Layers Of Equal Thickness Research Articles

An Efficient Algorithm for Gravity Forward Modeling (GFM) with Masses of Arbitrary Shapes and Density Distributions

Summary Currently, gravimetric forward modelling of mass density structures with arbitrary geometries and density distributions typically involves subdividing the mass body into individual geometric elements (such as rectangular prisms), calculating their gravitational contributions that are then summed up to obtain the gravitational attraction of the whole body. To achieve a more accurate approximation of the true geometric shape and density distribution, this rectangular prism model requires fine dividing, which significantly increases computational load and reduces numerical efficiency. To address this issue, we propose the algorithm for gravimetric forward modeling of arbitrary geometric shapes and density distributions in spectral domain that significantly improves numerical efficiency while preserves computational accuracy. The novelty of our proposed algorithm lies in dividing the masses into multiple layers of equal thickness in the vertical direction, providing constant upper and lower bounds. This allows to extended Parker's formulas and apply the Fast Fourier Transform (FFT) to increase numerical efficiency. The algorithm is tested using synthetic models and then used to compute gravitational effects of topography and sediments using real data from Tibet. Results show high accuracy and numerical efficiency than rectangular prism approach.

Scaling of turbulence-forced capillary waves

We simulate the propagation of capillary waves at the interface between two liquid layers of equal density, viscosity and thickness, which flow in stratified conditions inside a turbulent Poiseuille channel. This setup gives us the possibility to single out the effect of inertia and surface tension – in isolation from gravity – on the propagation of interfacial capillary waves. Numerical simulations, which are based on a combined pseudo spectral/phase field method, are run keeping the shear Reynolds number constant, Reτ=300, and considering four different values of the Weber number: We=0.5, We=1.0, We=1.5 and We=2.0. In the present case, waves are naturally forced by turbulence over a broad range of scales, from the larger ones, whose size is of order of the channel height h, down to the smaller dissipative scales. We show that, by increasing the Weber number, the interface is deformed more vigorously, and is prone to sustain the propagation of waves over a broader range of scales. Upon computation of the power spectra of wave elevation, we show that the behavior of waves agrees with the theoretical predictions given by the weak wave turbulence theory, which predicts a decay Sη(k)∼k−4 in the inertial regime, followed by a steeper decay at large k, in the surface-tension-dominated regime. We clearly show that the transition between the inertial and the surface-tension-dominated regime is pushed towards larger k by increasing the Weber number. In addition, we show that the two-dimensional frequency–wavenumber spectra of the wave elevation – the dispersion relation – is in good agreement with well established theoretical prediction, ω(k)∼k3/2, and that the range of validity of such prediction broadens for increasing Weber number.

Influence of the number of carded non-woven layers on mechanical and acoustic performance

Acoustic absorption consists basically of the transformation of mechanical energy into thermal energy, carried out through the interaction of the fibers with the sound wave through the breaking of such waves and their meeting with the surface of the fibers. Among the various materials that may be employed to this end, the use of non-woven fabrics has stood out. This study aimed to evaluate the influence of the number of carded non-woven web layers on the mechanical and sound absorption capacity. For this purpose, three groups of non-woven fabrics were produced with different numbers of web layers (24, 40, and 58 layers) of equal thickness and density, composed of a mixture of polyester fibers. Standard test procedures were used to measure the physical properties of the non-woven fabrics, the linear density of the fibers used as raw material, the tensile strength, and air permeability and to assess the sound absorption capacity. In addition, to identify a balance point between sound absorption and equipment productivity, the relationship between the acoustic performance of the non-woven fabrics produced and their production speed was evaluated. The greater the number of web layers is, the higher the absorption coefficient of the non-woven. However, the variation was not significant when the various sound absorption frequencies were observed. In this regard, developing a non-woven fabric with fewer layers was more productive and cost-effective without losing technical performance.

Kinetics of charge carriers in bilateral macroporous silicon

The kinetics of charge carriers in bilateral macroporous silicon with macroporous layers of equal thicknesses is calculated by the finite difference method. A diffusion equation for a monocrystalline substrate and macroporous layers is solved. The boundary conditions are defined at the boundaries between the monocrystalline substrate and the macroporous silicon layers on both sides. Stationary distribution of excess charge carriers in the bilateral macroporous silicon with the macroporous layers of equal thicknesses calculated by the finite difference method is set as the initial condition. Under stationary conditions, excess charge carriers are generated by light with the wavelengths of 0.95 µm and 1.05 µm. It is shown that at the counting times much longer than the relaxation time, all the distributions of the concentration of excess minority carriers generated by light with any wavelength approach the same distribution with exponentially decreasing value.

Size-dependent microstructural evolution and mechanical properties of crystalline/amorphous high-entropy alloy nanostructured multilayers: Cu/FeCoCrNiBSi vs Ni/FeCoCrNiBSi

Magnetron sputtering technique was employed to synthesize crystalline/amorphous high-entropy alloy (AHEA) X/AHEA (X = Cu and Ni, AHEA = Fe20Co20Cr20Ni20B10Si10) nanostructured multilayers (CANMs) with equal layer thickness h ranging from 5 to 150 nm, aiming at systematically investigating their plastic deformation and microstructural evolution. Unlike traditional crystalline/crystalline multilayers often with shear banding at small h, the present X/AHEA CANMs exhibit h-independent homogeneous deformation via the thinning of both constituent layers, while associated with h-dependent deformation-induced devitrification in AHEA layers with thickness below 25 nm. This homogeneous plasticity of AHEA layers with the large incubation size for mature shear bands can be ascribed to the coupling between dislocations in X layers and shear transformation zones in AHEA layers. Meanwhile, the absorption of abundant dislocations emitted from X layers by AHEA layers with small thickness facilitates the occurrence of devitrification behavior, implying the microstructural instability under strong constraint conditions. Moreover, both of Cu/AHEA and Ni/AHEA CANMs manifest size-dependent hardness with the fashion that “smaller is stronger”, which is captured well by the rule-of-mixture, based on the size-dependent strength of X nanolayers and size-independent homogenous flow of AHEA nanolayers.

ANALYSIS OF MESOSTRUCTURE AND FRACTURE KINETICS OF ELEMENTS OF LATTICE COMPOSITE STRUCTURES UNDER TRANSVERSAL COMPRESSION USING STOCHASTIC FEA MICROMECHANICS

The paper analyses the mesostructure of the structural elements of lattice aircraft shells – ribs consisting of alternating layers of equal thickness and made from unidi-rectional CFRP and pure matrix material. In experimental studies, the elastic characteristics of unidirectional CFRP were obtained under three-point bending and transversal compression. As a result, the longitudinal modulus of elasticity of the layered composite turned out to be 101 GPa, and the shear modulus was 2.95 GPa. Numerical modeling of the meso- and micromechanics of the interaction of the noticed layers under transversal compression has been performed up to failure. The ANSYS FEA software (explicit and implicit formulations) was used. The regular and stochastic stacking of fibres in the cross section under compression is considered. The fiber diameters in the composite element were measured on thin sections using a Zeiss Axio Observer D1m digital microscope and were equal to 5.1 ± 0.8 µm. Layers with a fiber volume fraction of about 60 % alternate with layers of pure epoxy. It is proposed to use only the first principal stress in the matrix as a micromechanical criterion for failure under com-pression and tension. At the first stage of calculations, the problem of transversal compression of a cell with a regular laying of fibres was solved (the error in the value of the transversal modulus of elasticity was less than 2 %). At the second stage, an assessment was made of the strength and accumulation of microdamages under compression in a model of a layered structure with stochastic fibre stacking. The analysis of stress-strain state of a layered mesostructure under compression made it possible to explain the reason that the rib has a trans-verse strength twice lower than that of a homogeneous CFRP. The calculated values of the ultimate strength in transversal compression of a layered rib are in good agreement with the experimental ones.

Experimental Realization of Silicon Micromachined Terahertz Diplexer-Antenna Module for Heterodyne Receiver

A novel integrated silicon micromachined diplexer-antenna module for compact terahertz (THz) heterodyne receiver is proposed. The module is composed of a radio frequency (RF) antenna, a local oscillator (LO) antenna, and a waveguide diplexer which are realized by using the silicon micromachining technology and stacking nine equal-thickness layers. The corrugated conical horn antenna and quasi-diagonal horn antenna are applied as the RF- and LO-antenna, respectively. The diplexer is composed of two third-order waveguide bandpass filters and an H-plane T-junction, providing the isolated RF and LO channels. An experimental study is carried out in the 340 GHz band, demonstrating its application potential in THz heterodyne receiver element and array.

Orientation relationships in Cu/Nb bilayers deposited on (001) and (111) NaCl substrate

Cu/Nb bilayers with equal layer thickness of 35 nm were grown on (001) and (111) NaCl substrates using electron beam evaporation at 350 °C. Plan-view Cu/Nb bilayer samples were prepared by dissolving NaCl substrate in water. Transmission electron microscopy (TEM) was performed to study the orientation relationships (ORs). It was found that ORs in Cu/Nb bilayers are dependent on the substrate orientation. For Cu/Nb deposited on (001) NaCl, the dominant OR is Pitsch. For Cu/Nb deposited on (111) NaCl, the dominant OR is Nishiyama-Wasserman (N-W). The preferential ORs found in the Cu/Nb bilayers can be successfully predicted by the invariant line model.

Interface-controlled mechanical properties and irradiation hardening in nanostructured Cr75Al25/Zr multilayers

As an efficient strategy to design accident-tolerant fuel (ATF) materials, nanostructured metallic multilayers (NMMs) have attracted significant research interest. In this work, Cr75Al25/Zr (CA/Zr) NMMs were prepared with equal individual layer thickness h spanning from 5 to 75 nm, and subjected to He+ implantation with a total fluence of 1 × 1017 ions cm−2 at room temperature. With decreasing h, the interface changed from crystalline/crystalline to crystalline/amorphous along with size-driven strengthening to softening behavior of CA/Zr NMMs at the critical thickness h = 25 nm. The size-dependent hardness consists well with the evolution of the back stress with respect to h, which is elucidated by the statistical dislocation absorption propensity by the interface. Moreover, notable irradiation hardening emerges in the CA/Zr NMMs, which is caused by He bubble-dislocation interactions at large h and by the cooperation of He bubble hardening and increased back-stress hardening at small h. The hardness of both as-deposited and irradiated CA/Zr NMMs was quantitatively explained by dislocation models operative at different length scales.

Unusual He-ion irradiation strengthening and inverse layer thickness-dependent strain rate sensitivity in transformable high-entropy alloy/metal nanolaminates: A comparison of Fe50Mn30Co10Cr10/Cu vs Fe50Mn30Co10Ni10/Cu

In this work, we prepare transformable HEA/Cu nanolaminates (NLs) with equal individual layer thickness (h) by the magnetron sputtering technique, i.e., Fe50Mn30Co10Cr10/Cu and Fe50Mn30Co10Ni10/Cu, and comparatively study He-ion irradiation effects on their microstructure and mechanical properties. It appears that the as-deposited HEA/Cu NLs manifest two size h-dependent hardness regimes (i.e., increased hardness at small h and hardness plateau at large h), while the He-implanted ones exhibit monotonically increased hardness. Contrary to the fashion that smaller h renders less irradiation hardening in bimetal NLs, the Fe50Mn30Co10Cr10/Cu NLs manifest the trend that smaller h leads to greater irradiation hardening. By contrast, the Fe50Mn30Co10Ni10/Cu NLs exhibit the maximum irradiation hardening at a critical h = 50 nm. Below this critical size, smaller h results in lower radiation hardening (similar to bimetal NLs), while above this size, smaller h results in greater radiation hardening (similar to Fe50Mn30Co10Cr10/Cu NLs). Moreover, these transformable HEA/Cu NLs display inverse h-dependent strain rate sensitivity (SRS m) before and after He-ion irradiation. Nevertheless, compared with as-deposited samples, the irradiated Fe50Mn30Co10Cr10/Cu NLs display reduced SRS, while the irradiated Fe50Mn30Co10Ni10/Cu NLs display enhanced SRS. Such unusual size-dependent irradiation strengthening and inverse h effect on SRS in irradiated samples were rationalized by considering the blocking effects of He bubbles on dislocation nucleation and motion, i.e., dislocations shearing or bypassing He bubbles.

Mechanical properties of thermoformed multilayer parts containing non thermoformable materials

Different viscous materials were chosen to simulate the behavior of degraded materials in the thermoforming process and to demonstrate the potential of using multilayer sheets for thermoforming non thermoformable materials without losing final part performance. The mechanical properties of thermoformed multilayer sheets with 3, 22, and 50 melt flow index (MFI) polypropylenes (PP) were investigated. Therefore, a thermoformable material (MFI-3) and difficult/non thermoformable (MFI-22 and MFI-50) material was combined in the bilayer sheet. The extruded bilayer sheets had equal layer thicknesses (A/B 50%/50%) and unequal layer thicknesses (A/B 70%/30%), whereby B is always the material difficult to thermoform. As the non thermoformable material can lead to inhomogenity in the wall thickness and therefore can cause different part performance, the investigation focused on how the non thermoformable material influenced the mechanical performance of the final part. This labortory scale thermoformability investigation of the extruded PP sheets with different viscosities showed that the low viscous layer position has only a marginal influence on the general mechanical properties of the thermoformed parts. The mechanical properties can be predicted more precisely by the mechanical properties of the thermoformable material used than by the rule of mixtures. Whereas the Young’s modulus and yield stress change only negligibly, the elongation at break after thermoforming significantly increases with the stable component.

Laboratory Study of Turbulent Mass Exchange in a Stratified Fluid

In this study, a laboratory experiment was conducted to investigate quantitatively turbulent exchange between two quasi-homogeneous layers of equal thickness and different density (salinity), as well as the fine structure of the density transition zone (interface) between the layers. The fluid was continuously stirred by a system of horizontally oscillating vertical rods, piercing through both layers and producing vertically homogeneous turbulent impact in a two-layered fluid. In every experimental run, the stirring process was carried out continuously from certain initial state up to the complete mixing of the layers. The buoyancy flux between the layers was estimated using the data on time changes of the salinity in both upper and lower layers. The fine structure of density interface was measured by vertically profiling conductivity microprobe. The results were presented in a dimensionless form and analyzed depending on two dimensionless parameters as follows: the Richardson number, Ri, and Reynolds number, Re. It was found that if Ri>Ri∗Re where Ri∗ is the critical Richardson number, the interface exists in “sharpening” mode and in “eroding” (diffusive) mode if Ri<Ri∗Re. The maximum mixing efficiency was achieved at critical Richardson number, when the density interface was in a transition state between the sharpening and diffusive modes.

Centrifuge Model Test on Anti-dip Rock Slopes with Unequal Thicknesses Subjected to Flexural Toppling Failure

Flexural toppling failure of anti-dip rock slopes (ADRSs) with layers of equal thicknesses has been investigated by many researchers, however, in natural slopes, rock layers in ADRSs are often of unequal thicknesses. To analyze this condition, six slope models were manufactured with glass plates and tests were conducted in a geotechnical drum centrifuge. In these experiments, deformation and interlayer force characteristics were obtained with cameras and film pressure sensors. The centrifuge test results show that the failure process can be divided into three stages: failure of the slope toe, development of fractures and failure of the slope. Initial toe failure has little effect on the stability of the upper rock mass. Through centrifuge test results, it is determined that slopes with only thick layers therein can be used in the evaluation of the stability of slopes with layers of unequal thicknesses. This is because thicker strata have a greater bending stiffness and bending strength than thin strata, thus influencing slope deformation and stability.

Highly impermeable Al2O3 moisture barriers prepared by multiple plasma oxidation of discontinuous aluminum layers for optoelectronic devices

We designed a method to fabricate highly transparent (optical loss < 0.5%), moisture-impermeable high-density Al2O3 moisture-barrier layers using a multiple oxidation process (MOP) of partially coated Al layers. The effectiveness of the moisture barrier was evaluated by measuring the variations in sheet resistance of underlying Cu layers as a function of time at a fixed temperature of 85 °C and a relative humidity of 85%. No resistance variations were observed with the 5-nm-thick Al2O3 layer formed by the proposed method, whereas a considerable resistance increase was displayed by the Al2O3 layer of equal thickness prepared following the conventional deposition methods such as sputtering an elemental Al2O3 target and reactive sputtering. We formed the MOP-Al2O3 layers on a ZnO/Cu/ZnO transparent heater, which validated the improved visible transparency as well as the excellent heater stability at temperatures beyond 100 °C.

Interface-affected mechanical properties and strengthening mechanisms in heterogeneous high entropy alloy nanolaminates

Introducing heterogeneous interfaces by constructing laminated structure is a promising avenue to achieve the controllable strengthening behavior of high entropy alloys. In this work, the microstructural evolution and mechanical properties of magnetron sputtered Ni/Fe50Mn30Co10Ni10 nanolaminates with equal layer thickness h ranging from 5 to 150 nm were investigated systematically. With reducing h, the nanoindentation hardness of Ni/FeMnCoNi nanolaminates firstly increased and subsequently decreased, emerging a maximum value at the critical h of ~25 nm due to the transformation of constraining barrier for dislocation slipping from the heterogeneous interfaces to columnar grain boundaries. Microstructural observation demonstrated that the interfacial structure of Ni/FeMnCoNi transformed from incoherent to completely coherent at h below ~25 nm, and both the constituent layers made comparable contribution to the plastic deformation of Ni/FeMnCoNi nanolaminates. The strong h-dependent mechanical behavior could be rationalized in terms of the co-deformation of constituent layers and the structural evolution of Ni/FeMnCoNi interface. Additionally, the strengthening mechanisms were discussed based on the confined slip of dislocation within the constituent layers and columnar grains.

Phonons in Short-Period GaN/AlN Superlattices: Group-Theoretical Analysis, Ab initio Calculations, and Raman Spectra.

We report the results of experimental and theoretical studies of phonon modes in GaN/AlN superlattices (SLs) with a period of several atomic layers, grown by submonolayer digital plasma-assisted molecular-beam epitaxy, which have a great potential for use in quantum and stress engineering. Using detailed group-theoretical analysis, the genesis of the SL vibrational modes from the modes of bulk AlN and GaN crystals is established. Ab initio calculations in the framework of the density functional theory, aimed at studying the phonon states, are performed for SLs with both equal and unequal layer thicknesses. The frequencies of the vibrational modes are calculated, and atomic displacement patterns are obtained. Raman spectra are calculated and compared with the experimental ones. The results of the ab initio calculations are in good agreement with the experimental Raman spectra and the results of the group-theoretical analysis. As a result of comprehensive studies, the correlations between the parameters of acoustic and optical phonons and the structure of SLs are obtained. This opens up new possibilities for the analysis of the structural characteristics of short-period GaN/AlN SLs using Raman spectroscopy. The results obtained can be used to optimize the growth technologies aimed to form structurally perfect short-period GaN/AlN SLs.

On delamination of bi‐layers composed by orthotropic materials: Exact analytical solutions for some particular cases

AbstractEarlier [1, 2, 3], exact analytical solutions were obtained for three configurations of composed bi‐layers with semi‐infinite interface cracks: (i) the bilayer composed of two isotropic layers of equal thicknesses; (ii) an orthotropic layer with the central semi‐infinite crack; (iii) an isotropic layer on isotropic half‐plane of a different material (may be considered as a bilayer, the thickness of one of its layers tending to infinity). In all cases the second Dundur's parameter were supposed to be equal to zero. Here by using a scaling technique all three solutions have been extended to cover wider range of elastic and geometric parameters (elastic constants and thicknesses). In particular, a 2‐D problem of a bilayer composed by dissimilar anisotropic layers partly separated by semi‐infinite crack arbitrary loaded at infinity is considered. The principle axes of elasticity tensor for both layers are supposed to coincide with the geometrical axes. The problem involves 10 constants: four elastic constants for each layer and two thicknesses of the layers. By choosing the proper scales for length and for elastic moduli, the number of dimensionless constants is reduced to 8. By using a scaling technique exact analytical solutions are obtained for two subclasses of the problem with four conditions imposed on the parameters for each case, so that four out of eight parameters remain arbitrary. Similarly a solution is obtained for 2‐D problem of a layer on a half‐plane partly separated by semi‐infinite crack arbitrary loaded at infinity. For all considered cases two modes of stress intensity factors are found in terms of four integral characteristics of the external loads.

Dispersion induced by non-Newtonian gravity flow in a layered fracture or formation

Abstract

Symposium 1: The role of maternal pre-pregnancy characteristics on maternal prenatal physiology and behavior: Evidence from three prospective birth cohorts

Nanostructured Ti/Zr multilayers, with different layer thicknesses h and modulation ratios ŋ (ratio of the thickness between Zr and Ti layers), were deposited on Si (1 0 0) substrate by using magnetron sputtering. Transmission electron microscopy observations suggested that the heterophase interfaces kept semi-coherent or coherent in all the multilayers. Hardness of the Ti/Zr multilayers was evaluated by nanoindentation experiments. In contrast with the general trend of “smaller is stronger”, the hardness of present Ti/Zr multilayers with equal layer thickness increased as increasing the layer thickness h, which can be explained by the IBS model extended to large h. For the Ti/Zr multilayers with a constant bilayer thickness but various ŋ, the hardness displayed a maximum as increasing ŋ, which should be related to the deformation heterogeneity in Ti/Zr multilayers with non-uniform layer thickness. Furthermore, the high strength achieved in the Ti/Zr multilayers superior to the constituent layers was discussed.

Microstructures and mechanical properties of Mg/Zr nanostructured multilayers with coherent interface

Nanostructured Mg/Zr multilayer films were fabricated by depositing magnesium and zirconium alternately onto a single-crystal Si substrate using magnetron sputtering. The Mg and Zr layers had equal individual layer thickness (h) which was varied from 2.5 to 100 nm. Epitaxial growth and coherent layer interface were identified for the as-deposited multilayers at all h using X-ray diffraction and scanning transmission electron microscopy techniques. The multilayers with relatively large h were highly textured along the c-axis. Columnar grains were detected in the h = 2.5 nm multilayer, accompanied with variations in crystallographic orientation. These multilayers exhibited impressive strength with the maximum value of 1.4 GPa. The flow strength increased with decreasing h when h ≥ 10 nm while the opposite trend was observed when h < 10 nm. The strain rate sensitivity exponent was measured to be 0.021–0.037. A comparison to other nanostructured multilayers composed of hexagonal close-packed metals is presented to understand the role of interface coherency on mechanical behavior.