MD simulation of the effect of contact area and tip radius on nanoindentation

Nanoindentation,namelydepth-sensingindentation(DSI),involvesforcingarigidindenterwithknowngeometryintothesurfaceofamaterialwhilecontinuouslymonitoringtheloadontheindenter,thedisplacementoftheindenterintothesurface,andthetimeoftheexperiment.Thedepthisthenusedtocalculatetheprojectedareaofcontactforthepurposeofcalculatingthehardnessandelasticmodulus.Infact,variouserrorsareassociatedwiththisprocedure.Oneofthemcomesfromthemeasurementofthepenetrationdepth.Ideally,thepenetrationdepthshouldbecalcula…     

Indentation analysis of nano-particle using nano-contact mechanics models during nano-manipulation based on atomic force microscopy

Atomic force microscopy is applied to measure intermolecular forces and mechanical properties of materials, nano-particle manipulation, surface scanning and imaging with atomic accuracy in the nano-world. During nano-manipulation process, contact forces cause indentation in contact area between nano-particle and tip/substrate which is considerable at nano-scale and affects the nano-manipulation process. Several nano-contact mechanics models such as Hertz, Derjaguin–Muller–Toporov (DMT), Johnson–Kendall–Roberts–Sperling (JKRS), Burnham–Colton–Pollock (BCP), Maugis–Dugdale (MD), Carpick–Ogletree–Salmeron (COS), Pietrement–Troyon (PT), and Sun et al. have been applied as the continuum mechanics approaches at nano-scale. In this article, indentation depth and contact radius between tip and substrate with nano-particle for both spherical and conical tip shape during nano-manipulation process are analyzed and compared by applying theoretical, semiempirical, and empirical nano-contact mechanics models. The effects of adhesion force, as the main contrast point in different nano-contact mechanics models, on nano-manipulation analysis is investigated for different contact radius, and the critical point is discussed for mentioned models.     

Quantitative assessment and prediction of contact area development during spherical tip indentation of glassy polymers

This paper describes the development of the contact area during indentation of polycarbonate. The contact area was measured in situ using an instrumented indentation microscope and compared with numerical simulations using an elasto-plastic constitutive model. The parameters in the model were obtained using macroscopic tests. Indentations were performed on samples with different thermal histories and at different speeds. For all cases, the numerical model correctly predicted the development of the contact area during indentation. For increasing strain rates, the contact area decreased at equal indentation depths. Annealing the samples resulted in a smaller contact area at equal indentation depth. Using only numerical simulation, it was also shown that pile-up around the indenter resulted from localization effects and was, thus, promoted by strain-softening properties of the indented material. Strain hardening, on the other hand, will tend to promote sink-in. Finally, we performed simulations of load relaxation during indentation. The results indicate that about 40% of the total observed relaxation may be assigned to plastic effects.     

Mapping of Two-Dimensional Contact Problems on a Problem with a One-Dimensional Parametrization

We discuss a possible generalization of the ideas of the method of dimensionality reduction (MDR) for the mapping of two-dimensional contact problems (line contacts). The conventional formulation of the MDR is based on the existence and uniqueness of a relation between indentation depth and contact radius. In two-dimensional contact problems, the indentation depth is not defined unambiguously, thus another parametrization is needed. We show here that the Mossakovskii-Jäger procedure of representing a contact as a series of incremental indentations by flat-ended indenters can be carried out in two-dimensions as well. The only available parameter of this process is, however, the normal load (instead of indentation depth as in the case of threedimensional contacts). Using this idea, a complete solution is obtained for arbitrary symmetric two-dimensional contacts with a compact contact area. The solution includes both the relations of force and half-width of the contact and the stress distribution in the contact area. The procedure is generalized for adhesive contacts and is illustrated by solutions of a series of contact problems.     

Probing viscosity of a polymer melt at the nanometre scale with an oscillating nanotip

The Navier-Stokes equation is used to analyze the additional phase delay when an oscillating nanotip touches intermittently an entangled polymer melt. Even when the tip oscillates at frequencies of several hundred kilohertz, it is shown that the inertial contributions are negligible as long as the indentation depth is no more than a few ten nanometers. Consequently, a stationary solution can be used leading to the simple Stokes formula. Two simple geometries of the tip are investigated. A smooth tip apex with a spherical shape and an elongated tip apex that aims at mimicking a single asperity. The tip shape has a drastic influence on the measured viscosity at the local scale. A simple calculation indicates that the viscous force acting against the tip motion may exhibit several different behaviors as a function of the indentation depth. Using the variational principle of least action, we derive the corresponding phase variation of the oscillator as a function of the indentation depth. It is shown that there exist situations for which an absolute value of the local viscosity could be measured. Received 13 April 2001 and Received in final form 1 August 2001     

Indentation on one-dimensional hexagonal quasicrystals: general theory and complete exact solutions

This paper presents a general account of the indentation responses of a one-dimensional hexagonal quasicrystal half-space pressed by an axisymmetric rigid punch. Based on Green's functions of the half-space subjected to point sources on the surface, the mixed boundary value problem is transformed to integral equations and solved exactly using the results of the potential theory method. Explicit expressions for the generalised pressures and indentation forces are derived for three common indenters (cylinder, cone and approximate sphere) in a systematic manner. For conical and spherical indenters, relations between the contact radius and indentation loads are determined. The coupling phonon–phason fields in the half-space under indentation are accurately expressed in terms of elementary functions. Numerical calculations are performed and discussions on related physical phenomena are given. The present exact solutions can serve as benchmarks for approximate or numerical analyses and can guide the experimental characterisation of material properties of quasicrystals.     

Nanosurface Mechanical Properties of Polymers Based on Continuous Stiffness Indentation

A systematic experimental study of the large strain surface mechanical properties of a number of polymers {polymethylmethacrylate (PMMA), polyetheretherketone (PEEK), polystyrene (PS), polycarbonate (PC), polypropylene (PP), and ultra-high molecular weight polyethylene (UHMWPE)} at the nanometer scale is described. The polymeric surfaces were indented and the data were analyzed using a contact compliance method in conjunction with a nano-indenter system. The indentation experiments were performed using a Berkovich Tip indenter with a continuous contact compliance indentation mode. The indentations were performed using a constant loading rate (300 μN/sec) to a maximum penetration depth of 5 μm. The experimental results showed a considerable strain-rate hardening effect for the polymers and a peculiarly harder response of these surfaces at the near-to-surface (submicron) layers. PMMA was the hardest polymer of the selection, whereas UHMWPE and PP were observed to be the softest polymers. The paper includes practical consideration of a creeping effect and appropriateness of tip calibration using harder surfaces for nanoindentation experimentation of polymers.     

Study on the nano machining process with a vibrating AFM tip on the polymer surface

The polymer has been proved to be nano machined by a vibrating tip in tapping mode of Atomic Force Microscope (AFM). The force between the tip and the surface is an important factor which determines success of the machining process. Controlling this force with high accuracy is the foundation of nanomachining in AFM tapping mode. To achieve a deeper understanding on this process, the tip is modeled as a driving oscillator with damping. Factors affecting the nano machining process are studied. The Hertz elastic contact theory is used to calculate the maximum contact pressure applied by the tip which is employed as a criterion to judge the deformation state of the sample. The simulation results show that: The driven amplitude can be used as a main parameter of controlling the machined depth. Sharper tips and harder cantilevers should be used for successful nanomachining with the vibrating tip. Under the same conditions, a larger tip radius will not only result in the machining error, but also lead to failure of the nanomachining process. The higher driving frequency will lead to a larger tapping force. However it cannot be used as a parameter to control the machined depth because of its narrow variation range. But it is a main error source for the nanomachining process in AFM tapping mode. Moreover, a larger Young's modulus polymer sample will induce a smaller machined depth, a larger maximum contact pressure and a bigger tapping force.     

Evaluation of the substrate effect on indentation behavior of film/substrate system

A method to evaluate the substrate effect quantitatively in film indentation is proposed. For the thin film deposited on the substrate, the power function relationship is used to describe the loading curve of the film indentation behavior. The loading curve exponent of the power function which is the fitting parameter can reflect the substrate effect quantitatively. The finite element method is used to simulate the nanoindentation process of the film/substrate system. The loading curve exponent can be obtained from the simulation results. A substrate effect factor based on the loading curve exponent is defined to characterize the effect of the substrate on film indentation. Meanwhile, the dimensionless function of the loading curve exponent related with the material properties and indentation depth is obtained. The results can be helpful to the measurement of the mechanical properties of thin films by means of nanoindentation.     

表面黏附导致的接触行为转变

应用大规模分子动力学方法, 模拟了具有不同原子级粗糙形貌的两种刚性球形探头与弹性平面基体的黏附接触行为. 研究了载荷与真实接触面积、接触界面排斥力与真实接触面积, 以及黏附力与真实接触面积之间的关系. 分子模拟得到的载荷与真实接触面积的关系, 与连续力学接触理论预测很好地定性一致. 无论是原子级光滑探头还是粗糙探头, 黏附接触下的排斥力与真实接触面积的关系, 都与无黏附接触时的规律相一致, 即黏附力对接触行为的影响作用, 可以等效为附加在真实外载荷基础上的虚拟载荷, 将对黏附接触行为的分析转变为无黏附接触分析. 两种探头的黏附力随真实接触面积都呈幂函数形式的增长, 但是, 原子级光滑探头的幂指数大于1, 而原子级粗糙探头的幂指数小于1. 关键词： 接触行为 表面黏附 分子动力学模拟     

粗糙热传导表面下激光介质的热效应

在考虑激光介质与热沉不完全接触导热的情况下,用面热源自适应调整算法计算了激光介质的温度场,研究了其热效应.表面附近相位差存在起伏且深入一定深度使热效应复杂化.随抽运功率的增大,表面附近相位差的起伏增强,而起伏深度变化不明显;接触面积增大,相位差起伏减小,起伏的深度有所减小.抽运功率较小时,热致衍射损耗随抽运功率的增大近似线性增大,高斯光半径越大,增大的斜率越大,当抽运功率增加到一定程度时,热致衍射损耗增大的趋势减缓,半径大的减缓较明显.在抽运光功率变化范围内,半径大的高斯光热致衍射损耗大于半径小的.高斯光半径较小时,接触面积对热致衍射损耗的影响不明显,当高斯光半径较大时,接触面积减小热致衍射损耗增大.     

Nanotribology of self-assembled monolayer with a probe tip investigated using molecular dynamics simulations

The nanotribology of an alkanethiol self-assembled monolayer (SAM) under tilt contact with a scanning probe tip is studied using molecular dynamics (MD) simulations. The tilt contact is described in terms of the tilt angle and the magnitude of the specimen–tip separation. The effects of tilt angle and magnitude of the specimen–tip separation on the normal force, friction force, friction coefficient, shear strength of the tip–SAM junction, and self-recovery characteristics are evaluated during the scanning probe tip process at a temperature of 300 K. The simulation results clearly show that the magnitudes and periods of the normal force and friction force increase with decreasing magnitude of the specimen–tip separation due to a large change of the tilt angle of the SAM chains during the deformation and recovery stages. For scanning and indentation processes, the effect of the tilt angle of the probe tip on the normal force is more significant than that on the friction force for the SAM. The behaviors of interfacial contact forces, friction coefficient, and shear strength strongly depend on the number of interacting atoms and the contact area, which increases with decreasing magnitude of the specimen–tip separation and increasing tilt angle of the probe tip. The self-recovery of SAM is significantly affected by the magnitude of the specimen–tip separation; the recovery ability of SAM is worse for magnitude of the specimen–tip separation below −0.9 nm with a large tilt angle of the probe tip.     

Derivation of tensile flow properties of thin films using nanoindentation technique

By regarding the tip blunting as a ball indentation at very low depth range (within about 80 nm in our experiments), the flow properties of Au thin films were derived from the indentation load–depth curve obtained by nanoindentation technique. The effects of pile-up or sink-in were considered in determining the real contact between the indenter and the specimen. The representative strain in indentation was defined in various ways and examined by comparing the flow properties derived from indentation load–depth curve with those measured by tensile test. The best definition was found to be the shear strain at contact edge multiplied by 0.1. When we considered the effects of pile-up or sink-in, the representative stress in indentation could also be determined, and was found to be one third of the mean contact pressure for fully plastic regime. As a more intrinsic property than hardness, the yield strengths of Au films with thickness of 0.56 and 0.99 μm were extrapolated from the derived true stress–true strain curve as 261±30 and 154±18 MPa, respectively.     

Atomistic simulations of the effect of a void on nanoindentation response of nickel

Three-dimensional molecular dynamics simulations have been performed to investigate the effect of a void on the nanoindentation of nickel thin film.The radius and depth of the void are varied to explore how they influence the nanoindentation.The simulation results reveal that the presence of a void softens the material and allows for a larger indentation depth at a given load compared to the no void case.The radius and depth of the void have a major effect on the indentation behaviors of the thin film.It is also observed that the void will collapse during the nanoindentation of crystal with void.And when the indentation depth is sufficiently large,the void will disappear.It is found that the indentation depth needed to make the void disappear depends on the void size and location.     

Effect of sample tilt on nanoindentation behaviour of materials

Analysis of nanoindentation is based on the elastic solution of a rigid indenter perpendicularly penetrating a flat contact surface. In reality, nanoindentation is often performed on a tilt sample surface due to sample tilt mounting or the existing roughness of a polished or raw surface. In this study, finite element simulations as well as nanoindentation experiments on a fused-quartz sample with different tilt angles were carried out to investigate the influence of sample tilt on nanoindentation behaviour of materials. It was found that sample tilt results in increases in the indentation load, contact area and contact stiffness at the same penetration depth. The contact area increase caused by sample tilt cannot be accounted for by Sneddon's equation, commonly used in nanoindentation analysis. This results in a significant underestimation of indentation projected contact area, which in turn leads to an overestimation of the mechanical properties measured by nanoindentation.     

环形浅液池内热毛细对流的热力学特性

为了了解径向温度梯度作用下环形浅液池内硅熔体热毛细对流的热力学特性,利用有限差分法进行了非稳态三维数值模拟。液池外半径r0=50 mm,内半径ri=15 mm,深度为d=3 mm。结果表明,当温度梯度较小时,流动为稳定轴对称流动,系统总熵产较小;随着温度梯度的增加,流动将失去其稳定性,首先转化为径向脉动波,此时系统总熵产呈周期性变化;温度梯度再增加时,流动转化为热流体波,系统总熵产较大,但不再随时间变化。     

Nanotack test: adhesive behavior of single latex particles

We present an investigation of the adhesive properties of latex films with nanometric thickness through force spectroscopy using an atomic force microscope (AFM). The AFM tip can be used to indent and excite mechanically one single latex particle, and provides an adhesion test which resembles macroscopic probe tack test, but at nanometric scales. We show that this AFM nanotack test can be analyzed quantitatively, normalizing the total rupture energy by the contact area formed during the indentation step. This contact area depends upon the mechanical properties and environment of the latex particle.     

Experimental Estimation of the Emission Directivity of a Moving Surface Vessel in Shallow Water

The possibility of constructing an acoustic model of a surface ship’s noise emission in the far field using monopole-type emitters uniformly distributed along the hull is investigated. Experimental data obtained in shallow water are used to calculate the characteristics of equivalent monopole emission sources that form a total sound field similar to the sound field from a moving surface ship. The powers of each monopole and the cross-correlations between them are calculated. For the selected discrete components and linear model of an extended source, the directivity patterns are constructed, reduced to the free space. In the experiments and calculations, technical tools and algorithms were used that ensure high-precision positioning of the vessel with respect to the receiving elements of the array. An equivalent model of the waveguide transfer function in the operations area was preliminarily obtained by acoustic waveguide calibration using specially developed equipment, experimental techniques, and processing algorithms. This made it possible to use adequate seafloor models and the waveguide transfer function when calculating the equivalent sound field and directivity pattern. Good agreement is shown between the calculated and experimental data, both of the directivity pattern and field distribution along the transit characteristics. Practical recommendations are given for developing methods to measure the noise fields of surface vessels.

     

Strain-rate effects on hardness of glassy polymers in the nanoscale range. Comparison between quasi-static and continuous stiffness measurements

Strain rate effects on Hardness and Young's modulus of two glassy polymers, poly(diethylene glycol bis allyl carbonate) (CR39) and bisphenol-A polycarbonate (PC), were studied in the nanoscale range. Before analyzing material behaviors, we focused on a particular phenomenon prevailing at the first stage of the contact between the surface of these polymers and the Berkovitch diamond tip used in the experiments, leading to an apparent increase of the tip defect (i.e., the missing tip of the diamond from having a shape equivalent to a perfect cone). The common methods based on calibration functions of the tip appear to be inaccurate to calculate correctly the contact area at the nanoscale range for these polymers. A new method based on Loubet et al.'s model to calculate the contact area by taking account of the apparent tip defect is proposed. The hardness values obtained this way were compared to the compressive yield stress using Tabor's relationship. A hardness-yield stress ratio close to 2.0, as expected on such polymers, was found. A strain-rate effect on the load-depth curve for these two polymers is interpreted as an increase of the hardness with the strain rate. The results from quasi-static and dynamic (the continuous stiffness method) measurements are compared. The strain-rate effect on Young's modulus in dynamic conditions should be taken into account in the hardness calculation.     

On the reduction method of dimensionality: The exact mapping of axisymmetric contact problems with and without adhesion

Starting from the classical theory of contact mechanics it is shown that the relationship between load, penetration and contact radius of any axisymmetric contact can be mapped exactly on a one-dimensional system, thus the reduction method of dimensionality is valid for conforming and non-conforming contacts. Furthermore the reduction method has been successfully extended to adhesive contact problems. The mapping of the classical theory of Johnson, Kendall and Roberts derived for spherical contacts as well as its application to axisymmetric contacts of arbitrary shape is possible; all results are reproduced precisely.