Some modifications in evaluation of the size effects related to surface stresses in nanostructures

In this work, addressing some contradictions, it is tried to interpret some gaps between surface stress theories and the size effects observed in experiments for nanowires through different examples. Due to mandatory self-equilibrium state of nanostructures at different states, in a generalized model, a balancing factor is defined for the surface residual stress and duly the clamped nanowires are classified into suspended and etched types. The claims are confirmed by observing similar results for bending and tensile tests of Ag nanowires that addresses alternative sources for size effects beside the surface stresses. In addition, the size effects and surface material properties are identified lower at larger deformation ranges and regarding tremendous gap between atomistic simulation and continuum core–shell models, it is verified that the surface elasticity may not be the entire source for size effects. In extension, due to anisotropicity of single crystals, two orientation dependent parameters are defined for nanoplates that are modeled based on Kirchhoff plate, von-Karman strains and surface stress models. It is shown that orientation of (100)-nanoplates changes the size effects for more than 70%. Meanwhile, some test setups are recommended for characterization of the size effects of nanowires and nanoplates.     

Nonlocal and surface effects on the buckling behavior of functionally graded nanoplates: An isogeometric analysis

The size-dependent static buckling responses of circular, elliptical and skew nanoplates made of functionally graded materials (FGMs) are investigated in this article based on an isogeometric model. The Eringen nonlocal continuum theory is implemented to capture nonlocal effects. According to the Gurtin–Murdoch surface elasticity theory, surface energy influences are also taken into account by the consideration of two thin surface layers at the top and bottom of nanoplate. The material properties vary in the thickness direction and are evaluated using the Mori–Tanaka homogenization scheme. The governing equations of buckled nanoplate are achieved by the minimum total potential energy principle. To perform the isogeometric analysis as a solution methodology, a novel matrix-vector form of formulation is presented. Numerical examples are given to study the effects of surface stress as well as other important parameters on the critical buckling loads of functionally graded nanoplates. It is found that the buckling configuration of nanoplates at small scales is significantly affected by the surface free energy.     

Prediction of compressive post-buckling behavior of single-walled carbon nanotubes in thermal environments

In the present investigation, the axial buckling and post-buckling configurations of single-walled carbon nanotubes (SWCNTs) are studied including the thermal environment effect. For this purpose, Eringen’s nonlocal elasticity continuum theory is implemented into the classical Euler–Bernoulli beam theory to represent the SWCNTs as a nonlocal elastic beam model. A closed-form analytical solution is carried out to analyze the static response of SWCNTs in their post-buckling state in which the axial buckling load is assumed to be beyond the critical axial buckling load. Common sets of boundary conditions, named simply supported–simply supported (SS–SS), clamped–clamped (C–C), and clamped–simply supported (C–SS), are considered in the investigation. Selected numerical results are given to represent the variation of the carbon nanotube’s mid-span deflection with the applied axial load corresponding to various nonlocal parameters, length-to-diameter aspect ratios, temperature changes, and end supports. Moreover, a comparison between the post-buckling behaviors of SWCNTs at low- and high-temperature environments is presented. It is found that the size effect leads to a decrease of the axial buckling load especially for SWCNTs with C–C boundary conditions. Also, it is revealed that the value of the temperature change plays different roles in the post-buckling response of SWCNTs at low- and high-temperature environments.     

Surface effect on buckling configuration of nanobeams containing internal flowing fluid: A nonlinear analysis

In this paper, the post-buckling behavior of supported nanobeams containing internal flowing fluid with two surface layers is studied based on a nonlinear theoretical model. The nonlinear governing equation, in which the surface effect and stretching-related nonlinearity are accounted for, is analytically solved for both clamped-clamped and pinned-pinned systems. The effects of nanobeam length, bulk thickness and several dimensionless parameters on the post-buckling behavior are analyzed. It is found that, the nanobeam with low flow velocity is stable at its original static equilibrium position and then undergoes a buckling instability at a critical flow velocity, which depends on the system parameters. When buckled, in all cases, the amplitude of the resultant buckling increases with the increasing flow velocity. Typically, the surface effect is explored by considering different nanobeam lengths and bulk thicknesses. The buckling amplitude is found to be length-dependent and thickness-dependent, showing that the effect of surface layers is considerably strong.     

Size-dependent resonance and buckling behavior of nanoplates with high-order surface stress effects

This work presents a theoretical study of the resonance frequency and buckling load of nanoplates with high-order surface stress model. A classical thin plate theory based on Kirchhoff–Love assumption is implemented with surface effects. Circular and rectangular nanoplates with simply supported end conditions are exemplified. The size-dependent solutions are compared with the simplified solutions based on simple surface stress model, and also on the classical theory of elasticity. We aim to explore the scope of applicability so that the modified continuum mechanics model could serve as a refined approach in the prediction of mechanical behavior of nanoplates.     

Face-centered-cubic to body-centered-cubic phase transformation of Cu nanoplate under [100] tensile loading

ABSTRACT

Molecular dynamics simulation was used to stretch Cu nanoplates along its [100] direction at various strain rates and temperatures. Under high strain rate and beyond the elastic limit, the Cu nanoplates underwent an unusual deformation mechanism with expansion along free surface lateral direction and contraction along the other lateral direction, which leaded to the face-centred-cubic phase transforming into unstressed body-centred-cubic phase. Under low strain rate, the deformation of the nanoplate went back to well-known dislocation mechanism. The face-centred-cubic to body-centred-cubic phase transformation mechanism was further discussed in terms of elastic stability theory and free surface stress effect.     

Size-dependent dispersion characteristics in piezoelectric nanoplates with surface effects

In this paper, surface effects on the dispersion characteristics of elastic waves propagating in an infinite piezoelectric nanoplate are investigated by using the surface piezoelectricity model. Based on the surface piezoelectric constitutive theory, the presence of surface stresses and surface electric displacements exerting on the boundary conditions of the piezoelectric nanoplate is taken into account in the modified mechanical and electric equilibrium relations. The partial wave technique is employed to obtain the general solutions of governing equations, and the dispersion relations with surface effects are expressed in an explicit closed form. The impacts of surface piezoelectricity, residual surface stress and plate thickness on the propagation properties of elastic waves are analyzed in detail. Numerical results show that the dispersion behaviors in piezoelectric nanoplates are size-dependent, and there exists a critical plate thickness above which the surface effects may vanish.     

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.     

Size effect of the elastic modulus of rectangular nanobeams:Surface elasticity effect

The size-dependent elastic property of rectangular nanobeams （nanowires or nanoplates） induced by the surface elas- ticity effect is investigated by using a developed modified core-shell model. The effect of surface elasticity on the elastic modulus of nanobeams can be characterized by two surface related parameters, i.e., inhomogeneous degree constant and surface layer thickness. The analytical results show that the elastic modulus of the rectangular nanobeam exhibits a distinct size effect when its characteristic size reduces below 1 O0 nm. It is also found that the theoretical results calculated by a mod- ified core-shell model have more obvious advantages than those by other models （core-shell model and core-surface model） by comparing them with relevant experimental measurements and computational results, especially when the dimensions of nanostructures reduce to a few tens of nanometers.     

Scale effects on thermal buckling properties of carbon nanotube

In this Letter, the thermal buckling properties of carbon nanotube with small scale effects are studied. Based on the nonlocal continuum theory and the Timoshenko beam model, the governing equation is derived and the nondimensional critical buckling temperature is presented. The influences of the scale coefficients, the ratio of the length to the diameter, the transverse shear deformation and rotary inertia are discussed. It can be observed that the small scale effects are significant and should be considered for thermal analysis of carbon nanotube. The nondimensional critical buckling temperature becomes higher with the ratio of length to diameter increasing. Furthermore, for smaller ratios of the length to the diameter and higher mode numbers, the transverse shear deformation and rotary inertia have remarkable influences on the thermal buckling behaviors.     

Buckling resistance of solid shell bubbles under ultrasound

Thin solid shell contrast agents bubbles are expected to undergo different volume oscillating behaviors when the acoustic power is increased: small oscillations when the shell remains spherical, and large oscillations when the shell buckles. Contrary to bubbles covered with thin lipidic monolayers that buckle as soon as compressed: the solid shell bubbles resist compression, making the buckling transition abrupt. Numerical simulations that explicitly incorporate a shell bending modulus give the critical buckling pressure and post-buckling shape, and show the appearance of a finite number of wrinkles. These findings are incorporated in a model based on the concept of effective surface tension. This model compares favorably to experiments when adjusting two main parameters: the buckling tension and the rupture shell tension. The buckling tension provides a direct estimation of the acoustic pressure threshold at which buckling occurs.     

Mechanical properties of copper nanocube under three-axial tensile loadings

The mechanical properties of copper nanocubes by molecular dynamics are investigated in this paper.The [100],[110],[111] nanocubes are created,and their energies,yield stresses,hydrostatic stresses,Mises stresses,and the relationships between them and strain are analyzed.Some concepts of the microscopic damage mechanics are introduced,which are the basis of studying the damage mechanical properties by molecular dynamics.The [100] nanocube exhibits homogeneity and isotropy and achieves a balance easily.The [110] nanocube presents transverse isotropy.The [111] nanocube shows the complexity and anisotropy because the orientation sizes in three directions are different.The broken point occurs on a surface,but the other two do not.The [100] orientation model will be an ideal model for studying the microscopic damage theory.     

Buckling and free vibration analysis of functionally graded cylindrical shells subjected to a temperature-specified boundary condition

Linear thermal buckling and free vibration analysis are presented for functionally graded cylindrical shells with clamped-clamped boundary condition based on temperature-dependent material properties. The material properties of functionally graded materials (FGM) shell are assumed to vary smoothly and continuously across the thickness. With high-temperature specified on the inner surface of the FGM shell and outer surface at ambient temperature, 1D heat conduction equation along the thickness of the shell is applied to determine the temperature distribution; thereby, the material properties based on temperature distribution are made available for thermal buckling and free vibration analysis. First-order shear deformation theory along with Fourier series expansion of the displacement variables in the circumferential direction are used to model the FGM shell. Numerical studies involved the understanding of the influence of the power-law index, r/h and l/r ratios on the critical buckling temperature. Free vibration studies of FGM shells under elevated temperature show that the fall in natural frequency is very drastic for the mode corresponding to the lowest natural frequency when compared to the lowest buckling temperature mode.     

A study of the effect of laser beam geometries on laser bending of sheet metal by buckling mechanism

Laser beam forming has emerged as a new and very promising technique to form sheet metal by thermal residual stresses. The objective of this work is to investigate numerically the effect of rectangular beam geometries, with different transverse width to length aspect ratio, on laser bending process of thin metal sheets, which is dominated by buckling mechanism. In this paper, a comprehensive thermal and structural finite element (FE) analysis is conducted to investigate the effect that these laser beam geometries have on the process and on the final product characteristics. To achieve this, temperature distributions, deformations, plastic strains, stresses, and residual stresses produced by different beam geometries are compared. The results suggest that beam geometries play an important role in the resulting temperature distributions on the workpiece. Longer beam dimensions in the scanning direction (in relation to its lateral dimension) produce higher temperatures due to longer beam–material interaction time. This affects the bending direction and the magnitude of the bending angles. Higher temperatures produce more plastic strains and hence higher deformation. This shows that the temperature-dependent yield stress plays a more dominant role in the deformation of the plate than the spread of the beam in the transverse direction. Also, longer beams have a tendency for the scanning line to curve away from its original position to form a concave shape. This is caused by buckling which develops tensile plastic strains along both ends of the scanning path. The buckling effect produces the opposite curve profile; convex along the tranverse direction and concave along the scanning path.     

Influences of Annealing on Residual Stress and Structure of HfO2 Films

HfO2 films are deposited on BK7 glass substrates by electron beam evaporation. The influences of annealing between 100℃ and 400℃ on residual stresses and structures of HfO2 films are studied. It is found that little differences of spectra, residual stresses and structures are obtained after annealing at lower temperatures. After annealing at higher temperatures, the spectra shift to short wavelength, the residual stress increases with the increasing annealing temperature. At the same time, the crystallite size increases and interplanar distance decreases. The variations of optical spectra and residual stress correspond to the evolutions of structures induced by annealing.     

国产纯铁的轧制与再结晶织构

用极固与金相研究工业纯铁的轧制与再结晶织构和组织。热轧后的试样经过两种冷轧方法：(1)压下率为98.8%,与(2)压下率为64.5%,中间700℃熟炼;二次冷轧和压下率63.5%。试样在氢气中分别于(a)650°和(b)1000℃熟炼。第一类材料的轧制织构经测定为(100)[011]+(112)[110]+(111)[112].试样在a与γ区域熟炼后的主要取向为(100)[011]和(111)[112]。第二类材料的轧制织构与第一类相似,惟偏离角度较大。表面与内部织构不同。第二类材料熟炼后的再结晶织构基本上相似,金相组织显出第二次再结晶现象。     

Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model

In this article, the buckling behavior of nanoscale circular plates under uniform radial compression is studied. Small-scale effect is taken into consideration. Using nonlocal elasticity theory the governing equations are derived for the circular single-layered graphene sheets (SLGS). Explicit expressions for the buckling loads are obtained for clamped and simply supported boundary conditions. It is shown that nonlocal effects play an important role in the buckling of circular nanoplates. The effects of the small scale on the buckling loads considering various parameters such as the radius of the plate and mode numbers are investigated.     

Electronic transport mechanism in polydiacetylene crystals — variable range hopping or phonon-assisted tunnelling

Experimental results on the current-voltage characteristics of polydiacetylene (PDA) single crystals reported by Aleshin et al [Phys. Rev. Vol. B 69, (2004) art. 214203] are reinterpreted in terms of the phonon-assisted electron tunnelling model. It is shown that the experimental results, measured in the temperature range from 1.8 K to 300 K are consistent with the tunnelling rate dependence on field strength, computed for the same range of temperatures. An advantage of this model over that of Aleshin et al, using the variable range hopping (VRH) model, is the possibility of describing the behaviour of I — V data measured at both high and low temperatures with the same set of parameters characterizing this material. This assertion is confirmed by comparison of the temperature-dependent current-voltage data extracted from Aleshin et al’s work with tunnelling rate dependence on temperature, computed using two different expressions of the phonon-assisted tunnelling theory. The temperature dependence of the conductivity of an ion implanted PDA crystals [B. S. Elman et al, Appl. Phys. Lett., Vol. 46, (1985) p. 100] and polypyrrole [P. Dutta et al, Synth. Met., Vol. 139 (2003) p. 201] are also explained on the basis of this model.      

Seebeck and magnetoresistive effects of Ga-doped ZnO thin films prepared by RF magnetron sputtering

In this paper, Ga-doped ZnO (GZO) films were deposited on glass substrates at different substrate temperatures by RF magnetron sputtering. The effect of substrate temperature on the structural, surface morphological properties, Seebeck and magnetoresistive effects of GZO films was investigated. It is found that the GZO films are polycrystalline and preferentially in the [0 0 2] orientation, and the film deposited at 300 °C has an optimal crystal quality. Seebeck and magnetoresistive effects are apparently observed in GZO films. The thermoelectromotive forces are negative. Decreasing substrate temperature and annealing in N₂ flow can decrease carrier concentration. The absolute value of the Seebeck coefficient increases with decreasing carrier concentration. The maximal absolute value of Seebeck coefficient is 101.54 μV/K for the annealed samples deposited at the substrate temperature of 200 °C. The transverse magnetoresistance of GZO films is related to both the magnetic field intensity and the Hall mobility. The magnetoresistance increases almost linearly with magnetic field intensity, and the films deposited at higher substrate temperature have a stronger magnetoresistance under the same magnetic field, due to the larger Hall mobility.     

Influence of surface orientation and defects on early-stage oxidation and ultrathin oxide growth on pure copper

We investigate oxidation and oxide growth on single-crystal copper surfaces using reactive molecular dynamics simulation. The kinetics of surface oxide growth are strongly correlated with the microstructure of the metal substrates. Simulating oxide layer growth along the (100), (110), and (111) orientations of crystalline copper, oxidation characteristics are investigated at temperatures of 300?K and 600?K. The oxidation kinetics are found to strongly depend on the surface orientation, ambient temperature, and surface defects. The effect of surface morphology on oxidation characteristics is analyzed by comparing oxygen adsorption on various sites and the structure factor. The surface oxide formed on (100) retains the initial crystal structure in the 300–600?K range. The (100) surface shows the highest oxidation rate at both temperature conditions but saturates, facilitating oxygen adsorption on hollow sites. The oxidation kinetics of the (100) orientation are found to be not significantly affected by surface defects. (110) shows modest oxidation at 300?K but the highest oxidation is observed at 600?K. By surface disorder and reconstruction, the oxide layer is produced continuously. The (111) surface is sensitive to ambient temperature and surface defects, showing that surface reconstruction is a key element for further oxidation. The charge distribution of oxidized Cu atoms indicates multiple groups of stoichiometric oxides, while the fraction of CuO-like characteristics increases significantly on the (110) and (111) orientations at higher temperature (600?K). The energetics and mechanisms of oxidation on Cu metal substrates at the nanoscale are discussed in detail, and comparisons with available experimental and other theoretical studies are presented wherever possible.