Surface Stress Effects Research Articles

Surface effects on stability of nanorings under uniform pressure

In this work, we study the effect of surface stress on the stability behavior of a circular ring with nano dimensions under uniform pressure. It is known that the surface elasticity and residual surface tension can have significant effects on the mechanical behavior of the nano-sized structures. Taking both effects into account, we present an analytical expression for the smallest critical radial load acting on the nanoring. It is shown that, depending on surface mechanical properties of the nanoring, these effects can stabilize or destabilize the nanoring under uniform pressure. The results, in this work, are expected to provide informative predictions on characterizing the stability behavior of nano elements used in nanostructured devices.

A Consistent Set of Nonlocal Bresse–Timoshenko Equations for Nanobeams With Surface Effects

In this study, we propose governing differential equations for beams, taking into account shear deformation, rotary inertia, locality, and surface stress effects. It is shown that the equation is both simpler and more consistent than the appropriate Bresse–Timoshenko equations extended to include locality and surface stress effects. The proposed equation contains 11 terms with respect to displacement versus 19 terms appearing in the equations that extend the Bresse–Timoshenko equations to include nonlocality and surface effects.

Effect of crack face residual surface stress on nanoscale fracture of piezoelectric materials

This paper investigates the problem of a nanoscale crack in piezoelectric nanomaterials by considering the effect of the residual surface stress on the crack surface. The solution of problem is obtained by the singular integral equation technique. The study of the fracture mechanics parameters confirms the fact that nanomaterials are crack-insensitive. It is also found that the effect of surface on the electric displacement intensity factor depends on the crack face electric boundary condition. Moreover, the electromechanical coupling fracture behavior of the piezoelectric materials is influenced by the residual surface stress on the entire crack surface.

Micromechanics Model for Nanovoid Growth in Nanocrystalline Materials

A theoretical model to describe the nanovoid growth by emission dislocation shear loop in nanocrystalline metal under equal biaxial remote stress was developed. The critical stress for emission of dislocation was derived by considering the effects of surface stress. Within our description, dislocations emitted from surface of nanovoid were piled up at grain boundaries and the stress field generated by arrested dislocations can prevent further dislocation emission. The effect of grain boundary of nanocrystalline materials on nanovoid growth was investigated, and the results showed that the smaller of the grain size, the harder for the nanovoid growth.

The effects of interface misfit strain and surface tension on magnetoelectric effects in layered magnetostrictive-piezoelectric composites

A nonlinear model is proposed to study low-frequency magnetoelectric (ME) effects in layered magnetostrictive-piezoelectric composites, taking into account the effects of interface misfit strain and surface stress. As a specific case, L-T mode of Terfenol-D/lead zirconate titanate (PZT) composites is investigated. The results show that flexural deformation can suppress the ME voltage coefficient, especially for elevated Terfenol-D volume fraction. Interface misfit strain demonstrates a notable impact on the ME voltage coefficient, and this strain-mediated ME effect is intensified with increasing interface misfit strain. Owing to residual surface tension, the ME voltage coefficient is found to be size-dependent when the thickness of Terfenol-D/PZT layered composite reduces to the nanoscale. In addition, substrate effect on ME voltage coefficients is evaluated.

The effect of surface stress on interfacial solitary wave propagation

The propagation of long wavelength disturbances on the surface of a fluid layer of finite depth is considered. Attention is focused on the effect of stress applied at the surface. Constant surface tension leads to a normal stress at the surface, but the presence of a surfactant or the application of an electric field can give rise to tangential stresses. In the large Reynolds number limit, the evolution equation for the surface elevation contains contributions from both boundary layers in the flow; one is adjacent to the free surface while the other lies at the base of the fluid layer.Aweakly non-linear analysis is performed leading to an evolution equation similar to the classic Korteweg-de Vries equation, but modified by additional terms due to the viscosity and to the tangential and normal stress at the surface. It is demonstrated that careful treatment of the boundary layer at the free surface is necessary when the tangential stress at the surface is non-zero. Particular cases of flows with tangential surface stress due the presence of a surfactant or due to an electric field are discussed, and a pseudo-spectral scheme is used in order to obtain some typical numerical results.

Melting Temperature of FeO under Pressure

The melting temperature-pressure phase diagram [Tm(P)-P] for wustite (FeO) is predicted through the Clapeyron equation where the pressure-dependent volume difference is modeled by introducing the effect of surface stress induced pressure. FeO plays an important role in many metallurgical processes and in the Earths mantle mineralogy. FeO is also of great interest in the field of state solid physics and chemistry because of its electrical, magnetic, structural and non-stoichiometric properties.

Bending and resonance behavior of nanowires based on Timoshenko beam theory with high-order surface stress effects

A high-order surface stress model is incorporated in a continuum mechanics model based on Timoshenko beam theory to investigate the bending and resonance behavior of nanowires (NWs). Closed-form expressions are derived for the deflection curves and the rotation angle for bending of NWs with different boundary conditions. Normalized maximum deflection, effective size-dependent Young's moduli, and resonance frequency of NWs are also presented in analytic forms in terms of the diameter of the NWs and other material parameters. Our results are compared with the experimental data and with previous results based on classical models of Euler–Bernoulli beam theory with simple and refined surface stress model. We find that for NWs with relatively small cross-sectional size the effect of high-order surface stress is significant. While for NWs with relatively large cross-sections the Timoshenko beam model, accounting for the shearing deformation effect, is critical to attain a sufficient accuracy. This suggests that, for a continuum mechanics modeling of NWs valid for a wide range of slenderness ratio, the present continuum mechanics method, utilizing the Timoshenko beam model together with the high-order surface stress effects, could be a feasible tool to analyze the bending and resonance behavior for NWs.

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

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

Postbuckling characteristics of nanobeams based on the surface elasticity theory

In the present paper, an attempt is made to numerically investigate the postbuckling response of nanobeams with the consideration of the surface stress effect. To accomplish this, the Gurtin–Murdoch elasticity theory is exploited to incorporate surface stress effect into the classical Euler–Bernoulli beam theory. The size-dependent governing differential equations are derived and discretized along with various end supports by employing the principle of virtual work and the generalized differential quadrature (GDQ) method. Newton’s method is applied to solve the discretized nonlinear equations with the aid of an auxiliary normalizing equation. After solving the governing equations linearly, to obtain each eigenpair in the nonlinear model, the linear response is used as the initial value in Newton’s method. Selected numerical results are given to show the surface stress effect on the postbuckling characteristics of nanobeams. It is found that by increasing the thickness of nanobeams, the postbuckling equilibrium path obtained by the developed non-classical beam model tends to the one predicted by the classical beam theory and this anticipation is the same for all selected boundary conditions.

Propagation of elastic wave in nanoporous material with distributed cylindrical nanoholes

The effective propagation constants of plane longitudinal and shear waves in nanoporous material with random distributed parallel cylindrical nanoholes are studied. The surface elastic theory is used to consider the surface stress effects and to derive the nontraditional boundary condition on the surface of nanoholes. The plane wave expansion method is used to obtain the scattering waves from the single nanohole. The multiple scattering effects are taken into consideration by summing the scattered waves from all scatterers and performing the configuration averaging of random distributed scatterers. The effective propagation constants of coherent waves along with the associated dynamic effective elastic modulus are numerically evaluated. The influences of surface stress are discussed based on the numerical results.

A finite element analysis of surface-stress effects on measurement of the Si lattice parameter

A stress exists in solid surfaces even if the underlying bulk material is stress-free. This paper investigates the effect of surface stress on the value of the Si lattice parameter measured by combined x-ray and optical interferometry. An elastic-film model has been used to provide a surface load in a finite element model on the x-ray interferometer crystal. Eventually, an interferometer design is proposed to determine a measurement where the effect of the surface stress is deemed to be detected.

Melting Temperature of MgO under Pressure

The melting temperature-pressure phase diagram [Tm(P)-P] for magnesium oxide (MgO) is predicted through the Clapeyron equation where the pressure-dependent volume difference is modeled by introducing the effect of surface stress induced pressure. MgO is a material of key importance to earth sciences and solid-state physics: it is one of the most abundant minerals in the Earth and a prototype material for a large group of ionic oxides.

Deformation modes in magnesium (0 0 0 1) and single crystals: simulations versus experiments

Magnesium is an excellent candidate as lightweight structural material, but has strong plastic anisotropy, and the activation of, operation of, and competition between different slip and twinning systems remain active areas of research. Here, the nucleation of twinning and basal slip in Mg single-crystalline nanopillars are studied using molecular dynamics over a range of strain rates allowing for reasonable extrapolation to experimental rates. Deformation along the [0 0 0 1] direction shows tension and compression twinning at stresses predicted to be ∼1400 and ∼1700 MPa at a strain rate of 10−3 s−1. Moreover, twin nuclei are shown to be absolutely stable only above 1170 MPa. No evidence of nanotwinning is found and the twin-growth velocities are very fast (∼400 m s−1). These results do not support recently proposed mechanisms for nanotwinning. Deformation along the direction shows basal dislocation nucleation at stresses of 1000–1300 MPa in tension and 670–900 MPa in compression, at experimental strain rates, with one EAM potential exhibiting compression/tension asymmetry. Size effects are observed between pillars of diameters between 5 and 10 nm, which are attributable to surface stress effects driving nucleation and expected to be irrelevant at experimental pillar sizes (200 nm and above). Overall, most of the observed deformation mechanisms mirror those found in experiments but the stress levels, even when extrapolated to experimental strain rates, remain well above those found in micro- and nanopillar experiments. This indicates that deformation in the experimental specimens is controlled by the motion of pre-existing dislocations or is associated with significant stress concentrations due to surface defects.

Influence of surface stress and atomic defect generation on Rayleigh wave propagation in laser-excited solids

The surface stress effects on the Rayleigh wave propagation characteristics in solids with distributions of laser-induced atomic defects (vacancies, interstitial atoms) are studied. Defect-density fields are governed by the strain-induced generation, recombination and diffusion of atomic defects. Formulation of the general surface wave propagation problem has been made, and the corresponding frequency equation has been derived and analyzed. Some important frequency equations, as obtained by other authors, have been deduced as special cases from the frequency equation for Rayleigh waves. The combined effects of surface stress and defect density field on the Rayleigh wave velocities are shown by numerical calculations and graphs. It is found that the Rayleigh waves are generally dispersive; and in the case of low frequency with residual surface tension, a critical wave length exists, below which the propagation of Rayleigh waves is not possible. This critical wave length depends on both the residual stress and the defect distribution.

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

Abstract The elastic behavior of an edge dislocation placed in the shell of a free-standing core–shell nanowire is considered within the theory of surface/interface elasticity. Using the method of complex potential functions the expressions for the stress field of the dislocation, image forces on the dislocation, and the dislocation strain energy are derived and studied in detail. A special attention is paid to non-classical effects revealed within the surface/interface elasticity approach where a characteristic length parameter referred to as surface/interface modulus is introduced. These effects are (i) the stress oscillations along the shell surface and core–shell interface for negative values of the surface/interface elastic moduli; (ii) a strong dependence of image forces on the core size; (iii) extra repelling (attraction) of the dislocation from (to) the shell surface and core–shell interface characterized by positive (negative) interface modulus; and (iv) a decrease of the dislocation strain energy in the central region of the shell and its local increase with an extra maximum in the vicinity of the shell surface for negative values of the surface/interface elastic moduli. These non-classical effects increase with diminishing core radius and shell thickness and are very strong in the layers of 1 nm thickness adjacent to the core–shell interface and shell surface. The effects of the residual surface stress are also addressed.

Modeling of magnetoelectric effects in flexural nanobilayers: The effects of surface stress

A model is developed for the effects of surface stress on low-frequency magnetoelectric (ME) effects in flexural magnetostrictive-piezoelectric bilayers, and we further take cobalt ferrite and lead zirconate titanate (PZT) as a specific case. The results show that flexural deformation can suppress the ME voltage coefficient, especially for moderate PZT volume fraction. Owing to residual surface tension, the ME voltage coefficient should depend on magnetic field, and this tendency is weakened with increasing magnetic field. Interestingly, the size dependence of ME voltage coefficient is found when the thickness of bilayer reduces to nanoscale.

Surface Stress Effect on the Vibrational Response of Circular Nanoplates With Various Edge Supports

The classical continuum theory cannot be directly used to describe the behavior of nanostructures because of their size-dependent attribute. Surface stress effect is one of the most important size dependencies of structures at this submicron size, which is due to the high surface to volume ratio of nanoscale domain. In the present study, the nonclassical governing differential equation together with corresponding boundary conditions are derived using Hamilton's principle, into which the surface energies are incorporated through the Gurtin-Murdoch elasticity theory. The model developed herein contains intrinsic length scales to take the size effect into account and is used to analyze the free vibration response of circular nanoplates including surface stress effect. The generalized differential quadrature (GDQ) method is employed to discretize the governing size-dependent differential equation along with simply supported and clamped boundary conditions. The classical and nonclassical frequencies of circular nanoplates with various edge supports and thicknesses are calculated and are compared to each other. It is found that the influence of surface stress can be different for various circumferential mode numbers, boundary conditions, plate thicknesses, and surface elastic constants.

Large-amplitude vibrations of nanowires with dissipative surface stress effects

In this study, nonlinear free vibrations of doubly clamped Euler–Bernoulli nanowires (NWs) have been considered. The von Karman strain–displacement relationships along with the classic Zener model are implemented to derive the nonlinear differential equation of the flexural motion of NW. Nonlinear natural frequencies are calculated using the computer package Mathematica. The effects of size-dependent surface dissipation, mode numbers, and amplitude of vibrations on the nonlinear natural frequencies are investigated. It is shown that the surface dissipation effect on the normalized nonlinear natural frequencies depends on the amplitudes of vibrations. Also, comparisons are made with the results published in previous studies.

Effect of surface stress and surface mass on elastic vibrations of nanoparticles

The elastic vibrations of nanoparticles, in the present work, have been studied theoretically by taking into account the size-dependent elasticity due to the surface effect. Surface elasticity has been resorted to where, in addition to the effect of surface stress, the effect of surface mass has also been taken into account in the model. The torsional and spherical modes for the free vibration have been obtained. Numerical calculations have been conducted, and the results have shown that both the surface stress and the surface mass affect significantly the eigenfrequencies of nanospheres. With those surface effects, the eigenfrequencies are no longer proportional to the radius inverse. Under appropriate circumstances, the surface effects may render the lowest eigenfrequency amount to the second lowest by classical elasticity.