Molecular dynamics study on mechanics of metal nanowire

The new concept of using nanowires as building blocks for logic and memory circuits makes it very necessary to fully understand the mechanical behaviors of these nanowires. Embedded-atom method is employed to carry out three-dimensional molecular dynamics simulations of the mechanical properties of rectangular cross-section copper nanowire. A stable free-relaxation state and the stress–strain relation of nanowire under extension are obtained. The elastic modulus, yielding strength and deformation are studied. The surface effect, size effect, and temperature effect on the extension property of metal nanowire are discussed in detail. The simulation results from our present work show that at nanoscale surface atoms play an important role on the mechanical behaviors of nano-structures. This study of mechanical properties of metal nanowires will be helpful to the design, manufacture and manipulation of nano-devices.     

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.     

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.     

Surface/interface effects on elastic behavior of a screw dislocation in an eccentric core–shell nanowire

The elastic behavior of a screw dislocation which is positioned inside the shell domain of an eccentric core–shell nanowire is addressed with taking into account the surface/interface stress effect. The complex potential function method in combination with the conformal mapping function is applied to solve the governing non-classical equations. The dislocation stress field and the image force acting on the dislocation are studied in detail and compared with those obtained within the classical theory of elasticity. It is shown that near the free outer surface and the inner core–shell interface, the non-classical solution for the stress field considerably differs from the classical one, while this difference practically vanishes in the bulk regions of the nanowire. It is also demonstrated that the surface with positive (negative) shear modulus applies an extra non-classical repelling (attracting) image force to the dislocation, which can change the nature of the equilibrium positions depending on the system parameters. At the same time, the non-classical solution fails when the dislocation approaches very close to the surface/interface with negative shear modulus. The effects of the core–shell eccentricity and nanowire diameter on dislocation behavior are discussed. It is shown that the non-classical surface/interface effect has a short-range character and becomes more pronounced when the nanowire diameter is smaller than 20 nm.     

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.     

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.     

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.     

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.     

Influence of anisotropic elasticity on the mechanical properties of fivefold twinned nanowires

Previous atomistic simulations and experiments have shown an increased Young's modulus and yield strength of fivefold twinned (FT) face-centered cubic metal nanowires (NWs) when compared to single crystalline (SC) NWs of the same orientation. Here we report the results of atomistic simulations of SC and FT Ag, Al, Au, Cu and Ni NWs with diameters between 2 and 50 nm under tension and compression. The simulations show that the differences in Young's modulus between SC and FT NWs are correlated with the elastic anisotropy of the metal, with Al showing a decreased Young's modulus. We develop a simple analytical model based on disclination theory and constraint anisotropic elasticity to explain the trend in the difference of Young's modulus between SC and FT NWs. Taking into account the role of surface stresses and the elastic properties of twin boundaries allows to account for the observed size effect in Young's modulus. The model furthermore explains the different relative yield strengths in tension and compression as well as the material and loading dependent failure mechanisms in FTNWs.     

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.     

NON-UNIQUE SOLUTIONS FROM SURFACE ELASTICITY FOR FUNCTIONALLY GRADED MATERIALS

This paper considers the unusual behavior of functionally graded materials/structures when the surface effect is involved. It is found that on the assumption that the surface energy is not positive semi-definite, the solution can be non-unique. Several examples are given for simple spherically-symmetric and axisymmetric FGM bodies with surface effects characterized by Gurtin-Murdoch surface elasticity. The results show that the conditions for non-uniqueness of solution emerge when the magnitude of negative effective surface modulus is of the order of a characteristic dimension of the problem multiplied by the bulk modulus near the surface, which is quite different from that for homogeneous materials.     

MECHANISMS UNDERLYING TWO KINDS OF SURFACE EFFECTS ON ELASTIC CONSTANTS

Recently, people are confused with two opposite variations of elastic modulus with decreasing size of nano scale sample： elastic modulus either decreases or increases with decreasing sample size. In this paper, based on intermolecular potentials and a one dimensional model, we provide a unified understanding of the two opposite size effects. Firstly, we analyzed the microstructural variation near the surface of an fcc nanofilm based on the Lennard-Jones potential. It is found that the atomic lattice near the surface becomes looser in comparison with the bulk, indicating that atoms in the bulk are located at the balance of repulsive forces, and the elastic moduli decrease with the decreasing thickness of the film accordingly. In addition, the decrease in moduli should be attributed to both the looser surface layer and smaller coordination number of surface atoms. Furthermore, it is found that both looser and tighter lattice near the surface can appear for a general pair potential and the governing mechanism should be attributed to the surplus of the nearest force to all other long range interactions in the pair potential. Surprisingly, the surplus can be simply expressed by a sum of the long range interactions and the sum being positive or negative determines the looser or tighter lattice near surface respectively. To justify this concept, we examined ZnO in terms of Buckingham potential with long range Coulomb interactions. It is found that compared to its bulk lattice, the ZnO lattice near the surface becomes tighter, indicating the atoms in the bulk are located at the balance of attractive forces, owing to the long range Coulomb interaction. Correspondingly, the elastic modulus of one-dimensional ZnO chain increases with decreasing size. Finally, a kind of many-body potential for Cu was examined. In this case, the surface layer becomes tighter than the bulk and the modulus increases with deceasing size, owing to the long range repulsive pair interaction, as well as the cohesive many-body interaction caused by the electron redistribution.     

A critical state sand model with elastic–plastic coupling

Soil elastic moduli are highly pressure-dependent. Experimental findings have indicated that the elastic shear modulus of sands depends on p^χ, where p is mean principal effective stress and χ is a non-dimensional parameter. χ practically remains unchanged for shear strains less than 10⁻⁵ where the mechanical behavior is purely elastic. However, experiments have revealed that the emergence of plasticity for shear strains larger than 10⁻⁵ provokes a gradual increase in χ. Technically, this observation is an elastic–plastic coupling effect in which plasticity causes to change the elastic characteristics. Here, this issue is considered in hyper-elasticity framework in conjunction with a critical state compatible bounding surface plasticity platform for granular soils. To this aim, constitutive equations linking χ to a proper kinematic hardening parameter are presented. Then, using the proposed approach, a hyper-elastic theory is modified to consider the mentioned elastic–plastic coupling effect in the whole domain of the elastoplastic behavior. Adopting the improved hyper-elasticity necessitates the modification of a number of basic plasticity platform elements. In this regard, dilatancy and plastic hardening modulus of the bounding surface platform are modified. Successful performance of the modified constitutive model is presented against experimental data of loading/unloading triaxial tests.     

Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic micro-plate based on surface stress and modified couple stress theories using differential quadrature method

The size-dependent effect on the biaxial and shear nonlinear buckling analysis of an isotropic and orthotropic micro-plate based on the surface stress,the modified couple stress theory(MCST),and the nonlocal elasticity theories using the differential quadrature method(DQM)is presented.Main advantages of the MCST over the classical theory(CT)are the inclusion of the asymmetric couple stress tensor and the consideration of only one material length scale parameter.Based on the nonlinear von K′arm′an assumption,the governing equations of equilibrium for the micro-classical plate considering midplane displacements are derived based on the minimum principle of potential energy.Using the DQM,the biaxial and shear critical buckling loads of the micro-plate for various boundary conditions are obtained.Accuracy of the obtained results is validated by comparing the solutions with those reported in the literature.A parametric study is conducted to show the effects of the aspect ratio,the side-to-thickness ratio,Eringen’s nonlocal parameter,the material length scale parameter,Young’s modulus of the surface layer,the surface residual stress,the polymer matrix coefficients,and various boundary conditions on the dimensionless uniaxial,biaxial,and shear critical buckling loads.The results indicate that the critical buckling loads are strongly sensitive to Eringen’s nonlocal parameter,the material length scale parameter,and the surface residual stress effects,while the effect of Young’s modulus of the surface layer on the critical buckling load is negligible.Also,considering the size dependent effect causes the increase in the stiffness of the orthotropic micro-plate.The results show that the critical biaxial buckling load increases with an increase in G12/E2and vice versa for E1/E2.It is shown that the nonlinear biaxial buckling ratio decreases as the aspect ratio increases and vice versa for the buckling amplitude.Because of the most lightweight micro-composite materials with high strength/weight and stiffness/weight ratios,it is anticipated that the results of the present work are useful in experimental characterization of the mechanical properties of micro-composite plates in the aircraft industry and other engineering applications.     

Surface effect on band structure of magneto-elastic phononic crystal nanoplates subject to magnetic and stress loadings

This paper presents a theoretical model for the size-dependent band structure of magneto-elastic phononic crystal(PC) nanoplates according to the Kirchhoff plate theory and Gurtin-Murdoch theory, in which the surface effect and magneto-elastic coupling are considered. By introducing the nonlinear coupling constitutive relation of magnetostrictive materials, Terfenol-D/epoxy PC nanoplates are carried out as an example to investigate the dependence of the band structure on the surface effect, magn...     

Sample boundary effect in nanoindentation of nano and microscale surface structures

Nanoindentation is a widely used technique to characterize mechanical properties of materials in small volumes. When the sample size is comparable to the indent size, the indentation-induced plastic zone can be affected by the sample boundary which may cause inaccurate interpretation of the mechanical properties. In this study, the sample boundary effect is investigated by performing experiments and atomistic simulations of nanoindentation into nano- and micro-scale Au pillars and bulk Au (0 0 1) surfaces. In experiments, a more compliant deformation is observed in pillar indentations compared to bulk Au. The elastic modulus decreases with increasing indent size over sample size ratio. Atomistic simulations are performed to gain insights on the mechanisms of pillar deformation and pillar boundary effect. The reduced modulus has a similar trend of decrease with increasing indent size over sample size ratio. Significantly different dislocation activities and dislocation interactions with the pillar boundary contribute to the lower value of the reduced modulus in the pillar indentation. The presence of the free surface would allow the dislocations to annihilate, causing a higher plastic recovery during the pillar unloading process.     

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.     

不锈钢表面等离子合金化渗铜层的纳米力学性能研究

为了研究不锈钢渗铜层的纳米力学性能,本文采用等离子表面合金化技术在304不锈钢表面制备了渗铜层。利用纳米压入硬度仪,采用连续刚度测试法,对渗铜层以及不锈钢基体的表面和横截面的纳米力学性能进行了测试,得到了纳米压入过程的载荷-压入深度曲线,发现渗铜层抵抗外载荷的能力低于不锈钢基体。并得到了渗铜层和不锈钢基体的表面、横截面方向的硬度以及杨氏模量,经对比得到渗铜层的杨氏模量和硬度都要比不锈钢基体的低,并且渗铜层的力学性能表现出各向异性。对纳米压入的数据进行分析,发现渗铜层在小尺度压入时硬度和杨氏模量表现出明显的"尺度效应"。     

Surface effects on the persistence length of nanowires and nanotubes

Surface effects on the persistence length of quasi-one-dimensional nanomaterials are investigated by using the theory of surface elasticity and the core–shell model of nanobeams. A simple and unified expression is provided to determine the persistence length of nanowires and nanotubes with any regular polygonal cross-sections. It is demonstrated that surface effects have a distinct influence on the persistence length when the characteristic sizes of materials shrink to nanometers. This work is helpful not only for understanding the size-dependent behavior of nanomaterials but also for the design of devices based on nanotubes or nanowires.