Effect of uncertainty parameters on graphene sheets Young’s modulus prediction

Software based on molecular structural mechanics approach (MSMA) and using finite element method (FEM) has been developed to predict the Young’s modulus of graphene sheets. Obtained results have been compared to results available in the literature and good agreement has been shown when the same values of uncertainty parameters are used. A sensibility of the models to their uncertainty parameters has been investigated using a stochastic finite element method (SFEM). The different values of the used uncertainty parameters, such as molecular mechanics force field constants k _r and k _θ , thickness (t) of a graphene sheet and length (L _B ) of a carboncarbon bonds, have been collected from the literature. Strong sensibilities of 91% to the thickness and of 21% to the stretching force (k _r ) have been shown. The results justify the great difference between Young’s modulus predicted values of the graphene sheets and their large disagreement with experimental results.     

Numerical simulation of 2-D laminar flow subjected to the Lorentz force effect in a channel with backward-facing step

This paper presents the numerical solutions of a two-dimensional laminar flow over a backward-facing step in the presence of the Lorentz body force. The Navier-Stokes equations in a vorticity-stream function formulation are numerically solved using a uniform grid mesh of 2001 × 51 points. A second-order central difference approximation is used for spatial derivatives. The solutions progress in time with a fourth-order Runge-Kutta method. The unsteady backward-facing step flow solution is computed for Reynolds numbers 100 to 800. The size and genesis of the recirculating regions are dramatically affected by applying the Lorentz force. The results demonstrate that using an appropriate configuration for applying the Lorentz force can make it an essential tool for controlling the flow in channels with a backward-facing step.     

Numerical investigation of cross-flow around a circular cylinder at a low-reynolds number flow under an electromagnetic force

The effect of the electromagnetic force (or Lorentz force) on the flow behavior around a circular cylinder is investigated by computation. Two-dimensional unsteady flow computation forR _e =10² is carried out using a numerical method of finite difference approximation in a curvilinear body-fitted coordinate system by solving the momentum equations including the Lorentz force as a body force. The effect of spatial variations of the Lorentz forcing region and forcing direction along the cylinder circumference is investigated. The numerical results show that the Lorentz force can effectively suppress the flow separation and oscillation of the lift force of circular cylinder cross-flow, leading to reduction of drag.     

C2H2 interaction with Ni nanocrystals: towards a better understanding of carbon nanotubes nucleation in CVD synthesis

We present a study of the early stages of carbon nanotubes nucleation in CVD synthesis by combining field ion/electron emission microscopy (FIM/FEM) and atom-probe investigation (AP) of the nickel-carbon interaction. Acetylene decomposition on Ni tips at 873K is observed to induce additional step formation on an initially facetted (polyhedral) crystal. Carbon-enriched steps are then observed to act as preferential nucleation centers of graphene sheets formation. Atom-probe experiments reveal C(2) and C(3) species and frequency dependent studies demonstrate that the origin of these species is different from C(1). Experiments provide clear evidence for the crucial role of carbon-enriched steps as nucleation sites of graphene sheets on the Ni surface.     

High‐contrast optical microscopy of graphene sheets

In the way of making graphene an industry‐friendly material, it must be mass‐produced with high‐quality and reduced cost over large areas. Assisted by machine‐learning techniques, rapid, nondestructive and accurate determination of large graphene sheets on SiO₂/Si substrates has been made possible in recent years by the optical microscopy method. Optimization of the substrate to achieve the maximum contrast can further extend the application of the optical microscopy method for quality control of the mass‐produced graphene. Graphene/n₂/n₃three‐layer structures, where n₂ and n₃ are refractive indices, are routinely used for identifying the number of graphene layers by optical reflection microscopy. In this paper, two analytical equations are derived that can be easily used for high‐contrast optical imaging of graphene sheets without any need to resort to the cumbersome numerical methods. One of the equations is derived for choosing the best material with refractive index n₂ that when coated on a substrate with refractive index n₃, maximizes the optical contrast. The other equation is derived for finding the best thickness of the SiO₂ layer in graphene/SiO₂/Si structures, which are in common use for fabrication of graphene‐based devices. The results are implemented in a MATLAB GUI, see Supporting Information, to assist the users in using the equations.     

Adhesion Mechanics between Nanoscale Silicon Oxide Tips and Few-Layer Graphene

Finite element method (FEM) simulations of the adhesive contact between a nanoscale tip and a silicon oxide substrate covered with graphene were performed, modelling experimental atomic force microscopy pull-off measurements. Simulations showed a slight increase in the pull-off force as layer number increased. This small enhancement was within reported experimental error, agreeing with the experimental findings of layer-independent adhesion forces. Pull-off forces did not vary with the elastic strain in the system for a given number of layers, but were influenced by the greater adhesive stresses for tip–graphene interaction compared with tip–substrate interactions. FEM simulations were also performed on suspended graphene and showed that the adhesive forces increased slightly beyond one layer of graphene, but then varied little from two to four layers of graphene. The results indicate that while there is some local delamination of the graphene sheets from the substrate, the adhesive stresses between the graphene layers in multilayer graphene effectively prevent out-of-plane mechanical deformation of the graphene layers that could result from tip–graphene interactions. Thus, the increased pull-off forces observed beyond one monolayer results from a change in the amount of material between the tip and substrate, or in this case the number of graphene layers, thus increasing the van der Waals force between tip and graphene.     

Structural instability of carbon nanotubes embedded in viscoelastic medium and subjected to distributed tangential load

In this paper, the nonlocal Euler-Bernoulli beam model is used to predict the static and dynamic structural instability of carbon nanotubes (CNTs) subjected to a distributed tangential compressive load. The CNT is considered to be embedded in a Kelvin-Voigt viscoelastic medium. Equation of motion and boundary conditions are obtained using the extended Hamilton’s principle and the extended Galerkin’s method is applied in order to transform the resulting equations into a general eigenvalue problem. The derived equations are validated by comparing the results achieved from the new derivations with existing solutions in literature. Effects of several experimentally interesting boundary conditions are considered on the stability characteristics of the CNT. Moreover, the influences of small scale parameter and material properties of the surrounding viscoelastic medium on the stability boundaries are examined.     

Study of the sensitivity and resonant frequency of the torsional modes of an AFM cantilever with a sidewall probe based on a nonlocal elasticity theory

A relationship based on a nonlocal elasticity theory is developed to investigate the torsional sensitivity and resonant frequency of an atomic force microscope (AFM) with assembled cantilever probe (ACP). This ACP comprises a horizontal cantilever and a vertical extension, and a tip located at the free end of the extension, which makes the AFM capable of topography at sidewalls of microstructures. First, the governing differential equations of motion and boundary conditions for dynamic analysis are obtained by a combination of the basic equations of nonlocal elasticity theory and Hamilton's principle. Afterward, a closed‐form expression for the sensitivity of vibration modes has been obtained using the relationship between the resonant frequency and contact stiffness of cantilever and sample. These analysis accounts for a better representation of the torsional behavior of an AFM with sidewall probe where the small‐scale effect are significant. The results of the proposed model are compared with those of classical beam theory. The results show that the sensitivities and resonant frequencies of ACP predicted by the nonlocal elasticity theory are smaller than those obtained by the classical beam theory. Microsc. Res. Tech. 78:408–415, 2015. © 2015 Wiley Periodicals, Inc.     

Nonlocal beam models for buckling of nanobeams using state-space method regarding different boundary conditions

Buckling analysis of nanobeams is investigated using nonlocal continuum beam models of the different classical beam theories namely as Euler-Bernoulli beam theory (EBT), Timoshenko beam theory (TBT), and Levinson beam theory (LBT). To this end, Eringen’s equations of nonlocal elasticity are incorporated into the classical beam theories for buckling of nanobeams with rectangular cross-section. In contrast to the classical theories, the nonlocal elastic beam models developed here have the capability to predict critical buckling loads that allowing for the inclusion of size effects. The values of critical buckling loads corresponding to four commonly used boundary conditions are obtained using state-space method. The results are presented for different geometric parameters, boundary conditions, and values of nonlocal parameter to show the effects of each of them in detail. Then the results are fitted with those of molecular dynamics simulations through a nonlinear least square fitting procedure to find the appropriate values of nonlocal parameter for the buckling analysis of nanobeams relevant to each type of nonlocal beam model and boundary conditions.analysis.     

Calibration of the analytical nonlocal shell model for vibrations of double-walled carbon nanotubes with arbitrary boundary conditions using molecular dynamics

In the present study, the free vibration response of double-walled carbon nanotubes (DWCNTs) is investigated. Eringen's nonlocal elasticity equations are incorporated into the classical Donnell shell theory accounting for small scale effects. The Rayleigh-Ritz technique is applied to consider different sets of boundary conditions. The displacements are represented as functions of polynomial series to implement the Rayleigh-Ritz method to the governing differential equations of nonlocal shell model and obtain the natural frequencies of DWCNTs relevant to different values of nonlocal parameter and aspect ratio. To extract the proper values of nonlocal parameter, molecular dynamics (MD) simulations are employed for various armchair and zigzag DWCNTs, the results of which are matched with those of nonlocal continuum model through a nonlinear least square fitting procedure. It is found that the present nonlocal elastic shell model with its appropriate values of nonlocal parameter has the capability to predict the free vibration behavior of DWCNTs, which is comparable with the results of MD simulations.     

A meshless approach for free transverse vibration of embedded single-walled nanotubes with arbitrary boundary conditions accounting for nonlocal effect

A single-walled nanotube structure embedded in an elastic matrix is simulated by the nonlocal Euler-Bernoulli, Timoshenko, and higher order beams. The beams are assumed to be elastically supported and attached to continuous lateral and rotational springs to take into account the effects of the surrounding matrix. The discrete equations of motion associated with free transverse vibration of each model are established in the context of the nonlocal continuum mechanics of Eringen using Hamilton's principle and an efficient meshless method. The effects of slenderness ratio of the nanotube, small scale effect parameter, initial axial force and the stiffness of the surrounding matrix on the natural frequencies of various beam models are investigated for different boundary conditions. The capabilities of the proposed nonlocal beam models in capturing the natural frequencies of the nanotube are also addressed.     

Tribological Thermostability of Carbon Film with Vertically Aligned Graphene Sheets

Tribological thermostability of carbon film with vertically aligned graphene sheets was studied with annealing temperatures up to 1,750 °C. The carbon film was deposited on silicon carbide substrate by electron cyclotron resonance plasma sputtering. Tribological thermostabilities of the carbon film in terms of friction coefficient, wear life, and nanoscratch depth were investigated by Pin-on-Disk tribometer and atomic force microscopy. The evolution of nanostructure of vertically aligned graphene sheets in the carbon film as a function of annealing temperature was examined by Raman spectroscopy and transmission electron microscopy. The results showed that the friction coefficient, wear life, and nanoscratch depth of the carbon film were thermally stable up to 1,250 °C. When the annealing temperature was 1,500 °C, the friction coefficient and the nanoscratch depth increased, the wear life decreased, but still all were of considerable values. These variations were attributed to the initiation of tubular-like structure originated from graphene sheets stacks. After annealing at 1,750 °C, tribological performances degraded catastrophically due to the abundant formation of tubular-like structures and the appearance of a graphitic interlayer between the film and the substrate.     

平行于电场的磁场对磁力电解复合抛光的影响

在传统的磁力电解复合抛光中,外加磁场的方向与电场方向垂直。通过给电解抛光外加一个平行于电场的磁场,对带电离子的运动状况进行分析,建立了带电离子运动的数学模型。并求出了带电粒子的速度方程和轨迹方程,分析了磁场在磁力电解复合抛光中的作用。由于所加磁场的作用,减小了电化学反应的浓差极化,加速了电化学反应速度和效率。通过实验,验证了该模型的合理性和对磁场功能分析的正确性。     

Analysis on nonlinear dynamics of a thin-plate workpiece in milling process with cutting force nonlinearities

This paper aims to investigate the nonlinear dynamics of a thin-plate workpiece during milling process with cutting force nonlinearities. By modeling the thin-plate workpiece as a cantilevered thin plate and applying the Hamilton’s principle, the equations of motion of the thin-plate workpiece are derived based on the Kirchhoff-plate theory and the von Karman strain-displacement relations. Using the Galerkin’s approach, the equations of motion are reduced to a two-degree-freedom nonlinear system. The method of Asymptotic Perturbation is utilized to obtain the averaged equations in the case of 1:1 internal resonance and foundational resonance. Numerical methods are used to find the periodic and chaotic oscillations of the cantilevered thin-plate workpiece. The results show that the cantilevered thin-plate workpiece demonstrate complex dynamic behaviors under time-delay effects, the external and parametric excitations.     

Nonlinear sealing force of a seawater balance valve used in an 11000-meter manned submersible

Balance valve is a core component of the 11000-meter manned submersible “struggle,” and its sealing performance is crucial and challenging when the maximum pressure difference is 118 MPa. The increasing sealing force improves the sealing performance and increases the system’s energy consumption at the same time. A hybrid analytical–numerical–experimental (ANE) model is proposed to obtain the minimum sealing force, ensuring no leakage at the valve port and reducing energy consumption as much as possible. The effects of roundness error, environmental pressure, and materials on the minimum sealing force are considered in the ANE model. The basic form of minimum sealing force equations is established, and the remaining unknown coefficients of the equations are obtained by the finite element method (FEM). The accuracy of the equation is evaluated by comparing the independent FEM data to the equation data. Results of the comparison show good agreement, and the difference between the independent FEM data and equation data is within 3% when the environmental pressure is 0–118 MPa. Finally, the minimum sealing force equation is applied in a balance valve to be experimented using a deep-sea simulation device. The balance valve designed through the minimum sealing force equation is leak-free in the experiment. Thus, the minimum sealing force equation is suitable for the ultrahigh pressure balance valve and has guiding significance for evaluating the sealing performance of ultrahigh pressure balance valves.     

Experiment and numerical simulation on delamination during the laminated steel sheet forming processes

Laminated steel sheets, which have advantages in reducing vibration and noise, are widely used in home appliances, automotive components and building structures. With polymer layer laminated in steel sheets, the unique failure mode—delamination may occur in the forming process if the process parameters are defined improperly. In the presented work, firstly, the delamination is investigated by U channel forming in bending mode. Then, a step-bottom square cup drawing is also conducted to study the delamination in the deep drawing of the laminated sheet metal in more complex stress state. Nonlinear visco-elastic material model is applied to describe the mechanical behavior of polymer layer. Cohesive element and continuum shell elements are utilized to discretize the polymer layer and the outer steel sheets, respectively. The results of U channel forming indicate that increasing forming speed somewhat decreases the tendency of delamination, and increasing blank holding force (BHF) significantly diminishes the occurrence of delamination. Meanwhile, the results of the step-bottom square cup drawing reveal that the wrinkling of facial sheets often induces delamination. Increasing the BHF and the frictional coefficient prevents the occurrence of wrinkling and the delamination induced by wrinkling. However, when wrinkling is suppressed, further rising in BHF and frictional coefficient will increase the risk of direct delamination.     

Non-classical stiffness strengthening size effects for free vibration of a nonlocal nanostructure

New analytical solutions for free vibration of thick nanostructures are presented based on the nonlocal elastic stress field theory and the Timoshenko shear deformable nanobeam model. By applying the variational principle, new governing equations of motion and higher-order boundary conditions for these thick nanobeams are derived and their physical characteristics interpreted. The nonlinear history of straining involving higher-order strain gradients is considered in the derivation of strain energy and the contribution of higher-order strain gradients results in non-classical equations of motion thereby indicating that direct replacement of stress and moment quantities into the classical equations of motion is invalid. The Timoshenko nanobeam models are well suited for modeling and investigating the nonlocal behaviors of size-dependent carbon nanotubes. The effects of nanobeam size and various boundary conditions including simple supports, free and clamp constraints, such as a cantilevered nanotube, on the natural vibration frequency of nanotubes are discussed. The effects of nonlocal nanoscale are confirmed by comparing with molecular dynamic simulation solutions for (5,5) and (10,10) carbon nanotubes with four types of boundary conditions. The influence by nanoscale effect on the frequency ratio of nanotubes with different diameters is investigated. Further analysis based on the analytical nonlocal Timoshenko nanobeam model and the Euler–Bernoulli nanobeam model shows that the frequency ratio is more sensitive to nonlocal effect for free vibration of a nonlocal nanostructure if shear deformation is considered.     

Vibration analysis of nano-structure multilayered graphene sheets using modified strain gradient theory

In this paper, for the first time, the modified strain gradient theory is used as a new size-dependent Kirchhoff micro-plate model to study the effect of interlayer van der Waals (vdW) force for the vibration analysis of multilayered graphene sheets (MLGSs). The model contains three material length scale parameters, which may effectively capture the size effect. The model can also degenerate into the modified couple stress plate model or the classical plate model, if two or all of the material length scale parameters are taken to be zero. After obtaining the governing equations based on modified strain gradient theory via principle of minimum potential energy, as only infinitesimal vibration is considered, the net pressure due to the vdW interaction is assumed to be linearly proportional to the deflection between two layers. To solve the governing equation subjected to the boundary conditions, the Fourier series is assumed for w=w(x, y). To show the accuracy of the formulations, present results in specific cases are compared with available results in literature and a good agreement can be seen. The results indicate that the present model can predict prominent natural frequency with the reduction of structural size, especially when the plate thickness is on the same order of the material length scale parameter.     

Induced nonlocal electric wave propagation of boron nitride nanotubes

Axial displacement and electric wave propagation of single-walled Boron-Nitride nanotubes (SWBNNTs) induced by alternating current (AC) are investigated in this study. A single-walled zigzag structure BNNT is modeled based on nonlocal piezoelasticity theory and Euler-Bernoulli beam (EBB). Equations correspond to lateral displacement have been obtained. Using Hamilton’s principle and considering charge equation for coupling of electrical and mechanical fields, the higher order of governing equations are derived. Analytical solution is applied to solve governing equations. Also the axial and lateral displacement of a SWBNNT and electric potential induced by AC through it are presented. The detailed parametric study is conducted, focusing on the remarkable effects of the half wave number on the behavior of the SWBNNT. The results indicate applying alternating field, leads to propagation of axial displacement along the SWBNNT. Also the result of this study can be useful to design and manufacture of smart micro/nano-electro-mechanical systems in advanced biomechanics applications by controlling axial and lateral displacements.     

The influence of lubrication in rectangular deep drawing

Rectangular deep drawing is a widely used process in the electrical, automobile, and aeronautical industries, in military engineering, etc. Despite its popularity little information is available about the effect of lubrication on limiting drawing ratio, drawing force, and work done. In view of this, rectangular deep drawing experiments were conducted using mild steel, aluminium, and tin sheets in a 100 t double action hydraulic press. The maximum drawing force, the work done during drawing, and the limiting drawing ratio for a number of commercial lubricants were measured, and are reported in this paper. The effect of anodising has also been studied in the case of aluminium sheets. In the case of mild steel sheets the effect of shot blasting the blank has also been reported.