试样倾斜对熔融石英硅三棱锥纳米压痕测试的影响

使用三棱锥压头对不同倾斜角下的熔融石英硅进行纳米压痕实验。结果表明,试样倾斜会影响加载曲线的形状。在相同的载荷下,随着试样倾斜角的增加,压痕最大深度、残余深度及接触深度逐渐减小,但卸载曲线不受影响,彼此保持平行,卸载曲线的拟合参数m及接触刚度值保持恒定。另外,试样倾斜将导致测量的压痕接触面积偏小,从而使得测量的硬度和弹性模量偏大。     

A linear model of elasto-plastic and adhesive contact deformation

Rigorous non-linear models of elasto-plastic contact deformation are time-consuming in numerical calculations for the distinct element method (DEM) and quite often unnecessary to represent the actual contact deformation of common particulate systems. In this work a simple linear elasto-plastic and adhesive contact model for spherical particles is proposed. Plastic deformation of contacts during loading and elastic unloading, accompanied by adhesion are considered, for which the pull-off force increases with plastic deformation. Considering the collision of a spherical cohesive body with a rigid flat target, the critical sticking velocity and coefficient of restitution in the proposed model are found to be very similar to those of Thornton and Ning’s model. Sensitivity analyses of the model parameters such as plastic, elastic, plastic-adhesive stiffnesses and pull-off force on work of compaction are carried out. It is found that by increasing the ratio of elastic to plastic stiffness, the plastic component of the total work increases and the elastic component decreases. By increasing the interface energy, the plastic work increases, but the elastic work does not change. The model can be used to efficiently represent the force-displacement of a wide range of particles, thus enabling fast numerical simulations of particle assemblies by the DEM.     

Adhesive forces significantly affect elastic modulus determination of soft polymeric materials in nanoindentation

The present study investigated the effects of adhesion on the elastic modulus determined from nanoindentation curves for soft polydimethylsiloxane (PDMS) elastomers with five different crosslink concentrations. Indentation load-displacement curves were obtained for samples of all concentrations at four different peak loads. All load-displacement curves were nearly linear, resulting in load independent contact stiffnesses (p < 0.003) for the range of loads tested. As a result, elastic modulus calculated from nanoindentation curves with the Hertz contact model exhibited significant differences (p < 0.004) both at different peak loads for a single PDMS concentration and between different PDMS concentrations at a single peak load (p < 0.001). The differences for different peak loads were attributed to the presence of substantial adhesive forces at the tip-sample interface. By taking these adhesive interactions into account with the Johnson, Kendall, Roberts (JKR) contact model, the differences in elastic modulus at different peak loads could be reconciled. Significant differences (p < 0.001) in moduli between different PDMS concentrations were still present. The results highlight the importance of considering adhesive forces in nanoindentation analyses of low modulus polymeric materials.     

Mechanical compliance of photolithographically defined vertically aligned carbon nanotube turf

We describe the micro-mechanical properties of vertically aligned carbon nanotubes (VACNTs) fabricated using a photolithographically patterned iron catalyst prepared using sol–gel techniques. The carbon nanotubes (CNTs) were grown via chemical vapor deposition. The relative mechanical stiffness of the resultant structure was measured using nanoindentation based techniques and is shown to be related to the number of contact sites between tubes. Elastic deformation occurs during compression at large strains, however energy is dissipated during deformation, likely through tube–tube interactions. The effective elastic modulii are depth dependent, due to the compression of pre-buckled geometries. The effective elastic modulii range between 0.03 and 0.08 GPa for a low number of contact sites and 0.1 and 0.3 GPa for a high number of contact sites.     

Mechanical properties of multilayered films using different nanoindenters

The effects of interface, contact hardness, deformation, and adhesion of Al/Ni multilayered films under nanoindentation were investigated using molecular dynamics (MD) simulations. The results show that the indentation force of the sphere indenter is the largest among nanoindentations using sphere, cone, Vickers, or Berkovich type indenters at the same penetration depth. Force increasing, relaxation and adhesion took place during loading, holding depth and unloading, respectively. The interface occurred along the {111} (110) slip systems and the maximum width of the glide bands was about 1 nm. The reaction force and plastic energy of the indented films are also discussed.     

基于纳米压痕法的羟基磷灰石/聚乳酸复合材料力学性能表征

采用准静态和动态纳米压痕技术研究了羟基磷灰石/聚乳酸（HA/PLA）复合材料在微纳尺度的表面力学性能。在静态模式下研究了保载和卸载时间对模量和硬度测试结果的影响。结果发现,当保载时间小于45 s时,由于蠕变使保载和卸载时间对测试结果产生显著影响;保载时间短且卸载时间长时,在卸载段会形成"鼻子",为了避免"鼻子"选择保载时间为45 s。在动态模式下研究了材料的动态力学性能,结果表明,存储模量和硬度均随着压入深度的增加而减小。压痕和划痕实验结果均表明：HA显著提高了PLA的力学性能,与纯PLA相比,9wt% HA/PLA复合材料的模量增加了35.5%,硬度增加了44.7%,蠕变深度下降了9.5%,相同载荷下的最大划痕深度和残余深度均小于纯PLA,表现出良好的弹性恢复能力和抗变形能力。     

Quantitative characterization of carbon nanotube turf topology by SEM analysis

A procedure has been developed to quantify various parameters that affect the mechanical stiffness of vertically aligned multi-walled carbon nanotube turfs from secondary electron images. A representative measure of density, tortuosity, and path connectedness is obtained from the images as these parameters are presumed to correlate with measured properties for this class of materials. Elastic moduli were determined using nanoindentation techniques. Experimental evidence indicates that an increase in turf density does not necessarily result in an increase in elastic modulus. Six turfs analyzed in this work along with four additional structures selected from a previous publication support the conclusion that an increase in density is not necessarily responsible for an increase in mechanical stiffness of a turf. Tortuosity and path connectedness tend to show more of a correlation with stiffness, though no direct correlation with these parameters was identified.     

On the measurements of viscoelastic functions of a sphere by nanoindentation

Nanoindentation using such instruments as instrumented nanoindenter and scanning probe microscope is effective for measurements of viscoelastic functions of a sphere in micron or sub-micron scale. In this paper, we provide methods for nanoindentation measurements of linearly viscoelastic functions in both time- and frequency-domains for a viscoelastic sphere under small deformations. In the time-domain, both relaxation and creep functions are determined from three types of loading histories, namely constant-rate loading, ramp loading, and step loading. In the frequency-domain, methods are given for the calculation of complex modulus, or complex compliance under a small amplitude of sinusoidal load superimposed on a carrier load. The effects of the radius of the viscoelastic sphere relative to the indenter tip radius, as well as the deformation of the sphere induced by contact with the flat substrate supporting the sphere are discussed.     

Self-sensing and dispersive evaluation of single carbon fiber/carbon nanotube (CNT)-epoxy composites using electro-micromechanical technique and nondestructive acoustic emission

Self-sensing and interfacial evaluation were investigated with different dispersion solvents for single carbon fiber/carbon nanotube (CNT)-epoxy composites by electro-micromechanical technique and acoustic emission (AE) under loading/subsequent unloading. The optimized dispersion procedure was set up to obtain improved mechanical and electrical properties. Apparent modulus and electrical contact resistivity for CNT-epoxy composites were correlated with different dispersion solvents for CNT. CNT-epoxy composites using good dispersion solvents exhibited a higher apparent modulus because of better stress transferring effects due to the relatively uniform dispersion of CNT in epoxy and enhanced interfacial adhesion between CNT and the epoxy matrix. However, good solvents exhibited a higher apparent modulus but lower thermodynamic work of adhesion, W_a for single carbon microfiber/CNT-epoxy composite. It is attributed to the fact that hydrophobic behavior with high advanced contact angle was observed for CNT-epoxy in the good solvent, which might not be compatible well with the carbon microfiber. Damage sensing was also detected simultaneously using AE combined with electrical resistance measurement. Electrical resistivity increased stepwise with progressing fiber fracture due to the decrease in electrical contact by the CNT.     

一种钠钙硅酸盐玻璃的纳米压痕测试分析

采用纳米压痕测试技术对一种钠钙硅酸盐玻璃进行微观力学性能的测试分析.测得加载-卸载过程载荷与压入深度曲线,发现被测玻璃的最大压深、残余深度和弹性回复量随最大加载力的增加而增大,但其相对弹性回复率系数基本稳定,平均值为58.2%.通过电子显微镜观察了不同最大载荷下的压痕形貌,发现压痕区域出现了边界沉陷现象.当最大加载力为1 000 mN左右时,三棱锥工具头测试的压痕区域出现了较明显的微裂纹;采用四棱锥工具头时出现微裂纹的最大加载力要小于该值,且裂纹取向均与金刚石工具头的棱角取向一致.利用非线性有限元软件MSC.Marc对纳米压痕过程进行了仿真分析,得到载荷与压入深度的仿真曲线,该曲线与试验结果基本相符;分析了载荷作用下材料内部的应力分布.利用Oliver-Pharr模型得到不同压入深度下被测玻璃的接触刚度值,该值随压入深度的增加而增大.     

Influence of friction and adhesion on the onset of plasticity during normal loading of spherical contacts

Increasing contact loading causes early transformation from elastic to elastic–plastic deformations in many conventional systems as well as micro/nano-electro-mechanical systems. The load required for yielding and the location of the onset of plasticity is critical in the robustness of systems with contacts. For frictionless (such as fully-lubricated) contacts, inception of plastic yielding occurs beneath the contact surface. However, frictional slip (contact shear) and adhesion push the inception of plastic yielding toward the contact surface. The influence of elastic mismatch, shear tractions and adhesive normal tractions on the subsurface stress field is studied analytically by superposition of the Hertzian stress field and the stress field created by the shear and additional (due to adhesion) normal tractions. Specifically, three contact conditions have been studied in this work: (i) frictionless, (ii) finite friction, and (iii) infinite friction (full stick). Also, a finite-element model is developed to verify certain assumptions in the analytical solution for the contact with finite friction. The results obtained are applied to two sets of in situ nanoindentation experiments to explain the change in the yielding behavior of submicrometer polycrystalline aluminum grains.     

Indenter surface area and hardness determination by means of a FEM-supported simulation of nanoindentation

Stress–strain curves are obtained through a finite element method (FEM) simulation of nanoindentation, and the actual indenter tip geometry is determined by additional experimental and FEM-based procedures. Based on such material stress–strain laws and on the actual indenter tip geometry, the following are determined employing the “HANI” algorithm (HArdness determination by means of a FEM-based simulation of NanoIndentation): first, the contact surface due to elastic and plastic deformations during the loading phase of nanoindentation; second the occurring impression geometry after unloading and finally the related hardness values after Martens, Vickers, etc.Moreover, the indenter surface area functions of Vickers and Berkovich indenters are determined experimentally/analytically, by nanoindentations on Si(100) reference material of known Martens hardness. Applying these functions, Martens and Vickers hardness are determined correspondingly for various materials and they are compared to hardness values obtained by the “HANI” algorithm. Significant deviations occur, if the hardness of the reference material is quite different than the hardness of the test pieces.     

On elastic nanoindentation of coated half-spaces by point indenters of non-ideal shapes

The elastic contact of non-ideal conical and Berkovich indenters with bi-layer half-spaces is investigated. Blunted tips are simulated as smooth surfaces. The boundary element method is employed to carry out the numerical simulations of nanoindentation. An analytical analysis of the influence of the coating thickness and the tip bluntness magnitude on the nanoindentation loading curve is realized. The dimensionless compression force is introduced in order to describe the nanoindentation at different approaches between the indenter and the coated half-space. A practical technique for determining the Young's modulus of coatings is proposed. The technique is based on the modelling of indentation of the blunted indenter tip into the coating/substrate composite. This technique is applied to the nanoindentation study of nanocrystalline Cr?coatings on silicon and glass substrates being tested by a diamond Berkovich indenter with a blunted tip.     

Simulation of Adhesive–Dissipative Behavior of a Microparticle Under the Oblique Impact

The adhesive–dissipative behavior of a microparticle under the oblique impact is investigated numerically and the new discrete element method (DEM)-compatible interaction model is elaborated. The modeling approach is based on the Derjaguin–Muller–Toporov model of normal interaction for the adhesive elastic contact. Adhesion hysteresis is specified by the loss of the kinetic energy governed by the fixed amount of the adhesion work, required to separate two adhesive contacting surfaces. This effect is captured in the new interaction model by adding an additional dissipative force component to normal contact during unloading and detachment. The essential feature of this approach, differing from that of the viscous damping model, is that, according to the proposed method, the amount of the dissipated energy is not influenced by the actual initial velocity during the entire contact. The influence of adhesion on slip friction is reflected by considering the adhesive normal force components in the Coulomb's law of friction. The contribution of the adhesion-related dissipation is illustrated by a comparison of the behavior of the attractive–dissipative and attractive–non-dissipative models. The oblique impact of a microparticle on the plane surface at the intermediate impact angle is also investigated numerically. The link between adhesion and friction is supported by the numerical results.     

Fracture mechanics analysis of asperity cracking due to adhesive normal contact

A two-dimensional linear-elastic fracture mechanics analysis of asperity cracking induced by adhesive normal contact was performed with the finite element method. Normal contact between two elastic asperities was analyzed with the equivalent contact system of an elastic asperity with equivalent radius of curvature and effective elastic modulus compressed by a rigid plane. Surface adhesion was modeled by nonlinear springs obeying a constitutive force-distance law derived from the Lennard–Jones potential. The maximum ranges of the tensile and shear stress intensity factors were used to determine the crack-growth direction and the dominant mode of asperity fracture in terms of the Maugis parameter (a function of the equivalent radius of curvature, work of adhesion, effective elastic modulus, and intermolecular equilibrium distance), friction coefficient at the crack interface, maximum surface interference, and crack position. Finite element simulation results indicate that the direction and the rate of crack growth are mostly affected by the Maugis parameter and the maximum surface interference. A transition from shear to tensile dominant mode of crack growth is encountered with the increase of the Maugis parameter and/or the decrease of the maximum surface interference. Opening, slip, and stick between the crack faces during loading and unloading are discussed in the context of crack mechanism maps.     

Inherent sensing and interfacial evaluation of carbon nanofiber and nanotube/epoxy composites using electrical resistance measurement and micromechanical technique

Inherent sensing of load, micro-damage and stress transferring effects were evaluated for carbon nanotube (CNT) and carbon nanofiber (CNF)/epoxy composites (with various added contents) by an electro-micromechanical technique, using the four-point probe method. Carbon black (CB)/epoxy composites, with conventional nanosize material added, were used for the comparison with CNT and CNF composites. Subsequent fracture of the carbon fiber in the dual matrix composites (DMC) was detected by acoustic emission (AE) and by the change in electrical resistance, ΔR due to electrical contacts of neighboring CNMs. Stress/strain sensing of the nanocomposites was detected by an electro-pullout test under uniform cyclic loading/subsequent unloading. CNT/epoxy composites showed the best sensitivity to fiber fracture, matrix deformation and stress/strain sensing, whereas CB/epoxy composite exhibited poorer sensitivity. From the apparent modulus (as a result of matrix modulus and interfacial adhesion), the stress transferring effects reinforced by CNT was highest among three CNMs. The thermodynamic work of adhesion, W_a as found by dynamic contact angle measurements of the CNT/epoxy composite as a function of added CNT content was correlated and found to be consistent with the apparent mechanical modulus. Uniform dispersion and interfacial adhesion appear to be key factors for improving both sensing and mechanical performance of nanocomposite. Thermally treated-CNF composites exhibited a slightly higher apparent modulus, whereas higher testing temperatures appeared to lower the apparent modulus.     

A critical appraisal of the nanoindentation creep 'nose' effect in Ni thin films

The creep behaviour of polycrystal Ni thin films under the same maximum load (Pmax = 8000 microN) and different unloading periods (ranging from 1 to 250 s) has been investigated at room temperature using nanoindentation tests. A 'nose' has been observed in the unloading segment of the load-penetration depth curve when the holding time at peak load is short and/or the unloading rate is small, and when the peak load is sufficient high. When a 'nose' presents, the apparent unloading stiffness Su, defined as dP/dh, is negative, and the reduced modulus can no longer be calculated from the Oliver-Pharr method. Taking such uncertainties into account, a critical appraisal is proposed for ranking creep propensities exhibited during nanoindentation under specified conditions.     

A New Model Developed to Evaluate the Contact Area Arising During Nano-indentation Tests With Pileup Behavior of Metal Materials

A new mechanical model is developed in this paper for metal materials to investigate the behavior arising during the loading/unloading process of an indentation test. Two governing differential equations are derived for the depth solution of the indenter tip and the depth solution formed at the separation point, expressed in a power form. All spring/block and damping coefficients shown in these governing differential equations associated with the elastic/plastic and viscous behaviors are determined by the real-coded genetic algorithm. With the aid of experimental results of the depth at the indenter tip shown at large and small indentation depths, aluminum and steel were used as two examples of soft materials in this paper. The pileup behavior is implicitly included in the evaluation of the contact projected area (A) in the present model. A significant difference in is caused if the pileup is not considered in the model. Under a constant maximum load, the contact area is slightly increased by decreasing the loading/unloading rate.     

Determination of the young modulus from elastic section of the Berkovich indenter loading curve

A new procedure for the determination of a local elastic modulus is suggested, which is based on the comparison between the nanoindentation data and the results of a numerical modelling of the contact interaction in the indenter-sample system. An image of an indent of the Berkovich indenter in a material with a low elastic recovery have been obtained by atomic force microscopy and the geometry of an equivalent indenter in the form of a body of revolution required for the adequate setting of a model contact problem have been defined. A procedure for the determination of the Young modulus by solving the inverse problem of the theory of elasticity from the condition of the best correlation between the experimental and calculated loading curves has been suggested. The data reported in the paper show that the taking into account of the real tip shape of the Berkovich indenter allows more precision measurements of the elastic modulus in nanoindentation as compared with other methods.     

Hertzian analysis of the self-consistency and reliability of the indentation hardness measurements on superhard nanocomposite coatings

The measurement of elastic properties of superhard nanocomposite coatings can be subject to a number of possible errors, such as indentation size effects (indenter tip blunting, non-representative small volume of the material to be tested upon nanoindentation and a too small stress under the indenter which does not reach the yield stress of that material if a too low load is used), the composite effect of the system of superhard coating on a softer substrate, high compressive or tensile stress in the coatings, drifts and/or stiffness of the indenter etc. We shall present a systematic study of these possible artefacts on superhard coatings using a large range of applied loads on a number of super- and ultrahard samples. The hardness values obtained from the indentation measurements are compared with the Vickers hardness calculated from the projected area of the plastic deformation. The data will be also compared with finite element method computer modeling in order to obtain a deeper insight into the complex problems. It will be shown that reliable results can be obtained if sufficiently thick coatings are used which allows one to obtain load independent values of hardness measured at sufficiently large indentation depths. Hertzian analysis of the non-linear elastic response upon unloading provides analytical solutions that can be used in order to check if the hardness values measured on the super- and ultrahard coatings are self-consistent. In particular, it is possible to estimate the maximum tensile stress that the coatings survive without failure. This stress occurs at the periphery of the contact between the coating and the indenter and, in the case of ultrahard coatings, it can reach values in the range of tens of GPa. The results show a very good agreement with the theoretical predictions based on the Universal Binding Energy Relation.