSP samples, (R_ave = 0.024 with R_σ = 0.017). The AR coating did not improve the mid-infrared optical performance of the PS samples; however, the R characteristics for the 0.5 ≤ λ ≤ 2.5 μm portion of the optical spectrum were reduced by more than 50%.     

A fracture criterion for three-dimensional crack problems

A criterion for predicting the growth of three-dimensional cracks is developed on the basis of the strain energy density concept which has been used successfully for treating two-dimensional crack problems. Fracture is assumed to initiate from the nearest neighbor element located by a set of spherical coordinates (r, θ, φ) attached to the crack border. The new fracture surface is described by a locus of these elements whose locations correspond to the strain energy function, dW/dV, being a minimum. The function dW/dV is found to be singular of the type 1/r and is of quadratic form in the three stress intensity factors k₁, k₂ and k₃ expressed through the strain energy density factor S. It is postulated that unstable crack propagation initiates from a region where S reaches a critical value S_cr = r₀(dW/dV)_cr. The locations of failure lying on the fracture surface is determined by holding (dW/dV)_cr = S_min/r₀ constant. The quantity S_min stands for the value of S minimized with respect to θ and φ and r₀ is a radial distance measured from the crack border.

An example of failure prediction for an embedded elliptical crack subjected to both normal and shear loads is presented. According to the S-criterion, fracture initiation takes place at the ends of the minor axis. An unexpected result is that for a narrow elliptical crack and Poisson's ratio of 1/3 the lowest failure load occurs when the uniaxial tensile load makes an angle of approximately 60° with the crack surface and is in the plane of the major axis. This is in contrast to the expectation that the lowest critical load occurs when the uniaxial tension is perpendicular to the crack surface. In the limit as the elliptical crack becomes increasingly narrower, the result reduces to the two dimensional line crack case of Mode I and III loading. The S-criterion is also applied to the failure prediction of three dimensional cracks under compressive loads.     

The effect of the stress ratio on fatigue crack growth in a 3% NaCl solution

Corrosion fatigue crack growth tests have been carried out at various stress ratios for a low alloy steel SNCM 2 and type 304 stainless steel.

Measurements of the effective stress intensity factor range ratio U were performed to explain the effect of stress ratio R.

The corrosive environment decreased da/dN at R = 0.1, 0.4 and little affected da/dN at R = 0.9 for SNCM 2 and increased da/dN at all R ratios for SUS 304.

It was confirmed that there exists a threshold stress intensity factor ΔK_thCF in 3% NaCl solution for both materials tested.

The corrosive environment decreased ΔK_thCF for all conditions tested except at R = 0.1 and 0.4 for SNCM 2, where ΔK_thCF-values were nearly equal to ΔK_th-values in air. ΔK_thCF/ΔK_th was 0.6 at R = 0.9 for SNCM 2 and 0.8, 0.5 and 0.7 at R = 0.1, 0.7 and 0.9 for SUS 304, respectively.

It was shown that the complicated effect of stress ratios on crack growth for SNCM 2 can be explained using effective stress intensity factor ΔK_eff.     

初始压力和富氧系数对CH4/O2/N2预混气体爆炸特性的影响

为了探究甲烷CH4在富氧和非常压条件下的爆炸危险性,确保CH₄气体在不同工况下的安全使用,借助5 L圆柱形爆炸装置,研究了初始压力p₀和富氧系数E对CH₄/O₂/N₂爆炸特性的影响。包括最大爆炸压力p_max、最大压力上升速率（dp/dt）_max和最大压力到达时间t_c等衡量CH₄爆炸安全性的指标。结果表明:当E为 0.21、0.25和0.30时,p_max随p₀的增加始终线性上升;而当E为 0.35和0.40时,p_max随p₀的增加先缓慢线性上升、后快速线性上升;（dp/dt）_max随p₀的增加分为线性上升和一阶指数快速上升。在E为0.21和0.25时,t_c随p₀的增加而线性增大,因为在燃烧初始阶段CH₄活化自由基的销毁速率增加,降低了反应速率和燃速,引起预混气体t_c的延长;但随着E的增加,氧气的促进作用与自由基销毁的抑制作用形成新的竞争效应,使得t_c先增加、后下降。     

Benzene insertion within the CsC24 graphite intercalation compound: a kinetic neutron diffraction study

The reaction of CsC₂₄ with deuterated benzene (C₆D₆)vapours has been studied in situ by neutron diffraction on a 5 min per spectrum time scale. As in the case of KC₂₄ and RbC₂₄ compounds, we first observed a second-stage ternary CsC₂₄(C₆D₆)y compound (y<2), but it quickly turned into a first-stage ternary CsC₂₄(C₆D₆)₂ compound. Structure model calculations suggest that each Cs⁺ ion is surrounded by two benzene rings, with a tilt angle of 39°, with respect to the c axis.     

Analysis of strain rate dependence of tensile elongation for a mechanical milling Al–1.1Mg–1.2Cu alloy tested at 748 K from a dislocation dynamics viewpoint

Tensile deformation was carried out for a mechanically milled and thermo-mechanically treated Al–1.1Mg–1.2Cu (at.%) alloy at 748 K and three nominal strain rates of 10⁻³, 10⁰, and 10² s⁻¹. Despite the prevailing belief that superplasticity occurs by grain boundary sliding which requires slow strain rates at high temperatures, the maximum elongation was observed at the intermediate strain rate of 10⁰ s⁻¹, neither at the lowest nor the highest strain rates. In order to explain this phenomenon, the true stress–true strain behaviors at these three nominal strain rates were analyzed from a viewpoint of dislocation dynamics by computer-simulation with four variables of the thermal stress component σ*, dislocation immobilization rate U, re-mobilization probability of unlocked, immobile dislocations Ω and dislocation density at yielding ρ₀. It can then be concluded that the large elongation (>400% in nominal strain) at the intermediate strain rate is produced by a combination of a very large Ω and a moderate U, resulting in a large strain rate sensitivity m value.     

Sur les coefficients de Hall et l'aimantation spontanée des films minces de nickel déposés et étudiés sous ultra-vide

A phenomonological theory of the Hall effect in ferromagnetics shows that, in contrast to the usual interpretation, the study of the experimental curve which represents the Hall resistivity versus the applied field does not permit the Hall coefficients R₀ and R₁ to be determined unless the exact value of the spontaneous magnetization M_s is known.

This theory is shown to fit qualitatively very well with the experimental results and assuming that M_s has the same value as in bulk nickel, the calculated values of R₀ and R₁ for thick films are in good agreement with the tabulated ones for bulk nickel.     

Anomalous elastic response of amorphous alloys suggesting collective motions of many atoms

The dynamic Young’s modulus, E, of amorphous (a-) Zr₆₀Cu₃₀Al₁₀ (numbers indicate at.%) alloy was measured as a function of frequency, f, with a strain amplitude, _t, of 10⁻⁶, E(10⁻⁶,f), and also as a function of _t for f near 10² Hz, E(_t,10² Hz), by means of the vibrating reed methods. The elasticity study under the passing of electric current (PEC) was carried out too. E(10⁻⁶,f) is lower than E₀ for f between 10 and 10⁴ Hz showing local minima near 5×10, 5×10² and 5×10³ Hz, which are indicative of the resonant collective motion of many atoms, where E₀ is the static Young’s modulus. E(_t,10² Hz) increases showing saturation with increasing _t. Qualitatively, the outlines of E(10⁻⁶,f) and E(_t,10² Hz) observed for a-Zr₆₀Cu₃₀Al₁₀ are similar to those reported for various a-alloys. Quantitatively, a change in E(_t,10² Hz) for a-Zr₆₀Cu₃₀Al₁₀ is smallest among that reported for various a-alloys, presumably reflecting that the crystallization volume, (ΔV/V)_x, is smallest for a-Zr₆₀Cu₃₀Al₁₀. The effective charge number, Z^*, estimated from the change in E(10⁻⁶,10² Hz) due to PEC is 3.0×10⁵, which is comparable with Z^* reported for various a-alloys. We surmise that the number of atoms in the collective motions excited near 10² Hz is similar among various a-alloys. The E(10⁻⁶,f) data suggest that the spatial sizes of the density fluctuations may show a distribution.     

Physics and diagnostics of laser ablation plume propagation for high-Tc superconductor film growth

The formation, composition and propagation of laser-produced plasmas used for pulsed laser deposition (PLD) of Y₁Ba₂Cu₃O_7−x have been studied under film growth conditions. Four complementary spatially and temporally resolved in situ diagnostic techniques are applied to characterize the expansion of the laser plume into both vacuum and ambient gases: optical emission and absorption spectroscopy, fast ion probe measurements, and fast photography with a gated, image-intensified charge-coupled detector-array (ICCD) camera system. Transient optical absorption spectroscopy reveals large densities of ground state atoms, ions, and molecules in the plume as well as a slower component to the plume transport than is indicated by the plasma fluorescence and ion current.

Ablation into background gases results in scattering and attenuation of the laser plume. The exponential attenuation of the positive ion flux transmitted through 50–300 mTorr background oxygen is measured and used to define an overall ion-oxygen reaction cross-section σ_i−O2 = 2.3 × 10⁻¹⁶ cm² under the described film growth conditions.

The slowing of the laser plasma and formation of shock structures due to collisions with the ambient gas are described using ion probe measurements and ICCD photographic comparisons of expansion into vacuum and background oxygen. At the pressures used for PLD, distance-time R−t plots derived from the photographs and ion probe waveforms indicate that the higher pressure plume initially expands through the ambient gas in accordance with a drag model (where R = x_f[1 − exp( − βt)]), experiencing little slowing until a visible shock structure forms. Following a transition period, in which the plume appears to have two components, a single-component shock structure propagates in better agreement with a shock, or blast wave (R = ξ₀(E/₀)^1/5t^2/5) model.     

Griffith's theory of brittle fracture in three dimensions

The Griffith theory of brittle fracture is extended to the three-dimensional problem of a flat elliptical crack in an otherwise uniform field of tensile and shear stresses. A method for finding the correct expressions of the change in strain energy due to the elliptical crack is developed. This is done by expressing the stresses and displacements in terms of the radius R₀ of a large sphere around the crack and by imposing the condition of equilibrium that the stresses or displacements across the spherical surface should agree with the prescribed boundary conditions as R₀ → ∞. The strain energy due to the presence of the elliptical crack is found to be independent of the tension applied parallel to the crack plane at infinity. On the basis of the thermodynamic argument of Griffith, it is also observed that the critical tensile and shear stresses increase rapidly as the ratio of major to minor semi-axes of the ellipse approaches unity.     

Segregation of Cu in Cu (Ti) alloys during nitridation in NH3

Cu(Ti 27 at.%) alloys on SiO₂ were reacted in NH₃ for 30 min over the temperature range 400–700 °C. Rutherford backscattering spectrometry in conjunction with high resolution transmission electron microscopy were utilized to investigate reaction products. At 400–450 °C, Ti is observed to segregate to the free surface to react with NH₃, forming an Ti oxynitride layer. Above 500 °C, Ti segregates to both the free surface and to the alloy/SiO₂ interface, leaving relatively-pure Cu layer. Reaction between Ti and SiO₂ results in a TiO/Ti₅Si₃ bilayer structure. By use of high spatial resolution energy dispersive X-ray spcctroscopy, the presence of a Cu-containing layer at the TiO/Ti₅Si₃ interface is observed. This layer may also contain Ti, Si and/or O. We propose a mechanism for Cu segregation to this interface which requires Cu diffusion across TiO and subsequent dissociation of Ti₅Si₃. Thermodynamic calculations support this mechanism.     

Probabilistic description of fatigue crack growth in polycrystalline solids

A stochastic model describing the crack evolution and scatter associated with the crack propagation process has been built on the basis of the discontinuous Markovian process. The evolution and scatter are identified in terms of constant probability curves whose equation is derived as In P_r(i) = B(e^KI₀ − e^Ki), i ≥ I₀, where i is the number of cycles, B and K are crack-length-dependent variables, P_r(i) is the probabiliity of the crack being at position r along the fracture surface after i cycles elapse and I₀ is the minimum number of cycles required for the crack to advance from one position on the fracture surface to the next. The validity of the model is established by comparing the crack growth curves generated for Al 2024-T3 at a specific loading condition with those experimentally obtained.     

Preparation and characterization of YBa2Cu3O7−x high Tc superconducting thin films deposited by S-gun sputtering

We have prepared YBa₂Cu₃O_7−x high T_c superconducting (HTS) thin films on (100) yttria-stabilized zirconia (YSZ) and LaAlO₃ (LAO) substrates, using a 2 kW S-gun in an off-axis mode. By varying the temperature of the substrates, films with a axis and c axis orientations were readily obtained. The X-ray diffraction pattern and Laue pattern confirmed that films with a axis orientation exhibited a single-crystal texture. All films had a good mirror-like surface. For films grown on YSZ substrates, scanning electron microscopy (SEM) revealed a clear distinction between the surfaces of the films grown at various temperatures (520–780°C). Films grown on LAO substrates exhibited even smoother and flatter surfaces. The SEM changes will be discussed in correlation with J_c. The best HTS thin films were obtained on LAO substrates at a temperature of 820°C, with T_c=89 K and J_c=1×10⁶ A cm^-2 (77 K).     

Computations of the Energetics of C60F36 Isomers

Three isomers of C₆₀F₃₆ are known from experiment (C₃, T, and C₁ symmetry). However, computations do not agree on their relative stabilities. In order to clarify the situation, DFT computations are carried out with different basis sets and several functionals. While lower level computations yield the C₃ isomer as the most stable, higher computational treatments consistently point out the T isomer as the lowest potential-energy species.     

Crystal structure and spectroscopic studies of NaGd(PO3)4

Single crystals of gadolinium–sodium polyphosphate NaGd(PO₃)₄ were grown for the first time using a flux method and characterized by X-ray diffraction. This phosphate crystallizes in a monoclinic system with P2₁/n space group and with the following unit-cell dimensions: a = 9.767(3) Å, b = 13.017(1) Å, c = 7.160(2) Å, β = 90.564(5)°, V = 910.3(4) Å³ and Z = 4. The crystal structure was solved from 3451 X-ray independent reflections with final R(F²) = 0.0219 and R_w(F²) = 0.056 refined with 164 parameters (). The atomic arrangement can be described as a long chain polyphosphate organization. Two infinite (PO₃)∝ chains with a period of eight tetrahedra run along the [0 1 1] direction. The structure of NaGd(PO₃)₄ consists of GdO₈ polyhedra sharing oxygen atoms with phosphoric group PO₄. Each Na⁺ ion is bonded to eight oxygen atoms.