Surface deformation-dependent mechanical properties of bending nanowires: an ab initio core-shell model

An ab initio core-shell model is proposed to evaluate the surface effect in bending nanowires, in which the elastic modulus depends on the surface relaxation and deformation induced by external loading. By using first-principles calculations based on the density functional theory(DFT), the surface and bulk properties are calculated for Ag, Pb, and Si nanowires. The obtained theoretical predictions of the effective Young’s modulus of nanowires agree well with the experimental data, which shows th...     

Surface stress effects on the resonant properties of metal nanowires: The importance of finite deformation kinematics and the impact of the residual surface stress

We utilize the recently developed surface Cauchy-Born model, which extends the standard Cauchy-Born theory to account for surface stresses due to undercoordinated surface atoms, to study the coupled influence of boundary conditions and surface stresses on the resonant properties of gold nanowires with surfaces. There are two major purposes to the present work. First, we quantify, for the first time, variations in the nanowire resonant frequencies due to surface stresses as compared to the corresponding bulk material which does not observe surface effects within a finite deformation framework depending on whether fixed/free or fixed/fixed boundary conditions are utilized. We find that while the resonant frequencies of fixed/fixed nanowires are elevated as compared to the corresponding bulk material, the resonant frequencies of fixed/free nanowires are reduced as a result of compressive strain caused by the surface stresses. Furthermore, we find that for a diverse range of nanowire geometries, the variation in resonant frequencies for both boundary conditions due to surface stresses is a geometric effect that is characterized by the nanowire aspect ratio. The present results are found to agree well with existing experimental data for both types of boundary conditions.The second major goal of this work is to quantify, for the first time, how both the residual (strain-independent) and surface elastic (strain-dependent) parts of the surface stress impact the resonant frequencies of metal nanowires within the framework of nonlinear, finite deformation kinematics. We find that if finite deformation kinematics are considered, the strain-independent surface stress substantially alters the resonant frequencies of the nanowires; however, we also find that the strain-dependent surface stress has a significant effect, one that can be comparable to or even larger than the effect of the strain-independent surface stress depending on the boundary condition, in shifting the resonant frequencies of the nanowires as compared to the bulk material.     

Modification of the elastic properties of nanostructures with surface charges in applied electric fields

The influences of applied electric fields and surface charges on elastic modulus of nanostructures such as nanowires and nanofilms are investigated within the framework of classic continuum mechanics. Under an applied electric field, the surfaces of structures are subjected to the electrostatic forces (negative pressure) along the direction of the electric field, and the resulting surface charges also change the surface mechanical properties due to the Hellman–Feynman (H–F) forces. Through incorporating the surface energy from the negative pressure and the H–F forces into surface free energy, the exact and analytical expressions of the effective elastic modulus of nanowires and nanofilms are addressed by considering the surface energy effects on the elastic modulus of nanostructures, which involves the contribution of the applied electric field and surface charges. The numerical results indicate that applied electric fields parallel to the axis of the nanowire and nanofilms enhance the transverse Young's modulus while reducing axial modulus of nanostructures. The effective modulus of nanowires and nanofilms with lateral surface charges depends on the surface charges density and the sign of the charges. In addition, the effect of electric field and surface charges on Young's moduli of nanowires and nanofilms has been found to be sensitive to structural geometric dimensions such as the thickness of the film and the diameter of the wire.     

Molecular dynamics study of the mechanics of metal nanowires at finite temperature

Three-dimensional molecular dynamics simulations for mechanical properties of copper nanowires at finite temperatures were conducted with the Embedded-atom method (EAM). The stable free-relaxation state was simulated for a rectangular cross-section copper nanowire. The stress–strain curve under extension loading, elastic modulus, yielding strength and plastic deformation were studied. The results demonstrate that the strain-rate scale for nanowire is different from that for the bulk, and an explanation is presented. The dislocation movements corresponding to the plastic deformation are clearly depicted through transient atomic images. The necking and break-up phenomena are observed. This study can give more fundamental understanding of nanoscale machines from atomistic motions and contribute to the design, manufacture and manipulation of nano-devices.     

Size and strain rate effects in tensile strength of penta-twinned Ag nanowires

Penta-twinned Ag nanowires(pt-AgNWs) have recently attracted much attention due to their interesting mechanical and physical properties. Here we perform largescale atomistic simulations to investigate the influence of sample size and strain rate on the tensile strength of pt-AgNWs. The simulation results show an apparent size effect in that the nanowire strength(defined as the critical stress for dislocation nucleation) increases with decreasing wire diameter. To account for such size effect, a theoretical model involving the interaction between an emerging dislocation and the twin boundary has been developed for the surface nucleation of dislocations. It is shown that the model predictions are in quantitative agreement with the results from atomistic simulations and previous experimental studies in the literatures. The simulations also reveal that nanowire strength is strain-rate dependent, which predicts an activation volume for dislocation nucleation in the range of 1–10b~3,where b is the magnitude of the Burgers vector for a full dislocation.     

Dynamic stress concentration around two interacting coated nanowires with surface/interface effect

In coated nanowires, the surface/interface effects are particularly prominent due to a larger ratio of surface area to volume. In this paper, the effect of surface/interface stress on the macroscopic dynamic stress concentration around two nanowires under anti-plane shear waves is studied. The analytical solutions of displacements around the coated nanowires, in the coating layers, and inside the nanowires are expressed by wave function expansion method. The expanded mode coefficients are determined by satisfying the boundary conditions at the two interfaces around the nanowires. To accomplish the superposition of displacement fields, the addition theorem for cylindrical wave function is employed. Analyses show that the effect of interface properties on the dynamic stress is significantly related to the wave frequency, the material properties of nanowires and coating layers, and the relative position and distance between the two nanowires. If the wires and coating layers are softer, the dynamic stress decreases greatly, and the interface effect on the dynamic stress is also little. The results may be potentially useful for providing information on the mechanical properties and interactions among array of nanowires under different external mechanical stimulus.     

Simulations of nanowire bend tests for extracting mechanical properties

Mechanical properties of nickel nanowires are characterized based on the numerical simulations of bend tests performed with a customized atomic force microscope (AFM) and scanning electron microscope (SEM). Nickel nanowire specimens are subjected to bending loads by the tip of the AFM cantilever. The experimental force versus bending displacement curves are compared against simulations from finite element analysis and peridynamic theory, and the mechanical properties are extracted based on their best correlations. Similarly, SEM images of fractured nanowires are compared against peridynamic failure simulations. The results of this study reveal that nickel nanowires have significantly higher strengths than their bulk counterparts, although their elastic modulus values are comparable to bulk nickel modulus values.     

A continuum model for the mechanical behavior of nanowires including surface and surface-induced initial stresses

The continuum modeling of the mechanical behavior of nanowires has recently attracted much attention due to its simplicity and efficiency. However, there are still some critical issues to be solved. In this paper, we demonstrate the importance of accounting for the effects of initial stresses in the nanowires that are caused by deformation due to surface stresses; we note that such initial stresses have previously been neglected in most existing continuum models. By considering the local geometrical nonlinearity of strains during the incremental flexural motion, a new formulation of the Euler–Bernoulli beam model for nanowires is developed through the incremental deformation theory, in which effects of the surface stress, the surface-induced initial stress and surface elasticity are naturally incorporated. It is found through comparisons to existing experimental and computational results for both fcc metal and ceramic nanowires that the surface-induced initial stresses, which are neglected in the Young–Laplace model, can significantly influence the overall mechanical properties of nanowires. We additionally demonstrate and quantify the errors induced by using the Young–Laplace model due to its approximation of surface stresses acting on only the top and bottom surfaces of nanowires.     

Dynamic multi-axial behavior of shape memory alloy nanowires with coupled thermo-mechanical phase-field models

The objective of this paper is to provide new insight into the dynamic thermo-mechanical properties of shape memory alloy (SMA) nanowires subjected to multi-axial loadings. The phase-field model with Ginzburg–Landau energy, having appropriate strain based order parameter and strain gradient energy contributions, is used to study the martensitic transformations in the representative 2D square-to-rectangular phase transformations for FePd SMA nanowires. The microstructure and mechanical behavior of martensitic transformations in SMA nanostructures have been studied extensively in the literature for uniaxial loading, usually under isothermal assumptions. The developed model describes the martensitic transformations in SMAs based on the equations for momentum and energy with bi-directional coupling via strain, strain rate and temperature. These governing equations of the thermo-mechanical model are numerically solved simultaneously for different external loadings starting with the evolved twinned and austenitic phases. We observed a strong influence of multi-axial loading on dynamic thermo-mechanical properties of SMA nanowires. Notably, the multi-axial loadings are quite distinct as compared to the uniaxial loading case, and the particular axial stress level is reached at a lower strain. The SMA behaviors predicted by the model are in qualitative agreements with experimental and numerical results published in the literature. The new results reported here on the nanowire response to multi-axial loadings provide new physical insight into underlying phenomena and are important, for example, in developing better SMA-based MEMS and NEMS devices     

Low-Cycle Fatigue Testing of Ni Nanowires Based on a Micro-Mechanical Device

Despite extensive research on the mechanical properties of one-dimensional (1-D) nanomaterials such as nanowires and nanotubes in the past two decades, experimental data on the fatigue behavior of 1-D building blocks are still very limited. Here, we demonstrate the first quantitative in situ tensile fatigue testing of individual nanowires inside a high-resolution scanning electron microscope (SEM), based on the nanoindenter-assisted “push-to-pull” dynamic tensile straining mechanism. With the robust micro-mechanical devices and independent quantitative nanoindenter for actuation and force sensing, we achieved both stress- and strain-controlled cyclic tensile loading on nanowire samples with variable loading frequencies up to 10 Hz, and demonstrated the low-cycle fatigue behavior of pristine single crystalline nickel (Ni) nanowires.     

Effect of surface/interface stress on the plastic deformation of nanoporous materials and nanocomposites

Surface and interface play an important role on the overall mechanical behaviors of nanostructured materials. We investigate the effect of surface/interface stress on the macroscopic plastic behaviors of nanoporous materials and nanocomposites, where both the surface/interface residual stress and surface/interface elasticity are taken into account. A new second-order moment nonlinear micromechanics theory is developed and then reduced to macroscopically isotropic materials. It is found that the effect of surface/interface residual stress is much more prominent than that of the surface/interface elasticity, causing strong size effect as well as asymmetric plastic deformation for tension and compression. The variation of yield strength is more prominent with smaller pore/inclusion size or higher pore/inclusion volume fraction. For a representative nanoporous aluminum, the surface effect becomes significant when the pore radius is smaller than about 50 nm. When hard inclusions are embedded in a ductile metal matrix, the interface effect and resulting size effect are much smaller than that of nanoporous materials. The results may be useful for evaluating the mechanical integrity of nanostructured materials.     

Atomistic simulation of the structure and elastic properties of gold nanowires

We performed atomistic simulations to study the effect of free surfaces on the structure and elastic properties of gold nanowires aligned in the 〈100〉 and 〈111〉 crystallographic directions. Computationally, we formed a nanowire by assembling gold atoms into a long wire with free sides by putting them in their bulk fcc lattice positions. We then performed a static relaxation on the assemblage. The tensile surface stresses on the sides of the wire cause the wire to contract along the length with respect to the original fcc lattice, and we characterize this deformation in terms of an equilibrium strain versus the cross-sectional area. While the surface stress causes wires of both orientations and all sizes to increasingly contract with decreasing cross-sectional area, when the cross-sectional area of a 〈100〉 nanowire is less than , the wire undergoes a phase transformation from fcc to bct, and the equilibrium strain increases by an order of magnitude. We then applied a uniform uniaxial strain incrementally to 1.2% to the relaxed nanowires in a molecular statics framework. From the simulation results we computed the effective axial Young's modulus and Poisson's ratios of the nanowire as a function of cross-sectional area. We used two approaches to compute the effective elastic moduli, one based on a definition in terms of the strain derivative of the total energy and another in terms of the virial stress often used in atomistic simulations. Both give quantitatively similar results, showing an increase in Young's modulus with a decrease of cross-sectional area in the nanowires that do not undergo a phase transformation. Those that undergo a phase transformation experience an increase of about a factor of three of Young's modulus. The Poisson's ratio of the 〈100〉 wires that do not undergo a phase transformation show little change with the cross-sectional area. Those wires that undergo a phase transformation experience an increase of about 10% in Poisson's ratio. The 〈111〉 wires show, with a decrease of cross-sectional area, an increase in one of Poisson's ratios and small change in the other.     

Harmonic behavior of silicon nanowire by molecular dynamics

Silicon nanowires (SiNW) have attracted increasing interests as potential core parts for nanoscale devices due to their distinguished mechanical and electrical properties. Using molecular dynamics (MD) method, we investigated the vibration behaviors of SiNW on the atomic scale, including the fundamental mode frequency and quality factor. The quality factor as low as 120 is attributed to the energy loss process coming from atomic friction and nonlinearity. We also found that the energy of lattice vibration (phonon energy) is much larger than the macroscale beam vibration energy. And both the energies are less than the surface relaxation energy of the beam. The comparison between MD and FEM has been made to discuss the validity of continuum approximation for the study of SiNW.     

分子动力学模拟金属纳米杆

纳米结构（包括纳米杆）的力学性能是纳米超微型器件设计的基础，分子动力学是研究纳米结构力学为的有效方法，采用EAM势模拟金属铜纳米杆在轴向压力作用下的力学行为，结果表明，当外力较小时，纳米杆受压发生纵向收缩；当外力达到某一临界值时，纳米杆发生横向弯曲（即屈曲）行为；稳定的弯曲状态能继承受外载，当外力继续增大时，纳米杆发生倾覆而失效。     

蛇纹石矿物作为润滑油添加剂对锡青铜摩擦学行为的影响

采用SRV滑动磨损试验机考察了蛇纹石天然矿物粉体作为添加剂对油润滑条件下与钢对磨时锡青铜摩擦磨损的影响. 借助扫描电镜、能谱仪、X射线光电子能谱仪、纳米压痕仪等对磨损表面形貌、元素组成与化学状态，以及纳米力学性能进行了分析，探讨了蛇纹石添加剂改善锡青铜摩擦学性能的作用机制. 结果表明:蛇纹石矿物在锡青铜表面形成了1层由金属氧化物、氧化物陶瓷、石墨和有机物构成的复合摩擦反应膜，其纳米硬度和弹性模量呈表面低、内部高的梯度变化，从而显著改善了油润滑条件下锡青铜的摩擦学性能.      

Static and fatigue behavior of metal cylinders with enhanced surface property

Effects of surface property on the static and fatigue strength of metal cylinders is determined by analysis of the redistribution of stress and energy density. Because the mechanical constraints on the material elements in a surface layer differ so drastically from those in the interior or bulk, changes of mechanical properties in a thin surface layer can significantly alter the global behavior of a metal part. Desirable gain in mechanical strength due to surface treatments such as laser spraying, ion implantation, etc. is now well known. Developed in this work is a method for evaluating the enhancement of the static and fatigue life of metals when their mechanical properties in a thin surface layer of material are improved. An extensive increase in the surface layer thickness does not lead to appreciable changes of mechanical strength.     

侧向受拉脆性岩石压缩本构及蠕变失效研究

轴向压缩作用下,脆性岩石侧向应力严重影响岩石力学特性。侧向压应力影响下的轴向压缩岩石力学行为已经得到广泛研究,然而侧向拉应力对轴向压缩岩石力学行为影响研究很少。本文基于脆性岩石翼型裂纹扩展模型中,初始裂纹面法向应力与剪切应力的正负方向为判断依据,研究了侧向拉应力对轴向压缩力学行为的影响。发现恒定的侧向拉应力作用下,轴向压缩应力渐进变化过程中,脆性岩石内部细观初始裂纹面的法向应力只能为压缩应力,不存在拉应力情况。分析了从侧向压应力到拉应力转化过程中,脆性岩石轴向压应力与细观裂纹扩展长度关系、轴向压应力与轴向应变关系、岩石峰值强度、裂纹启裂应力及初始弹性模量的变化规律。并分析了侧向拉应力对岩石蠕变裂纹长度、裂纹速率、轴向应变及应变率演化曲线,以及对蠕变失效时间及稳态蠕变应变率的影响。讨论了侧向拉压应力突变转化以及侧向拉应力分级增大对轴向压缩岩石蠕变演化行为影响。该研究为深部地下工程围岩稳定性评价提供了一定理论依据。     

Electronic band energy of a bent ZnO piezoelectric semiconductor nanowire

The electric band energy variation in a bent piezoelectric semiconductor(PSC) nanowire of circular cross-section induced by the mechanical force is analyzed based on a six-band k · p method. The electric-mechanical fields are first obtained analytically in a cantilever bent PSC nanowire by solving the fully-coupled electro-mechanical equations. Then, the band energy is acquired numerically via the six-band Hamiltonian.By considering further the nonlinear coupling between the piezoelectric and semiconducting quantities, the contribution of the redistribution carriers to the electric field is analyzed from the Gauss' s law. Numerical examples are carried out for an n-type Zn O nanowire in different locations induced by an applied concentrated end force. They include the electric potential, heavy hole(HH), light hole(LH), spin-orbit split-off(SO),and conduction band(CB) edges along the axial and thickness directions. Our results show that the applied force has a significant effect on the band energies. For instance, on the bottom surface along the axial direction, the bandgaps near the fixed end are greater than those near the loading end, and this trend is reversed on the top surface. Moreover,at a fixed axial location, the energy level of the lower side can be enhanced by applying a bending force at the end. The present results could be of significant guidance to the electronic devices and piezotronics.     

SURFACE STRESS EFFECT IN MECHANICS OF NANOSTRUCTURED MATERIALS

This review article summarizes the advances in the surface stress effect in mechanics of nanostructured elements,including nanoparticles,nanowires,nanobeams,and nanofilms,and heterogeneous materials containing nanoscale inhomogeneities.It begins with the fundamental formulations of surface mechanics of solids,including the definition of surface stress as a surface excess quantity,the surface constitutive relations,and the surface equilibrium equations.Then,it depicts some theoretical and experimental studies of the mechanical properties of nanostructured elements,as well as the static and dynamic behaviour of cantilever sensors caused by the surface stress which is influenced by adsorption.Afterwards,the article gives a summary of the analytical elasto-static and dynamic solutions of a single as well as multiple inhomogeneities embedded in a matrix with the interface stress prevailing.The effect of surface elasticity on the diffraction of elastic waves is elucidated.Due to the difficulties in the analytical solution of inhomogeneities of complex shapes and configurations,finite element approaches have been developed for heterogeneous materials with the surface stress.Surface stress and surface energy are inherently related to crack propagation and the stress field in the vicinity of crack tips.The solutions of crack problems taking into account surface stress effects are also included.Predicting the effective elastic and plastic responses of heterogeneous materials while taking into account surface and interface stresses has received much attention.The advances in this topic are inevitably delineated.Mechanics of rough surfaces appears to deserve special attention due to its theoretical and practical implications.Some most recent work is reviewed.Finally,some challenges are pointed out.They include the characterization of surfaces and interfaces of real nanomaterials,experimental measurements and verification of mechanical parameters of complex surfaces,and the effects of the physical and chemical processes on the surface properties,etc.