Effects of high-order surface stress on static bending behavior of nanowires

Studies on surface effects in nano-sized materials or structures are often based on the framework of linear membrane theory, in which the field jumps at the interface are characterized by the generalized Young–Laplace equation. Here a recently proposed theoretical framework of high-order surface stress is implemented in a continuum mechanics model to simulate the bending behavior of nanowires. The high-order surface stress considers not only the effect of in-plane membrane surface stresses, but also the surface moments induced from the non-uniform surface stress across the layer thickness. We investigate the extent to which the high-order surface stress will influence the bending behavior of nanowires deviated from that predicted by the generalized Young–Laplace equation. Closed-form expressions for the deflection curves are derived for nanowires with different boundary conditions. These solutions are utilized to characterize the size-dependent overall Young's moduli of NWs. We demonstrate that, in comparison to the reported experimental data, the present framework provides more accurate results than those by the conventional surface stress model. This study might be helpful to accurately characterize the behavior of bending nanowires in a wide range of applications.     

On the bending strength of ZnO nanowires

Compared to bulk samples, the bending strength of ZnO nanowires exhibits nearly two orders of magnitude increase and approaches their theoretical value. Statistical analysis on the scatter strength data of ZnO nanowires by using three versatile distributions has shown that, in contrast to Young's modulus, no obvious size effect was observed, and the bending strengths were insensitive to aspect ratios and flaws at the nanoscale. The reasons for this surprising tolerance behavior can be explained by the collective interaction of “flaws” in a nontraditional sense.     

Effect of surface layer thickness on buckling and vibration of nonlocal nanowires

In this Letter, the buckling and vibration behavior of nonlocal nanowires by incorporating surface elasticity is investigated. A modified core–shell model is developed to depict the size effect of Youngʼs modulus and validated by the reported experimental data. Our results show that the buckling load and natural frequency of nanowires increase when the effect of surface layer thickness is taken into account. Moreover, as the diameter of nanowires is smaller than 50 nm, the influence of surface layer thickness becomes obvious. This work can be helpful in characterizing and predicting the buckling and vibration behavior of NWs.     

Frequency analysis of piezoelectric nanowires with surface effects

In this paper, the modified Timoshenko beam model is used to analyze the vibration of piezoelectric nanowires in the presence of surface effects. Analytical relations are given for the natural frequency of nanowires by accounting for the effects of surface elasticity, residual surface tension, and transverse shear deformation. Through an example, it is shown that the natural frequency depends on both the surface stresses and piezoelectricity. This study is expected to provide useful insights for the design of piezoelectric-nanowire-based nanodevices.     

Mechanical properties of ZnO nanowires

Semiconductor nanowires are unique as functional building blocks in nanoscale electrical and electromechanical devices. Here, we report on the mechanical properties of ZnO nanowires that range in diameter from 18 to 304 nm. We demonstrate that in contrast to recent reports, Young's modulus is essentially independent of diameter and close to the bulk value, whereas the ultimate strength increases for small diameter wires, and exhibits values up to 40 times that of bulk. The mechanical behavior of ZnO nanowires is well described by a mechanical model of bending and tensile stretching.     

Effects of surface and interface energies on the bending behavior of nanoscale multilayered beams

A modified continuum model of the nanoscale multilayered beams is established by incorporating surface and interface energies. Through the principle of minimum potential energy, the governing equations and boundary conditions are obtained. The closed-form solutions are presented and the overall Young's modulus of the beam is studied. The surface and interface energies are found to have a major influence on the bending behavior and the overall Young's modulus of the beam. The effect of surface and interface energies on the overall Young's modulus depends on the boundary condition of the beam, the values of the surface/interface elasticity constants and the initial surface/interface energy of the system. The results can be used to guide the determinations of the surface/interface elasticity properties and the initial surface/interface energies of the nanoscale multilayered materials through nanoscale beam bending experiments.     

The elastic properties and energy characteristics of Au nanowires: an atomistic simulation study

This paper have performed molecular static calculations with the quantum corrected Sutten Chen type many body potential to study size effects on the elastic modulus of Au nanowires with [100], [110] and [111] crystallographic directions, and to explore the preferential growth orientation of Au nanowires. The main focus of this work is the size effects on their surface characteristics. Using the common neighbour analysis, this paper deduces that surface region approximately consists of two layer atoms. Further, it extracts the elastic modulus of surface, and calculate surface energy of nanowire. The results show that for all three directions the Young＇s modulus of nanowire increases as the diameter increases. Similar trend has been observed for the Young＇s modulus of surface. However, the atomic average potential energy of nanowire shows an opposite change. Both the potential and surface energy of [110] nanowire are the lowest among all three orlentational nanowires, which helps to explain why Au nanowires possess a [110] preferred orientation during the experimental growth proceeds.     

Elastic vibrations of a cylindrical nanotube with the effect of surface stress and surface inertia

Vibration frequency analysis of nanostructures may be essential for study of their thermal conductivity and mechanical characterization. Given the high surface-to-volume ratio, the elastic vibrations of an infinitely long cylindrical nanotube have been studied by considering both the effects of surface stress and that of surface inertia within the framework of surface elasticity. The phonon dispersion and the resonant frequencies for the specific vibration modes have been calculated. Numerical results have indicated that the surface stress and the surface inertia have equally important effect on the vibration behavior of the nanotube that may depend on the vibration modes as well. Due to the surface effect, the vibration modes of lower order by the classical elasticity may be indeed the modes of higher order. The surface effect on the low-frequency Raman shift has also been found.     

Flexural vibration of non-uniform beams having double-edge breathing cracks

Flexural vibration of non-uniform Rayleigh beams having single-edge and double-edge cracks is presented in this paper. Asymmetric double-edge cracks are formed as thin transverse slots with different depths at the same location of opposite surfaces. The cracks are modelled as breathing since the bending of the beam makes the cracks open and close in accordance with the direction of external moments. The presented crack model is used for single-edge cracks and double-edge cracks having different depth combinations. The energy method is used in the vibration analysis of the cracked beams. The consumed energy caused by the cracks opening and closing is obtained along the beam's length together with the contribution of tensile and compressive stress fields that come into existence during the bending. The total energy is evaluated for the Rayleigh-Ritz approximation method in analysing the vibration of the beam. Examples are presented on simply supported beams having uniform width and cantilever beams which are tapered. Good agreements are obtained when the results from the present method are compared with the results of Chondros et al. and the results of the commercial finite element program, Ansys^©. The effects of breathing in addition to crack depth's asymmetry and crack positions on the natural frequency ratios are presented in graphics.     

Flexural waves on narrow plates

Flexural wave speeds on beams or plates depend upon the bending stiffnesses which differ by the well-known factor (1 - nu2). A quantitative analysis of a plate of finite lateral width displays the plate-to-beam transition, and permits asymptotic analysis that shows the leading order dependence on the width. Orthotropic plates are analyzed using both the Kirchhoff and Kirchhoff-Rayleigh theories, and isotropic plates are considered for Mindlin's theory with and without rotational inertia. A frequency-dependent Young's modulus for beams or strips of finite width is suggested, although the form of the correction to the modulus is not unique and depends on the theory used. The sign of the correction for the Kirchhoff theory is opposite to that for the Mindlin theory. These results indicate that the different plate and beam theories can produce quite distinct behavior. This divergence in predictions is further illustrated by comparison of the speeds for antisymmetric flexural, or torsional, modes on narrow plates. The four classical theories predict limiting wave speeds as the plate width vanishes, but the values are different in each case. The deviations can be understood in terms of torsional waves and how each theory succeeds, or fails, in approximating the effect of torsion. Dispersion equations are also derived, some for the first time, for the flexural edge wave in each of the four "engineering" theories.     

Effect of spraying power on the microstructure and mechanical properties of supersonic plasma-sprayed Ni-based alloy coatings

The aim of this paper was to investigate the microstructure and mechanical properties of the supersonic plasma-sprayed Ni-Cr-B-Si-C coatings prepared at different spraying powers. The microstructure, phase composition, porosity, Young's modulus, micro-hardness, and residual stresses of the coatings were investigated and determined. The variations of the porosity, Young's modulus and micro-hardness of the coatings were evaluated by using statistical method. Results showed that the variations of porosity, Young's modulus and micro-hardness of the coatings followed the Weibull distributions. With increasing the porosity, the micro-hardness and Young's modulus of the coating decreased. The mean value of the Young's modulus of the coating calculated from Weibull plot was almost proportional to the square root of the micro-hardness of the coating. With increasing the power, Young's modulus of the coating increased, which, in turn, resulted in the increment of the residual stress at the coating surface.     

Effect of surface morphology on the mechanical properties of ZnO nanowires

Although studies of ZnO nanostructured materials have concentrated on the electric, optical, and magnetic properties, applicational devices with nanoscale moving parts usually suffer mechanical fatigue and failure for reasons that are less understood. Here, differing from vertical bending and tension measurements, conventional three-point bending tests are employed to study the elastic modulus and bending strength of ZnO nanowires (NWs) in an atomic force microscopy system. To shed new light on the extensive disagreement regarding the mechanical behavior of ZnO NWs, the effect of the surface morphology of the prepared NWs is mainly investigated. An average Young’s modulus of 148 GPa close to that of the bulk ZnO materials is obtained, and the size dependence is found to be unaffected by the detailed micro and macro surface morphology. On the other hand, the bending strain of 0.2–0.7% is one order of magnitude lower than that reported in the literature. It indicates that an irregular surface such as cracks, flaws, curved and neck-like surface, and body defects dominates the fracture properties of ZnO NWs, rather than the elastic behavior.     

Analysis of flexural wave velocity and vibration mode in thin cylindrical shell

The relationship between the flexural wave velocity and the excited vibration mode of a thin cylindrical shell is investigated. The natural frequency corresponding to the vibration mode is obtained as the solution of characteristic equation of thin cylindrical shell. However, all of these vibration modes are not excited actually. To estimate the excited vibration mode, the concept of "modified bending stiffness" is introduced, and the influence of each stress component upon the modified bending stiffness is analyzed. The excited mode is theoretically discriminated from the nonexcited mode based on the smallness of this modified bending stiffness. The validity of our theory is confirmed by an excellent agreement between theoretical and experimental results on flexural wave velocity.     

Performance of a cantilever piezoelectric energy harvester impacting a bump stop

Piezoelectric cantilever beam energy harvesters are commonly used to convert ambient vibration into electrical energy. In practical applications, energy harvesters are subjected to large shocks which can shorten the service life by causing mechanical failure. In this work, a bump stop is introduced into the design of a piezoelectric cantilever beam energy harvester to limit the maximum displacement of the cantilever and prevent excessively high bending stresses developing as a result of shocks. In addition to limiting the maximum displacement of the beam, it is inevitable that the deflected shape of the beam and the electrical output are modified. A theoretical model for a piezoelectric cantilever beam harvester impacting against a stop is derived, which aims to develop an understanding of the vibration characteristics of the cantilever and quantify how the electrical output of the harvester is affected by the stop. An experiment is set up to measure the dynamics and the electrical output of a bimorph energy harvester and to validate the theoretical model. Numerical simulation results are presented for energy harvesters with different initial gaps and different stop locations, and it is found that the reduction in maximum bending stress is at the expense of the electrical power of the harvester.     

Stress and magnetic field-dependent Young's modulus in single crystal iron-gallium alloys

The variability in Young's modulus of single crystal iron-gallium (Galfenol) alloys having 16, 17.5, 19, 24.7 and 29 at% gallium is investigated using experiments and simulations. Some of these alloys showed more than 60% change in Young's modulus along the 〈1 0 0〉 directions on varying their magnetization and stress states compared to their modulus at magnetic saturation. A function, ΔE(σ,H), is defined such that the variability of modulus is bound between 0% and 100%. The observations are related to the inherent magnetomechanical coupling in the material. An energy-based non-linear constitutive model is used to predict the variable modulus in Galfenol as a continuous function of stress and magnetic field. Model predictions showed good correlation with experimental results.     

Effect of a rippling mode on resonances of carbon nanotubes

A recent study determined the Young's modulus of carbon nanotubes by measuring resonance frequency and using the modulus-frequency relation resulting from the linear vibration theory. It leads to the report that the Young's modulus decreases sharply, from about 1 to 0.1 TPa with the diameter D increasing from 8 to 40 nanometers, and the investigators attributed this decrease to the emergence of an unusual bending mode during the measurement that corresponds to rippling on the inner arc of the bent nanotubes. The nonlinear analysis presented in this paper that captures the rippling mode suggests that the effective Young's modulus can indeed decrease substantially with increasing diameter, and that the results from the classical linear theory may be invalid in such measurements.     

Dynamic fracture behavior of syntactic epoxy foams: optical measurements using coherent gradient sensing

Dynamic fracture behavior of syntactic foams made of thin-walled microballoons dispersed in epoxy matrix is studied. Monotonically decreasing dynamic Young's modulus with increasing volume fraction of microballoons is observed using ultrasonic pulse-echo and density measurements. The results are also in good agreement with the Hashin–Shtrikman lower-bound predictions for elastic porous solids. Dynamic crack initiation toughness and crack growth behaviors are examined using instrumented drop-tower tests and optical measurements. Crack initiation toughness shows a linear relationship with Young's modulus over the entire range of volume fraction of microballoons studied. A proposed model based on simple extension of micromechanics prediction agrees well with the measurements. The optical method of coherent gradient sensing (CGS) has been used along with high-speed photography to record crack tip deformation histories in syntactic foam samples subjected to impact loading. Pre- and post-crack initiation events have been successfully captured and apparent dynamic stress intensity factor histories are extracted from the interferograms. Results suggest increasing crack speeds with volume fraction of microballoons. No significant dependence of dynamic fracture toughness on crack speed in any of the volume fractions is observed.     

全息干涉法在实验应力分析中的应用

通过对简支梁受力前后的双曝光全息图进行再现,利用透过全息图的条纹解释办法,分别用目测和数字图像处理办法测量物面上干涉条纹间距,从而得出简支梁的挠度;再利用最小二乘法求出被测物件的弹性模量。     

Modeling and simulating of V-shaped piezoelectric micro-cantilevers using MCS theory considering the various surface geometries

Atomic force microscopy (AFM) is widely used as a tool in studying surfaces and mechanical properties of materials at nanoscale. This paper deals with mechanical and vibration analysis of AFM vibration in the non-contact and tapping modes for V-shaped piezoelectric micro-cantilever (MC) with geometric discontinuities and cross section variation in the air ambient. In the vibration analysis, Euler-Bernoulli beam theory based on modified couple stress (MCS) theory has been used. The governing equation of motion has been derived by using Hamilton's principle. By adopting finite element method (FEM), the MC differential equation has been solved. Damping matrix was considered in the modal space. Frequency response was obtained by using Laplace transform, and it has been compared with experimental results. Newmark algorithm has been used based on constant average acceleration to analyze time response of MC, and then time response results in the vibration mode, far from the sample surface have been compared with experimental data. In vicinity of sample surface, MC is influenced by various nonlinear forces between the probe tip and sample surface, including van der Waals, contact, and capillary forces. Time response was examined at different distances between MC base and sample surface, and the best distance was selected for topography. Topography results of different types of roughness showed that piezoelectric MC has been improved in the air ambient. Topography showed more accurate forms of roughness, when MC passes through sample surface at higher frequencies. The surface topography investigation for tapping and non-contact modes showed that using of these two modes are suitable for topography.     

Ni,Pd和Pt的表面应力

半经验的修正嵌入原子方法用于Ni，Pd和Pt的低指数面的表面应力计算，得到了与第一原理计算相符合的结果．给出了（110）表面［110］方向的应力是［001］方向应力的两倍左右；阐明了应力各向异性是所有fc金属（110）面的一般特性．预言了Pd和Pt（100）的表面应力的大小． 关键词：