Thermomechanical behavior of a plate composed of layers with different transparencies under the action of thermal radiation

We study the thermal and mechanical processes running in a two-layer plate (in the case of perfect mechanical contact between the opaque and semitransparent layers) caused by the thermal radiation of a heated plane surface parallel to the composite plate and located on the side of the opaque layer. The contact boundary-value problem of heat conduction is reduced to an equivalent system of three nonlinear Volterra-type equations solved by the method of successive approximations. The dependences of the distributions of temperature and stresses in the plate on the ratio of thicknesses of the layers are investigated. It is shown that the influence of the thermal radiation of the opaque layer on the computed temperature in the plate is significant at temperatures higher than 530°K. As the thickness of the semitransparent layer decreases for a fixed thickness of the opaque layer, the temperature gradient across the thickness of the semitransparent layer sharply increases. The maximum tensile stresses in the plate may appear in the opaque or semitransparent layer depending on the ratio of the their thicknesses. For certain thicknesses of the semitransparent layer, they can attain the maximum permissible values. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 6, pp. 17–26, November–December, 2007.     

Geometry Effect on Deposition and Residence Time of Polydisperse Fine Drops in Mini-Risers Under Developing Flow Condition

Mini-riser geometry effect on the transport, dispersion and deposition of fine water drops in the three-dimensional laminar developing flow was investigated numerically and experimentally. Circular, triangular and rectangular cross-section risers with a hydraulic diameter of 14 mm were examined. Microscopic high-speed particle shadow velocimetry (PSV) technique was employed for planar velocity measurement of droplets. The experimental data were used to validate the simulation results obtained with an Eulerian–Lagrangian computational code. In addition, simulation results of the penetration were compared with the existing theoretical model, and a close agreement was found. In these simulations the polydispersed fine droplets were randomly distributed at the inlet of the risers in a size range of 0.01 to 10 µm. For comparison of the effect of riser shapes, the airflow rate was assumed to be constant. Simulation results indicated significantly more droplets were deposited on the walls of the triangular and high aspect ratio rectangular risers. Brownian diffusion tends to increase the residence time especially for risers with a corner. Employing the riser shapes with sharper corners and higher aspect ratio was found to be more beneficial for increasing the droplet size moving in a supersaturated carrier gas, especially at high flow rates, due to higher residence time.     

Geometrical considerations in analyzing isotropic or anisotropic surface reflections

The bidirectional reflectance distribution function (BRDF) represents the evolution of the reflectance with the directions of incidence and observation. Today BRDF measurements are increasingly applied and have become important to the study of the appearance of surfaces. The representation and the analysis of BRDF data are discussed, and the distortions caused by the traditional representation of the BRDF in a Fourier plane are pointed out and illustrated for two theoretical cases: an isotropic surface and a brushed surface. These considerations will help characterize either the specular peak width of an isotropic rough surface or the main directions of the light scattered by an anisotropic rough surface without misinterpretations. Finally, what is believed to be a new space is suggested for the representation of the BRDF, which avoids the geometrical deformations and in numerous cases is more convenient for BRDF analysis.     

Optical properties (bidirectional reflectance distribution function) of shot fabric

To study the optical properties of materials, one needs a complete set of the angular distribution functions of surface scattering from the materials. Here we present a convenient method for collecting a large set of bidirectional reflectance distribution function (BRDF) samples in the hemispherical scattering space. Material samples are wrapped around a right-circular cylinder and irradiated by a parallel light source, and the scattered radiance is collected by a digital camera. We tilted the cylinder around its center to collect the BRDF samples outside the plane of incidence. This method can be used with materials that have isotropic and anisotropic scattering properties. We demonstrate this method in a detailed investigation of shot fabrics. The warps and the fillings of shot fabrics are dyed different colors so that the fabric appears to change color at different viewing angles. These color-changing characteristics are found to be related to the physical and geometrical structure of shot fabric. Our study reveals that the color-changing property of shot fabrics is due mainly to an occlusion effect.     

Optical constants and Drude analysis of sputtered zirconium nitride films

Opaque and semitransparent dc magnetron-sputtered ZrN films on glass and silicon have been optically characterized with spectral reflectance measurements and ellipsometry. High rate sputtered ZrN has good optical selectivity, i.e., higher than 90% infrared reflectance and a pronounced reflectance step in the visible to a reflectance minimum of less than 10% at 350 nm. The results are comparable with those obtained for single crystalline samples and those prepared by chemical vapor deposition. The complex optical constant (N = n v ik) for opaque films has been determined in the 0.23-25-μm wavelength range with Kramers-Kronig integration of bulk reflectance combined with oblique incidence reflectance for p-polarized light. A variable angle of incidence spectroscopic ellipsometer has been used for determination of the optical constants in the 0.28-1.0-μm wavelength region. The results of the two methods show excellent agreement. The results indicate that ZrN is free electronlike and the Drude model can be applied. The best opaque films had Drude plasma energies (?ω(p) between 6.6 and 7.5 eV and relaxation energies (?/τ) between 0.29 and 0.36 eV. Ellipsometer data for the semitransparent films show that the refractive index (n) in the visible increases with decreasing film thickness whereas the extinction coefficient (k) is essentially unchanged. The optical properties are improved by deposition upon a heated substrate.     

Total internal reflection ellipsometry: principles and applications

A concept for a measurement technique based on ellipsometry in conditions of total internal reflection is presented. When combined with surface plasmon resonance (SPR) effects, this technique becomes powerful for monitoring and analyzing adsorption and desorption on thin semitransparent metal films as well as for analyzing the semitransparent films themselves. We call this technique total internal reflection ellipsometry (TIRE). The theory of ellipsometry under total internal reflection combined with SPR is discussed for some simple cases. For more advanced cases and to prove the concept, simulations are performed with the Fresnel formalism. The use of TIRE is exemplified by applications in protein adsorption, corrosion monitoring, and adsorption from opaque liquids on metal surfaces. Simulations and experiments show greatly enhanced thin-film sensitivity compared with ordinary ellipsometry.     

Prediction of the bidirectional reflectance-distribution function from atomic-force and scanning-tunneling microscope measurements of interfacial roughness

Computer codes that are based on Elson's theory for light scattering by interfacial roughness in multilayer coatings were used to predict the bidirectional reflectance-distribution function (BRDF) of several opaque coatings from surface-roughness profiles measured by either a scanning-tunneling microscope or an atomic-force microscope. The predictions usually agreed with measured BRDF values to within a factor of 2. The coatings consisted of single layers of Ag or Ni and dielectric stacks with up to three layers.     

Scattering by random particles on optical surfaces

An analytical technique has been developed for calculating the angle-resolved light scattering by contaminant particles on smooth opaque surfaces. The analytical method was tested by a comparison of measured and calculated bidirectional reflectance distribution function (BRDF) values for contaminated surfaces. BRDF values were calculated from particle sizes, shapes, and areal densities obtained from scanning electron microscope images of the contaminated surfaces by a Princeton gamma-tech image analyzer. Measured and calculated BRDF values agreed to within the uncertainty associated with the particle characterization process for most scattering angles.     

三角形状压电振子压电特性分析与仿真

(压电振子的几何形状是影响其振动发电的重要因素之一。在相同压电材料体积下,三角形压电振子相比于矩形和梯形压电振子具有更大的发电能力。选用悬臂梁式三角形状压电振子作为研究对象,利用有限元分析软件ANSYS进行仿真研究。建立有限元模型;通过静力学和模态分析,研究压电振子的几何形状对其输出电压、固有频率的影响规律,然后在满足原来输出电压不下降的前提下对其进行尺寸优化,提高单位体积的发电能力。在相同边界条件和外力作用下,优化尺寸模型的体积是原来的0.94倍,输出电压是原来的1.03倍,取得了很好的优化效果。     

Effect of solvents and catalysts on monolithicity and physical properties of silica aerogels

The effect of various solvents and catalysts on the monolithicity and physical properties of silica aerogels is reported. The aerogels were prepared by hydrolysis and polycondensation of tetramethoxysilane, followed by hypercritical drying, using 6 solvents of different chain lengths, and 17 catalysts consisting of strong and weak acids, bases and their mixtures. It was found that solvents of longer chain lengths and strong basic catalysts resulted in semitransparent to opaque aerogels, whereas strong acids and their combinations with a weak basic catalyst produced transparent but cracked aerogels. While weak acids and their combinations with a weak base were found to produce shrunk and semitransparent (opaque for CH₃COOH + NH₄OH) aerogels, the best quality transparent, monolithic, low-density and refractive index, and large surface area aerogels were obtained for a combination of weak basic catalysts and solvents of shorter branching and chain lengths. The physical properties of the aerogels were studied by BET analysis, porosity, density, refractive index and optical transmission measurements.     

Variation in flexural properties of photo-pultruded composite archwires: analyses of round and rectangular profiles

Prototype continuous, unidirectional, fiber-reinforced composite archwires were manufactured into round and rectangular profiles utilizing a photo-pultrusion process. Both 0.022 inch (0.56 mm) diameter and 0.021 × 0.028 inch (0.53 × 0.71 mm) rectangular composites were formed utilizing commercially available S2-glass® reinforcement within a polymeric matrix. Reinforcement was varied according to the number, denier and twists per inch (TPI) of four S2-glass® yarns to volume levels of 32–74% for round and 41–61% for rectangular profiles. Cross-sectional geometry was evaluated via light microscopy to determine loading characteristics; whereas two flexural properties (the elastic moduli and flexural strengths) were determined by 3-point bending tests. Morphological evaluation of samples revealed that as the TPI increased from 1 to 8, the yarns were more separated from one another and distributed more peripherally within a profile. For round and rectangular profiles utilizing 1 TPI fibers, moduli increased with fiber content approaching theoretical values. For round profiles utilizing 1 TPI and 4 TPI fibers, flexural strengths increased until the loading geometry was optimized. In contrast, the flexural strengths of composites that were pultruded with 8 TPI fibers were not improved at any loading level. Doubling the denier of the yarn, without altering the loading, increased both the moduli and flexural strengths in rectangular samples; whereas, the increases observed in round samples were not statistically significant. At optimal loading the maximum mean moduli and strengths equaled 53.6 ± 2.0 and 1.36 ± 0.17 (GPa) for round wire and equaled 45.7 ± 0.8 and 1.40 ± 0.05 (GPa) for rectangular wires, respectively. These moduli were midway between that of martensitic NiTi (33.4 GPa) and beta-titanium (72.4 GPa), and produced about one-quarter the force of a stainless steel wire per unit of activation. Values of strengths placed this composite material in the range of published values for beta-titanium wires (1.3–1.5 GPa). © 2000 Kluwer Academic Publishers     

Reciprocal vector theory for diffractive self-imaging

A reciprocal vector theory for analysis of the Talbot effect of periodic objects is proposed. Using this method we deduce a general condition for determining the Talbot distance. Talbot distances of some typical arrays (a rectangular array, a centered-square array, and a hexagonal array) are derived from this condition. Further, the fractional Talbot effect of a one-dimensional grating, a square array, a centered-square array, and a hexagonal array is analyzed and some simple analytical expressions for calculation of the complex amplitude distribution at any fractional Talbot plane are deduced. Based on these formulas, we design some Talbot array illuminators with a high compression ratio. Finally, some computer-simulated results consistent with the theoretical analysis are given.     

A finite element model for plane elasticity problems using the complementary energy theorem

A finite element stress analysis capability for plane elasticity problems, employing the principle of stationary complementary energy, is developed. Two models are investigated. The first is a 24 d.o.f. rectangular finite element. The second model consists of an 18 d.o.f. triangular element. In order to allow for self-equilibrating stresses which are continuous within the element, the well-known Airy stress function ø is used. The function ø is represented by means of quintic Hermitian polynomials within the finite element. The values of the ø function and its derivatives up to order two are used as nodal parameters. For matching the stress function with the prescribed boundary tractions, additional equations are developed considering the force and moment equilibrium equations on the boundary consistent with the assumed stress function. These additional boundary equations are incorporated into the system equations using the Lagrangian multiplier technique. Excellent results are obtained for linear elastic problems even with coarse finite element discretization. Some examples of plane elasticity problems are solved and results compared.     

Extended bidirectional reflectance distribution function for polarized light scattering from subsurface defects under a smooth surface

By introducing the scattering probability of a subsurface defect (SSD) and statistical distribution functions of SSD radius, refractive index, and position, we derive an extended bidirectional reflectance distribution function (BRDF) from the Jones scattering matrix. This function is applicable to the calculation for comparison with measurement of polarized light-scattering resulting from a SSD. A numerical calculation of the extended BRDF for the case of p-polarized incident light was performed by means of the Monte Carlo method. Our numerical results indicate that the extended BRDF strongly depends on the light incidence angle, the light scattering angle, and the out-of-plane azimuth angle. We observe a 180 degrees symmetry with respect to the azimuth angle. We further investigate the influence of the SSD density, the substrate refractive index, and the statistical distributions of the SSD radius and refractive index on the extended BRDF. For transparent substrates, we also find the dependence of the extended BRDF on the SSD positions.     

Transverse magnetic plane-wave scattering equations for infinite and semi-infinite rectangular grooves in a conducting plane

The transverse magnetic plane-wave scattering equations for infinite and semi-infinite rectangular grooves (RGs) in a conducting plane are proposed in terms of the overlapping T-block method and Floquet theorem. By utilising the Floquet theorem and taking the limit of multiple RGs as the number of RGs becomes infinity, the simultaneous solutions of infinite RG are then analytically obtained. Combining the analyses of infinite and large number of RGs yields approximate yet numerically efficient scattering equations for semi-infinite RG. Numerical computations are performed to verify that the solutions converge fast and agree with the mode-matching method.     

Effect of surface roughness on gas flow in microchannels by molecular dynamics simulation

Understanding the effect of surface roughness on gas flow in microchannels is highly desirable in microfluidic devices. Non-equilibrium molecular dynamics simulation is applied to investigate the effect of the surface roughness on slip flow of gaseous argon in submicron platinum channels. The geometries of the surface roughness are modeled by triangular, rectangular, sinusoidal and randomly triangular waves respectively. The results show that the boundary conditions of velocity slip, including slip, no-slip and negative slip, depend not only on the Knudsen number but also on the surface roughness. Induced by the roughness, the slip length of gas microflow over a rough surface is less than that predicted by the Maxwell model and shows a non-linear relationship with the Knudsen number. The friction coefficient increases not only with decreasing the Knudsen number but also with increasing the surface roughness. The impacts of the surface roughness and the gas rarefaction on the friction coefficient of gas microflow are strongly coupled. The roughness geometry also shows significant effects on the boundary conditions and the friction characteristics. The distortion of the streamlines and the enhancement of the penetrability near the rough surface are demonstrated to be responsible for the roughness effect.     

The Effect of Notch Geometry on Tensile Strength at Low and Intermediate Strain Rates

Abstract: Mechanical behaviour of notched components can significantly be influenced by notch geometry. In this work, triangular, circular and square notches are examined by experiment. Two materials including a st52 steel and brass are employed for the investigation. The experiments are conducted at low and intermediate strain rates. It is observed that: (i) the yield stress of the brass and the specimens with circular and square notches decreases as the notch length increases such that for 8 mm notches, the value of yield stress converges to the yield stress obtained for plain specimens at the same strain rate. (ii) For triangular notches the yield stress rises with the increase of notch length up to a minimum and then begins to decline. (iii) The effect of notch geometry on yield stress is significant such that for triangular notches, in particular for higher notch lengths, the increase of yield stress is much more profound than the other two notch geometries.     

Substrate wetting and topographically induced ordering of amorphous PI-b-PFS block-copolymer domains

The substrate wetting of an amorphous, low-glass-transition-temperature spherical poly(isoprene-block-ferrocenylsilane) (PI-b-PFS) block copolymer and the alignment of the microdomains in grooves of various geometry are studied. Compositional analysis by time-of-flight secondary ion mass spectrometry depth profiling (TOF-SIMS) indicates the presence of both PI and PFS directly at the film-substrate interface on silicon and silica substrates. The TOF-SIMS depth-profiling study indicates a transition in the packing of the domains between the two-dimensional (2D) monolayer and 3D, thicker layers. In a monolayer of domains, a hexagonal packing is adopted. In films of two or three layers, the hexagonal packing reorganizes towards a body-centered cubic (bcc) packing by the extension of the copolymer chains in the direction normal to the substrate, as indicated by an increase in spacing between PFS layers and an increase in domain size. For thicker layers, a bcc morphology with the (110) plane parallel to the substrate is found to extend from the free surface downwards. Films of one monolayer of domains of the copolymer exhibit long-range lateral ordering on the micrometer scale on flat substrates without high-temperature annealing. On topographically patterned silicon substrates the position of the domains of the minority PFS phase directly near the side walls is fixed by the neutral wetting condition. Successful positioning of the block-copolymer spheres in linear and hexagonal grooves is achieved in grooves up to 1.3 microm wide, whereby the hexagonal grooves demonstrate complete 2D alignment. In circular pits, this graphoepitaxial effect is absent.     

Measurement of strains in plain and perforated epoxy models by means of embedded strain gauges

In the embedded strain gauge technique, the use of miniature gauges with very thin copper leads minimises reinforcing effect on the model. The technique. in this form, was applied to the investigation of three–dimensional strain distributions. Suitability of the method was assessed by determining the mechanical properties of epoxy resin from strains measured in cylindrical and rectangular models subjected to uniaxial tension and in a rectangular beam model subjected to pure bending. The central portion of the beam was subsequently perforated with a triangular array of holes to simulate the geometry of a heat exchanger tube plate. Strains in the ligaments were then measured for various ligament efficiencies, with the model under bending and under tension.