粗糙表面接触的层级模型

真实的材料加工表面的粗糙度往往跨越了多个尺度。本研究建立了一种新的粗糙表面层级接触模型。对于较大尺度部分,截断过滤短波长的粗糙度,然后运用连续介质力学的方法计算出相应的近似接触面积和局部压力的分布;对于较小尺度部分,本研究基于分形理论,利用二维Cantor集来描述层叠的短波长微凸峰,然后对在较大尺度得到的近似接触面积进行细化修正,计算出了最终的接触面积。为了验证所建立的模型,将得到的整体接触响应与有限元法计算结果进行了比较。结果表明,该模型能够充分预测粗糙表面的弹性接触响应,而且大大降低了多尺度粗糙表面接触力学建模的计算规模。这对进一步研究跨尺度粗糙表面之间的接触和摩擦具有重要意义。

A universal method to calculate the surface energy density of spherical surfaces in crystals

Surface energy plays an important role in the mechanical performance of nanomaterials; however, determining the surface energy density of curved surfaces remains a challenge. In this paper, we conduct atomic simulations to calculate the surface energy density of spherical surfaces in various crystalline metals. It is found that the average surface energy density of spherical surfaces remains almost constant once its radius exceeds 5 nm. Then, using a geometrical analysis and the scaling law, we develop an analytical approach to estimate the surface energy density of spherical surfaces through that of planar surfaces. The theoretical prediction agrees well with the direct atomic simulations, and thus provides a simple and general method to calculate the surface energy density in crystals.

Nanoindentation of soft solids by a fla punch

Measuring the surface tension and elastic mod- ulus of soft materials and biological tissues under different physiological and pathological conditions is of significance for understanding various phenomena associated with defor- mation. In this paper, the nanoindentation of a circular fiat punch on a soft solid is analyzed with the influence of surface tension. By solving the corresponding singular integral equa- tion, the relation between load and indent depth is obtained. When the radius of the flat punch shrinks to the same order as the ratio of surface tension to elastic modulus, surface ten- sion significantly affects the indentation load-depth relation, which provides a facile method to measure surface tension in soft solids and biological tissues.

Analytical Expression for the Atomic Friction of a Single Asperity Based on the Prandtl-Tomlinson Model

The Prandtl-Tomlinson(PT)model has been widely applied to interpret the atomic friction mechanism of a single asperity.In this study,we present an approximate explicit expression for the friction force in the one-dimensional PT model under quasi-static conditions.The‘stick-slip’friction curves are first approximated properly by sawtooth-like lines,where the critical points before and after the‘slip’motion are described analytically in terms of a dimensionless parameterη.Following this,the average friction force is expressed in a closed form that remains continuous and valid forη>1.Finally,an analytical expression for the load dependence of atomic friction of a single asperity is derived by connecting the parameterηwith the normal load.With the parameters reported in experiments,our prediction shows good agreement with relevant experimental results.

Adhesive Contact of Elastic Solids with Self-Affine Fractal Rough Surfaces

The elastic adhesive contact of self-affine fractal rough surfaces against a rigid flat is simulated using the finite element method. An array of nonlinear springs, of which the force-separation law obeys the Lennard–Jones potential, is introduced to account for the interfacial adhesion. For fractal rough surfaces, the interfacial interaction is generally attractive for large mean gaps, but turns repulsive as the gap continuously shrinks. The interfacial interactions at the turning point corresponding to the spontaneous contact are shown for various surfaces. For relatively smooth surfaces, the probability density distributions of repulsion and attraction are nearly symmetric. However, for rougher surfaces, the simulation results suggest a uniform distribution for attraction but a monotonously decreasing distribution with a long tail for repulsion. The pull-off force rises with increasing ratio of the work of adhesion to the equilibrium distance, whereas decreases for solids with a higher elastic modulus and a larger surface roughness. The current study will be helpful for understanding the adhesion of various types of rough solids.

Effects of surface energy and substrate on modulus determination of biological films by conical indentation

Micro-/nano-indentation has become prevalent in evaluating the mechanical characteristics of biological samples,such as cells and tissues.However,the existing contact models describing conical indentation ignore the joint effects of surface energy and substrate,and consequently cannot accurately extract the Young's modulus of biological samples deposited on substrate.Through finite element methods,we examine the conical indentation of biological films on substrates while taking surface energy into account.Based on the dimensional analysis,the explicit relationship between load and indentation depth is achieved for films with their moduli varying from 0.001 to 100 times that of the substrate.If the classical Sneddon's model was employed to analyze the load-depth data,the measured modulus could reach 18 times the real modulus for films on harder substrates,but only 4%of the real modulus for films on softer substrates.Meanwhile,in micro-/nano-indentations,neglecting the contribution of surface energy would result in an overestimation of the Young's modulus of films depending on the contact size.The analytical expression provided here can be utilized to precisely deduce the mechanical characteristics of biological films deposited on substrate from the load and indentation depth data of a conical indentation.

ATOMISTIC CALCULATIONS OF SURFACE ENERGY OF SPHERICAL COPPER SURFACES

Surface plays an important role in the physical and mechanical behavior of nanos- tructured materials and elements, however surface energy of curved solid surfaces has not been fully understood. In the present letter, surface energy of spherical particles and cavities in FCC copper is calculated by embedded atom method. The numerical simulations reveal that the dis- tribution of atom energy is non-uniform on the curved surfaces. However, when the radius of spherical cavity or particle is larger than 4 nm, the average surface energy density keeps almost constant irrespective of its location and radius.

Statistical Characterization of the Yield Stress of Nanoparticles

Atomistic simulations are performed to study the statistical mechanical properties of gold nanoparticles.It is demonstrated that the yielding behavior of gold nanoparticles is governed by the dislocation nucleation around surface steps.Since the nucleation of dislocation is an activated process with the aid of thermal fluctuation,the yield stress at a specific temperature should vary statistically rather than being a definite constant value.Molecular dynamics simulations reveal that the yield stress follows a Gaussian distribution at a specific temperature.As the temperature increases,the mean value of yield stress decreases while the width of distribution becomes larger.Based on the numerical analysis,the dependence of mean yield stress on temperature can be well described by a parabolic function.This study illuminates the statistical features of the yielding behavior of nanostructured elements.