Geometrical Size Effect Research Articles

Free vibration and buckling analyses of a size-dependent axially functionally graded beam incorporating transverse shear deformation

A new size-dependent axially functionally graded (AFG) beam model with transverse shear deformation is proposed based on the modified couple stress theory (MCST). Besides, present new model incorporates only one material length scale parameter (MLSP) which can effectively capture the scale effects. Moreover, the first-order and third-order shear deformation theory are considered in this new model respectively, which differ from the existing micro AFG Euler-Bernoulli model. Subsequently, free vibration and buckling behaviors are investigated based on the rule of mixture. Related governing equations are derived and numerically solved by Hamilton’s principle and differential quadrature method (DQM) respectively. Afterwards, some results are compared with published literatures to demonstrate the validity and accuracy of current formulation. Finally, the effects of geometric size, shear deformation and material non-homogeneity on the critical loads and natural frequencies are discussed.

Analysis of hydrogenated zirconium alloys irradiated with gamma - rays

The paper represents the investigations concerning the geometrical size effect of hydrogenated zirconium alloys (Zr-1Ni-H) during gamma-ray irradiation on the amount of energy absorbed. The results have shown that the less the cross-sectional dimensions of the sample or product is, the less energy is absorbed. The paper provides theoretical calculations. The zirconium sample with a cross-section of 2.8х2.8 cm absorbs 30-35% of the energy of the incident gamma-ray flow. The increase in the cross-section of a product up to 28 cm leads to the increase in the absorbed energy by more than 2 times. At the same time, the thickness of the product is constant. This effect is explained by the multiple scattering of gamma-rays. It leads to the nonuniform distribution of defects which can accumulate hydrogen and should be considered when developing the analysis methods. These edge effects are confirmed by the measurement of the thermal electromotive force for the samples of zirconium alloys before hydrogenation and gamma-ray irradiation, and after irradiation.

Fatigue of weld ends under combined loading

The fatigue behaviour of weld ends, especially in thin sheet structures under multi-axial load conditions, has not yet been explored. A research project was initiated to gain more information on this topic which is of special interest to the automotive industry. In the present study fatigue tests on steel tube-tube joints were conducted. Notch stresses were calculated using an idealised weld end model. A numerical method combining the geometrical and statistical size effect into an integrated approach was used in order to take size effects into consideration. The out-of-phase effects on fatigue strength was covered using a multi-axial criterion. We propose a new approach combining the applied multi-axial criterion with the micro-support effect. That leads to a satisfactorily small scatter range of experimentally obtained fatigue lives around the S-N curve from regression analysis.

The effects of a geometrical size, external electric fields and impurity on the optical gain of a quantum dot laser with a semi-parabolic spherical well potential

In this paper, a GaAs/AlxGa1−xAs quantum dot laser with a semi-parabolic spherical well potential is assumed. By using Runge-Kutta method the eigenenergies and the eigenstates of valence and conduct bands are obtained. The effects of geometrical sizes, external electric fields and hydrogen impurity on the different electronic transitions of the optical gain are studied. The results show that the optical gain peak increases and red-shifts, by increasing the width of well or barrier, while more increasing of the width causes blue-shift and decreases it. The hydrogen impurity decreases the optical gain peak and blue-shifts it. Also, the increasing of the external electric fields cause to increase the peak of the optical gain, and (blue) red shift it. Finally, the optical gain for 1s–1s and 2s–1s transitions is prominent, while it is so weak for other transitions.

Effect of geometric size of curved delta winglet vortex generators and tube pitch on heat transfer characteristics of fin-tube heat exchanger

Vortex generator has received extensive attention and was widely applied for heat transfer enhancement. In order to further improve the heat transfer performance of compact heat exchanger, curved delta winglet vortex generators with different geometric sizes are experimentally studied for circular tube-and-fin heat exchanger in this paper. A total of 15 samples of circular tube-fin exchanger with three fin pitches, two tube pitches and two sizes of curved delta winglet vortex generators with different base length are carried out to find their effect on heat transfer and pressure losing. Colburn factor and friction factor are used to evaluate the performance of circular tube-and-fin heat exchanger with different parameters. The results showed that smaller vortex generator which locates close to the tube has the advantageous to heat transfer enhancement for flow with low Re and the larger vortex generator is more conducive to heat transfer enhancement for flow with large Re. The change of fin pitch has less effect on Colburn factor while friction factor is obviously affected by the change of fin pitch. Decreasing the tube pitch is beneficial to the heat transfer at the cost of increasing pressure loss and the overall heat performance increases when fin pitch is 2.3mm.

Fatigue of weld ends under combined in- and out-of-phase multiaxial loading

Weld start and end points are fatigue failure sensitive locations. Their fatigue behaviour especially in thin sheet structures under multiaxial load conditions is not sufficiently explored so far. Therefore, a research project was initiated to increase the knowledge concerning this topic, which is of special interest in the automotive industry. In the present study, fatigue tests on welded joints were conducted. In the numerical part of the study, notch stresses were calculated with an idealised weld end model. A numerical method which combines the geometrical and statistical size effect to an integrated approach was used, in order to consider the size effects.

A kinetic Monte Carlo simulation of center shift on template-induced surface

In this paper, the center shift of organic particles on template-induced surface is systematically studied by a series of kinetic Monte Carlo simulations. The morphology evolution of center shift, the dependence of center deviation on interactions and the effects of geometrical sizes are obtained. Based on the morphology evolution of center shift, two different mechanisms are proposed, i.e. nucleation deviation and growth deviation. The former is mainly induced by the lateral nucleation of deposited particles, and the latter is mainly determined by the randomly diffusion motion of deposited particles. The two mechanisms present a significant difference for the evolution of center deviation. Based on the details of the two mechanisms, a possible method for reducing the center deviation is also supplied in the simulation.

Electromagnetically induced transparency in the strained quantum wells: Effects of structural parameters and geometrical size

In this work, the electromagnetically induced transparency in a strained GaN/InGaN/AlGaN quantum well system, is theoretically studied. Energy levels and wave functions are calculated using the transfer matrix method. Effects of In and Al compositions, the well and barrier widths on the real and imaginary parts of the optical susceptibility are investigated. Results show that the electromagnetically induced transparency can be controlled via the structural parameters and geometrical size.

Multiple collinear Griffith cracks in a one-dimensional hexagonal quasicrystalline layer

The fracture behavior of multiple collinear Griffith cracks in a one-dimensional quasicrystalline layer is investigated in this paper. Using the Fourier transform technique, the mixed boundary value problem is reduced to a system of Cauchy singular integral equations. The integral equations are further reduced to a system of algebraic equations. The stress intensity factors of the phonon and phason fields and the energy release rate are determined. Numerical results reveal the effects of geometric size, the distance of the cracks and loading parameter ratio of the phonon and phason fields on crack propagation and growth. The results seem useful for the design of quasicrystalline materials, structures and devices of high performance.

Unusual angular dependent magnetoresistance in single-crystalline Co/Pt bilayers

The magnetoresistance (MR) of the single-crystalline Co/Pt(111) bilayers was studied systematically as a function of Co or Pt thickness at room temperature. For Co thickness dCo < 6 nm, the resistances with in-plane magnetization M parallel (R∥) and transverse (R⊥) to current and with a perpendicular M normal (RP) to film show the unconventional behavior of RP>R∥>R⊥. This MR behavior can be attributed to the combination effect of spin Hall MR with RP≈R∥>R⊥ and the geometrical size effect. In addition, the angular dependent magnetoresistance behavior of the (111)-oriented Co/Pt bilayer shows striking difference with that of the (001)-oriented Co/Pt bilayer.

Tunable angular-dependent magnetoresistance correlations in magnetic films and their implications for spin Hall magnetoresistance analysis

Angular-dependent magnetoresistance (MR) is considered to be intrinsic to spintronic materials, represented by the classical anisotropic MR (AMR) phenomenon and the recently emerged spin Hall MR (SMR). So far, isotropic AMR, AMR with geometric size effect and interfacial effect, and SMR have been treated separately to explain distinct MR correlations observed in various systems. Current study shows all four types of MR correlations can be reproduced in Fe thin films depending on the film thickness, texture, interface, and morphology. Results suggest previous explanations of the thin-film MR correlations are incomplete and it is inappropriate to use a specific MR angular-dependent correlation as the sole criterion in determining the origin of AMR or ascertaining the exclusive existence of SMR.

A kinetic Monte Carlo simulation of organic particles hetero-patterning on template-induced surface

Abstract In this paper, the hetero-patterning of organic particles on template-induced surface are systematically studied by a series of kinetic Monte Carlo simulations. The details of anisotropic growth process, the dependence of aggregation morphology on interactions and the effects of geometrical sizes are obtained. The simulated results showed that the size of prepattern plays a crucial role in the hetero-structure growth process. Especially for the deposited morphology, the thickness of organic film is relevant with the prepattern size. In the simulation, the dependence of deposition morphology on the amount of deposited particles is also obtained. The results also showed that the thickness ratio on two type squares even can be completely controlled by the amount of deposited particles. Besides the size of template and the amount of deposited particles, the interactions between different particles also exhibit strong influence on the deposited morphology. Both the weak and strong organic particle-organic particle interactions can reduce the anisotropic growth, while the moderate value can result in the maximum anisotropic growth.

Geometric size effect on the extrinsic Gilbert damping in laterally confined magnetic structures

We investigated spin dynamics in micron-length scale patterned thin films using the GPU-based micromagnetic simulation program. Spin precessional motion was induced by a Gaussian-pulse magnetic field. The effective Gilbert damping was examined by tracking the precessional motion of the spins, and we found that the damping constant depends on the size and shape of the pattern as well as the externally applied magnetic field. Additional extrinsic damping generated around the edge region was attributed to the dephasing effect between the fundamental spin wave and other spin wave modes. We find that the effect of extrinsic damping could be eliminated by proper adjustments of sample size, external bias field, position, and area of observation.

Circularly Polarized Microstrip Yagi Array Antenna with Wide Beamwidth and High Front-to-Back Ratio

A circularly polarized (CP) Microstrip Yagi array antenna (MSYA) is designed in order to achieve high front-to-back ratioR(F/B)and high gain over wide range in the forward radiation space. A Wilkinson power divider owning two output ways with the same magnitude and different phase is used to feed the antenna. Parametric studies are carried out to investigate the effects of some key geometrical sizes on the antenna’s performance. A prototype of the antenna is fabricated, and good agreement between the measured results and the numerical simulations is observed. The overlap bandwidth of VSWR ≤ 1.5 and AR ≤ 3 dB is about 11%. The steering angle (α) between the peak gain direction and the broadside can achieve 35°,R(F/B)reaches 19 dB, and the gain at the front point (G0) is only 4.3 dB lower than the maximum gain (Gm). The antenna has a wide beamwidth CP radiation pattern over wide spatial range including 0° ≤θ≤ 90° in vertical plane and −35° ≤φ≤ 55° in horizontal plane.

Optical absorption coefficients and refractive index changes of an on-center hydrogenic impurity in a multi-layered spherical quantum dot: effects of external fields and geometrical size

Effects of an on-center hydrogenic impurity, external electric and magnetic fields on the electronic structure, optical absorption coefficients and refractive index changes of a multi-layered spherical quantum dot are investigated. To this end, the direct matrix diagonalization method and the compact density matrix approach are respectively, used to calculate energy eigenvalues and optical properties of the system. It is found that the geometrical size, hydrogenic impurity and external fields change the electronic structure of the system. Therefore, these parameters have a great influence on the linear and the third-order nonlinear optical absorption coefficients as well as the refractive index changes of the system.

Investigating geometrical size effect on the flexural strength of the ultra high performance fibre reinforced concrete using the cohesive crack model

Geometrical size effect on the flexural strength of the ultra high performance fibre reinforced concrete was investigated by experimental test data and numerical simulation. Comparison of the simulation results to existing experimental test results indicates that the Cohesive Crack Model (CCM) with a bilinear traction–separation curve can provide predictions of both the load–deflection curves and peak load of 100 and 150mm deep UHPFRC test specimens to =/−6% with a little size effect observed on the flexural strength. However, for the 50mm deep beams a difference of =/−25% was observed between model predictions of the peak load and experiment test data possibly due to a surface layer size effect.

Experimental study on formability of phosphor bronze thin sheet in micro bead forming process

This study analyzed the effects of geometric size and grain size on the forming characteristics of a phosphor bronze thin sheet during micro bead forming processes. Specimens with different thicknesses were first heated at various temperatures for obtaining objective grain sizes. A tensile test was conducted to determine the mechanical properties of the specimens. A bead forming machine was used to conduct a bead forming test to measure and analyze curled angles, springback, and forming load; the measurement and analysis were conducted for investigating the geometric size and grain size effects in addition to the chamfer and lubrication effects during bead forming. The geometric size effect showed that the springback decreased with the thickness decreasing, and the grain size effect indicated that the springback increased with an increase in the grain size. Incorporating chamfers into the specimens enabled the specimens to be curled effectively, thus rendering chamfers the essential parameters for ensuring successful bead forming.

Approach for J–R curve determination based on sub-size specimens using a triaxiality dependent cohesive zone model on a (ferritic–martensitic) steel

An approach has been developed which is able to predict J–R curves of standard-size specimen geometries. The general idea is based on the assumption that the finite element method in combination with the cohesive model, which is based on the traction–separation relationship, is able to cover the geometrical size effects of fracture mechanics specimens. This means that cohesive zone parameters can be identified independent on geometry. For ductile crack growth a stress triaxiality dependent cohesive zone model developed by Scheider (2000) is used to cover different stress states within the specimens. The evaluation procedure is verified on steel T91.

N-type conversion of SnS by isovalent ion substitution: Geometrical doping as a new doping route.

Tin monosulfide (SnS) is a naturally p-type semiconductor with a layered crystal structure, but no reliable n-type SnS has been obtained by conventional aliovalent ion substitution. In this work, carrier polarity conversion to n-type was achieved by isovalent ion substitution for polycrystalline SnS thin films on glass substrates. Substituting Pb2+ for Sn2+ converted the majority carrier from hole to electron, and the free electron density ranged from 1012 to 1015 cm−3 with the largest electron mobility of 7.0 cm2/(Vs). The n-type conduction was confirmed further by the position of the Fermi level (EF) based on photoemission spectroscopy and electrical characteristics of pn heterojunctions. Density functional theory calculations reveal that the Pb substitution invokes a geometrical size effect that enlarges the interlayer distance and subsequently reduces the formation energies of Sn and Pb interstitials, which results in the electron doping.

A mechanistic cutting force model with consideration of the intrinsic and geometric size effects decoupled

In machining processes, the specific cutting energy increases nonlinearly as the uncut chip thickness decreases. This phenomenon is called the size effect and can be classified into two types by its cause—geometric and intrinsic. The geometric size effect is caused by the decrease of the effective rake angle with the decrease of the uncut chip thickness when the tool has a finite radius of the cutting edge. The intrinsic size effect results from the nature of the material, in which the resistance against plastic deformation (flow stress) increases as the length scale of the material deformed decreases. In order to improve the prediction accuracy of a cutting force model in micro-machining, it is important to understand each of these size effects and reflect them into the cutting force model accurately. In this regard, this study develops an experimental method to decouple the geometric and intrinsic size effects and models them individually. Based on this, a mechanistic cutting force model including the geometric and intrinsic size effects in separate terms is constructed and compared to the existing models which do not consider them separately.