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.     

Second-order constitutive equation for the surface stress tensor of a fluid–fluid interface

In this paper a constitutive equation is derived for the surface stress tensor of a simple fluid–fluid interface. The equation is an extension of the linear Boussinesq surface fluid model, and is correct up to second order in the rate of deformation tensor. It is valid for simple fluid–fluid interfaces, without memory effects and yield stresses.     

Vague concept of “reversible cleavage” in the theory of the surface tension of solids

Numerous derivations of the well-known Shuttleworth equation have been based on the unclear concept of “reversible cleavage” leading to the decisive step in any derivation - equalization of the surface free energy and surface stress. This is the key concept in contemporary surface thermodynamics of solids. But “cleavage” is not a surface process and, in this field, it cannot be a reversible operation. Besides, the “reversible cleavage” has no formal definition in the domain of the surface tension of solids that is an abnormal for any exact science. Consequently, this concept and all its corollaries including the Shuttleworth and generalized Lippmann equations have to be recognized as incorrect.     

Dynamics of nuclear fluid: (I). Foundation

Starting with the time-dependent Hartree-Fock (TDHF) formulation of the many-body problem, we cast the equation into a set of conservation laws of classical type. Besides the equation of continuity, TDHF leads to an equation of motion which is analogous to the Euler equation in classical fluid dynamics. The forces do not come from the collective kinetic stress alone, but also from a density-dependent chemical potential, the surface tensional force which depends on density differences and the Coulomb interaction. With an assumed Navier-Stokes generalization of the stress tensor, such a set of differential equations provides a powerful tool for the study of complicated collective motions of nuclear systems such as those involved in heavy-ion reactions and nuclear fission. In the static case, the equation of motion leads to the Thomas-Fermi model of a finite nucleus as formulated by Bethe.     

Laser gas-assisted processing of carbon coated and TiC embedded Ti-6Al-4V alloy surface

Laser gas-assisted treatment of Ti-6Al-4V alloy surface is carried out. The alloy surface is initially coated by a carbon layer, in which the TiC particles are embedded prior to laser processing of the surface. The carbon coating with the presence of TiC particles on the workpiece surface is expected to result in carbonitride compound in the surface vicinity after the laser treatment process. Optical and scanning electron microscopes are used to examine the morphological and the metallurgical changes in the laser treated layer. The residual stress formed in the surface region after the laser treatment process is critical for the practical applications of the resulting surface. Therefore, the residual stress formed in the laser treated region is predicted from the analytically equation. The X-ray diffraction technique is incorporated to obtain the residual stress formed in the surface region. It is found that the residual stress predicted agrees with the X-ray diffraction data. The dense structures consisting of TiC_xN_1−x, TiN_x, Ti₂N, and TiC compounds are formed in the surface region of the treated layer. This, in turn, significantly increases the microhardness at the surface.     

Love-type waves in functionally graded piezoelectric material (FGPM) sandwiched between initially stressed layer and elastic substrate

This paper investigates the propagation behavior of Love-type surface waves in three-layered composite structure with initial stress. The composite structure has been taken in such a way that a functionally graded piezoelectric material (FGPM) layer is bonded between initially stressed piezoelectric upper layer and an elastic substrate. Using the method of separation of variables, frequency equation for the considered wave has been established in the form of determinant for electrical open and short cases on free surface. The bisection method iteration technique has been used to find the roots of the dispersion relations which give the modes for electrical open and short cases. The effects of gradient variation of material constant and initial stress on the phase velocity of surface waves are discussed. Dependence of thickness on each parameter of the study has been shown explicitly. Study has been also done to show the existence of cut-off frequency. Graphical representation has been done to exhibit the findings. The obtained results are significant for the investigation and characterization of Love-type waves in FGPM-layered media.     

Lubricated sliding dynamics: Flow factors and Stribeck curve

We study the fluid flow at the interface between elastic solids with randomly rough surfaces. We derive (approximate) analytical expressions for the fluid flow factors which enter in the equation describing the fluid flow, and for the frictional shear stress factors which enter in the equation for the frictional shear stress. Numerical results for a rubber cylinder with surface roughness sliding on a flat lubricated substrate, under “low” and “high” pressure conditions, are presented and discussed. Finally we discuss the role of the fluid-induced elastic deformations of the surface roughness profile.     

Theories of surface elasticity for nanoscale objects

The emergence of nanotechnology has driven recent interest in systems having surface atoms as a significant fraction of all atoms present, in particular nano-sheets (ultra-thin slabs), nano-wires, and nano-particles. In these systems, the bulk (i.e. non-surface region or interior) is typically strained in response to the stress of the surface. This elastic strain of the bulk in turn changes the surface lattice constants. Since the bulk and the surface are coupled, the problem must be solved self-consistently. Solving this problem requires a quantitative model of the surface elastic properties which are different from the bulk. In this paper we consider various models that have been proposed for surface elasticity. Our goal is to elucidate the relationship between two contrasting approaches: (1) the Shuttleworth equation which defines a surface stress based on the strain derivative of the surface energy and (2) the Gurtin-Murdoch (GM) theory which considers the surface layer as a membrane with residual strain and with elastic constants different from the bulk. The GM theory is analogous to the 2-D Frenkel-Kontorova (FK) model and can be used to obtain quantitative parameters for the FK model. We present an embedded atom method calculation of the surface elastic constants of Cu(1 1 1) using the GM theory with the surface represented by a membrane one atomic layer thick. This quantitative approach describes the elastic properties of surfaces in a physically appealing way. Just as the bulk elastic constants provide direct information regarding the stress/strain relationship in a bulk material, the surface elastic constants provide similar information for a surface monolayer. This theory will allow elasticity analysis and atomistic calculations of properties of nano-scale objects.     

The dislocations in graphene with the correction from lattice effect

The dislocation widths and Peierls stresses of glide dislocations and shuffle dislocations in graphene have been studied by the improved Peierls-Nabarro (P-N) equation which contains the discrete correction. The discrete parameter is obtained from a simple dynamic model in which the interaction attributed to the variation of bond length and angle was considered. The restoring force in the improved P-N equation is given by the gradient of the generalized stacking fault energy surface (γ-surface). Our calculation shows that the widths of the shuffle dislocation and the glide dislocation are narrow and the width of the shuffle dislocation is about twice wider than the glide dislocation. The Peierls stress of a shuffle dislocation is one order of magnitude smaller than that of a glide dislocation. As a consequence, the shuffle dislocation moves more easily than the glide dislocation.     

Axisymmetric wave propagation of thermoelastic transversely isotropic half-space under buried loading using potential functions

By virtue of a new scalar potential function and Hankel integral transforms, the wave propagation analysis of a thermoelastic transversely isotropic half-space is presented under buried loading and heat flux. The governing equations of the problem are the differential equations of motion and the energy equation of the coupled thermoelasticity theory. Using a scalar potential function, these coupled equations have been uncoupled and a six-order partial differential equation governing the potential function is received. The displacements, temperature, and stress components are obtained in terms of this potential function in cylindrical coordinate system. Applying the Hankel integral transform to suppress the radial variable, the governing equation for potential function is reduced to a six-order ordinary differential equation with respect to z. Solving that equation, the potential function and therefore displacements, temperature, and stresses are derived in the Hankel transformed domain for two regions. Using inversion of Hankel transform, these functions can be obtained in the real domain. The integrals of inversion Hankel transform are calculated numerically via Mathematica software. Our numerical results for displacement and temperature are calculated for surface excitations and compared with the results reported in the literature and a very good agreement is achieved.     

Surface deformation induced by a variation in surface stresses in anisotropic half-regions

The deformations and the stresses in anisotropic half-regions taking into account surface stresses originating from surface energy, which exists originally at surfaces and interfaces dividing phases, are analysed theoretically. In the present paper, the equilibrium equation of force considering surface stresses is used to calculate the inelastic deformation induced by a variation in surface stresses. The problem of varying surface stresses in a half-surface of a half-infinite anisotropic domain is analysed using the theory of elasticity. This problem is related to the occurrence of cracks in contaminated, oxidized or chemisorbed surfaces. Stress analysis on the basis of continuum mechanics is performed precisely under the boundary condition taking into account surface stresses. The Fourier transform technique is applied to perform the analysis, and the components of stress and displacement are expressed in an explicit form. The shear component of bulk stress attains infinity at the edge of discontinuity of the surface stresses, and the free surface deforms like an edge dislocation. This result suggests that cracking in a chemically contaminant surface is easier than in a clean surface.     

An equation of state for anisotropic solids under shock loading

An anisotropic equation of state is proposed for accurate extrapolation of high-pressure shock Hugoniot states to other thermodynamics states for shocked single crystals and polycrystalline alloys. The proposed equation of state represents mathematical and physical generalization of the Mie-Grüneisen equation of state for isotropic material and reduces to this equation in the limit of isotropy. Using an anisotropic nonlinear continuum framework and generalized decomposition of a stress tensor [Int. J. Plasticity 24, 140 (2008)], the shock waves propagation along arbitrary directions in anisotropic solids of any symmetry can be examined. The non-associated strength model includes the distortion effect of the yield surface which can be used to describe the anisotropic strength differential effect. A numerical calculation showed that the general pulse shape, Hugoniot Elastic Limits (HELs), and Hugoniot stress levels for aluminum alloy 7010-T6 agree with the experimental data. The results are presented and discussed, and future studies are outlined.     

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.     

Study of characteristics of ultrasound pulse generated by a laser pulse

I.IntroductionThegenerationofacousticpulsebylaserirradiationofametalsurfacewasfirstsuggestcdbyWhitein1963[1l.SincethatdateLaserU1trasoundtechniquchasbeendcvclopedrapidly.Becausethistechniquehasanumberoftechnicalfcatures,suchasnon-contact,highbandwidth,highhme-spacia1resolution,quantitativeteshng,generationoflongitudinal,shcarandRay1cighwaves(simu1taniously),andsoon,ithasbccnwidelyapp1icdtomcasurementsofmatcrialproperties,detectionofdefects,andcalibrationoftransd.ccrsl'-'o].Inordertodcve1opth…     

On the calculation of forces and total energy changes via the quantum mechanical stress field

Many-electron systems are within density functional theory described in terms of an appropriately defined local stress tensor. The differential equation for its exchange and correlation part is solved also for the case of density gradient dependent exchange and correlation energy. Formulae are given (i) for the direct calculation of the global stress tensor of a homogeneously strained crystal via surface integrals of the local stress tensor along intercell boundaries, and (ii) similarly for the energy change of inhomogeneously strained crystals.     

Surface effect on the nonlinear forced vibration of cantilevered nanobeams

The nonlinear forced vibration behavior of a cantilevered nanobeam is investigated in this paper, essentially considering the effect due to the surface elastic layer. The governing equation of motion for the nano-cantilever is derived, with consideration of the geometrical nonlinearity and the effects of additional flexural rigidity and residual stress of the surface layer. Then, the nonlinear partial differential equation (PDE) is discretized into a set of nonlinear ordinary differential equations (ODEs) by means of the Galerkin’s technique. It is observed that surface effects on the natural frequency of the nanobeam is of significance, especially for the case when the aspect ratio of the nanobeam is large. The nonlinear resonant dynamics of the nanobeam system is evaluated by varying the excitation frequency around the fundamental resonance, showing that the nanobeam would display hardening-type behavior and hence the frequency-response curves bend to the right in the presence of positive residual surface stress. However, with the negative residual surface stress, this hardening-type behavior can be shifted to a softening-type one which becomes even more evident with increase of the aspect ratio parameter. It is also demonstrated that the combined effects of the residual stress and aspect ratio on the maximum amplitude of the nanobeam may be pronounced.     

Surface size effects under plastic deformation of microcrystals and nanocrystals

The size effects associated with the crystal surface as an effective sink for moving dislocations in a thin crystal and as a barrier for these dislocations in the presence of a high-strength film or a special hardened layer on the surface, which favor the accumulation of dislocations in the crystal, have been considered theoretically in terms of the kinetic equation for the density of dislocations concentrated in the crystal in the critical lengths of single-ended (unipolar) dislocation sources. The theoretical results have been illustrated by the experimental data available in the literature for microcrystals and nanocrystals of copper and aluminum. It has been found in accordance with these data that the dependence of the yield stress ??_2% of the crystal on the crystal transverse size D has the form ??_2% ?? D ^?0.75 when there is a free crystal surface for the escape ofthe dislocations and ??_2% ?? D ^?0.5 when there is a high-strength layer on the lateral surface of the crystal..     

急冷快速凝固过程中液相流动与组织形成的相关规律

研究了Fe58wt%Sn过偏晶合金的急冷快速凝固和组织形成特征． 实验发现, FeSn过偏晶合金的急冷快速凝固组织由规则排布的纤维状β-Sn相和分布其间的α-Fe相及少量金属间化合物相组成, β-Sn相的几何排列方向与合金条带表面成0—15°的夹角．根据急冷条件下金属熔体的热传导方程和Navier-Stokes方程, 对过偏晶合金的凝固行为和组织形成过程进行了理论分析, 揭示出熔体内部的动量传输对过偏晶合金的液相分离行为具有显著的影响．两相分离发生于液池底部约200μm的急冷区内, 分离的L2液滴在辊面驱 关键词： 液态 相分离 液相流动 快速凝固 晶体生长     

On the dynamic instability of nanowire-fabricated electromechanical actuators in the Casimir regime: Coupled effects of surface energy and size dependency

Herein, the dynamic pull-in instability of cantilever nanoactuator fabricated from conductive cylindrical nanowire with circular cross-section is studied under the presence of Casimir force. The Gurtin–Murdoch surface elasticity in combination with the couple stress theory is employed to incorporate the coupled effects of surface energy and size phenomenon. Using Green–Lagrange strain, the higher order surface stress components are incorporated in the governing equation. The Dirichlet mode is considered and an asymptotic solution, based on the path integral approach, is applied to consider the effect of the Casimir attraction. Furthermore, the influence of structural damping is considered in the model. The nonlinear governing equation is solved using analytical reduced order method (ROM). The effects of various parameters on the dynamic pull-in parameters, phase planes and stability threshold of the actuator are demonstrated.     

Improved formulation of electron kinetic theory approach for laser shortpulse heating: Thermal stress consideration

Nonequilibrium energy transport between excited electrons and lattice site is re-formulated after considering the ballistic contribution of the electron energy to the energy transport process. The improved formulation of the electron kinetic theory predictions are compared with the previously obtained electron kinetic and two-equation models. Thermal stress developed in the region irradiated by a laser beam is formulated during the heating pulse. Copper with variable properties is used in the simulations. It is found that improved electron kinetic theory model predicts less temperature rise than that corresponding to previously formulated electron kinetic theory and two equation models in the surface region; in this case, electron temperature attains high values. Thermal stress developed is compressive and attains the maximum at some depth below the surface. The thermal stress level is well below the yielding limit of the substrate material.