Nanoindentation hardness measurements using real-shape indenters: application to extremely hard and elastic materials

We study the technique of nanoindentation hardness measurement applied to extremely hard and elastic thin films. We do the study with the aid of Hertz’s solutions for elastic contacts. The effect of different apical angles in ideally sharp conical diamond indenters is analyzed. In addition, the blunt tip shape of practical diamond indenters is discussed. The area function of the tip of real indenters is deduced from experimental nanoindentation measurements performed with these indenters on fused quartz. Triangular-base pyramidal indenters with Berkovich and cube corner geometries are considered. Theoretical hardness values applying Hertz’s and Oliver and Pharr’s methods of analysis are obtained and compared with the experimental data deduced from nanoindentation measurements performed on very hard and elastic ta-C films. The theoretical analysis shows a necessary dependence of the calculated hardness values with the apical angle of the indenter in totally elastic materials and to some extent in elastoplastic materials. Moreover, when the indenter tip is blunt or when there are inaccuracies in the measured area function of the indenter tip, hardness values decrease for very small penetration depths. Besides, in these films, because of their very small thickness, measured hardness values also decrease for measurements with penetration depths larger than a fraction of film thickness, due to the effects of the softer substrate. Received: 13 June 2000 / Accepted: 21 June 2000 / Published online: 5 October 2000     

Effect of indenter-radius size on Au(001) nanoindentation

We address the question of whether results obtained for small indenters scale to indenter sizes in the experimental range. The quasicontinuum method is used in order to extend the computational cell size to 2x2x1 micro m(3), nominally containing of order 2.5x10(11) atoms, and in order to permit consideration of indenter radii in the range 70-700 A. The dislocation structures for the large indenter are found to be less sharp and to extend over a larger region than for the small indenter. In addition, the large-indenter force-displacement curve differs from that corresponding to the small indenter in one important respect, namely, the absence of force drops during indentation, despite profuse dislocation activity. Based on these observations, we conclude that the indenter force is not a reliable indicator of the onset of dislocation activity and plastic deformation for indenter sizes in the experimental range.     

Molecular dynamics study of the mechanical characteristics of Ni/Cu bilayer using nanoindentation

<正>In the present work,a three-dimensional molecular dynamics simulation is carried out to perform the nanoindentation experiment on Ni single crystal.The substrate indenter system is modeled using hybrid interatomic potentials including the many-body potential embedded atom method(EAM),and two-body morse potential.To simulate the indentation process,a spherical indenter(diameter = 80 A,1 A=0.1 nm) is chosen.The results show that the mechanical behaviour of a monolithic Ni is not affected by crystalline orientation.To elucidate the effect of a heterogeneous interface, three bilayer interface systems are constructed,namely Ni(100)/Cu(111),Ni(110)/Cu(111),and Ni(111)/Cu(111).The simulations along these systems clearly describe that mechanical behaviour directly depends on the lattice mismatch. The interface with the smaller mismatch between the specified crystal planes is proved to be harder and vice versa.To describe the relationship between film thickness and interface effect,we choose various values of film thickness ranging from 20 A to 50 A to perform the nanoindentation experiment.It is observed that the interface is significant only for the relatively small thickness of film and the separation between interface and the indenter tip.It is shown that with the increase in film thickness,the mechanical behaviour of the film shifts more toward that of monolithic material.     

利用分子动力学方法铁素体-渗碳体相界面效应探究

珠光体是十分重要的组织结构,因此本文构建了含铁素体-渗碳体相界面的模型,并采用分子动力学模拟方法模拟纳米压入的过程。通过对模拟结果的力学性能和组织结构分析,探究了铁素体-渗碳体相界面效应。研究发现,距铁素体-渗碳体晶界不同距离（位置压入）,在压入最初阶段,压头载荷随着压头与晶界距离的增大而增大,当压入深度达到一定深度后,载荷随着距离的增大而减小。杨氏模量和最大剪切模量受压头尖端下方原子结构的直接影响,硬度受到结构完整性和类型的共同影响。铁素体-渗碳体相界面影响了纳米压入过程中位错形核、增殖和扩展,宏观表现为在相同压入深度下,不同压入位置压头载荷的差异。     

球形压头与单晶铝材料纳米接触过程的多尺度分析

采用准连续介质多尺度理论及排斥力场函数, 建立了刚性球形压头与单晶铝材料表面纳米接触与脱离过程的跨尺度分析模型, 得到载荷-位移响应曲线、原子变化状态图及位移云纹图. 研究了接触与脱离过程中单晶铝材料微观变形时原子的排列情况以及压 头形状对位错的形核和发射产生的影响. 从微观角度分析了接触变形机理. 结果表明, 随着接触深度的增加, 球形压头下部两侧的原子受力方向不断变化, 使得载荷-位移响应曲线出现不同于方形压头的阶梯状. 由于压头形状的影响, 压头两侧的密排原子面实现部分滑移形成了肖克利不完全位错. 脱离过程中, 原子紧贴压头向上移动, 实现部分弹性恢复, 残余位移为0.3 nm, 非常接近单晶铝单位位错的伯格斯矢量的 模0.285 nm. 关键词： 准连续介质法 球形压头 单晶铝材料 位错     

The hardening and loss of strength of thin surface layers of LiF monocrystals and zirconium ceramics under conditions of cyclic nanoindenting

Low-cycle surface fatigue is still relatively poorly investigated, especially in the case of accumulation of surface fractures during nanocontact interactions between solids. A new technique of modeling fatigue during a short nanocontact interaction based on repeated dynamic nanoindenting is proposed. The results of investigation of model LiF crystals and industrial ZrO₂ ceramics show that, at a small number of cycles N of about 20, the material is hardened under the indenter. As N increases, the hardening is replaced by a loss of strength reflected in the formation and growth of microcracks.     

Quadrupole field in hairpin-type cathode gun and mechanism of axial-astigmatism production

Mechanism of axial astigmatism production in the hairpin-type cathode gun was investigated by numerical calculation. The electrostatic potential in the gun was first decomposed into the axially symmetric and quadrupole components, and then the trajectory behavior was investigated by the generalized trajectory method. The axial astigmatism of the hairpin-type cathode gun was found to depend strongly on the Wehnelt voltage; it is small as long as the Wehnelt voltage is close to cutoff condition but starts to increase rapidly when the drive voltage exceeds a certain threshold. The reason for a negligible axial astigmatism at or close to the cutoff lies in the mutual dependence of the tip electric field intensity and the quadrupole field strength near the cathode. The tip quadrupole field strength is given by the product of the tip field intensity and the difference in the cathode curvature in the two orthogonal cross sections. A negligible axial astigmatism of the hairpin-type cathode gun in usual operations is due to a small quadrupole field close to the cutoff condition where the tip field is weak.     

Reverse analysis in depth-sensing indentation for evaluation of the Young's modulus of thin films

This paper presents an approach to reverse analysis in depth-sensing indentation of composite film/substrate materials, which makes use of numerical simulation. This methodology allows the results of experimental hardness tests, acquired with pyramidal indenter geometry, to be used to determine the Young's modulus of thin film materials. Forward and reverse analyses were performing using three-dimensional numerical simulations of pyramidal and flat punch indentation tests to determine the Young's modulus of the thin films. The pyramidal indenter used in the numerical simulations takes into account the presence of the most common imperfection of the tip, so-called offset. The contact friction between the Vickers indenter and the deformable body is also considered. The forward analysis uses fictitious composite materials with different relationships between the values of the Young's modulus of the film and substrate. The proposed reverse analysis procedure provides a unique value for the film's Young's modulus. Depending on material properties, the value of the Young's modulus of the film can be more or less sensitive to the scatter of the experimental results obtained using the depth-sensing equipment. The validity of the proposed reverse analysis method is checked using four real cases of composite materials.     

Effect of scratching speed on deformation of soda–lime–silica glass

The grinding and polishing of a fundamentally brittle material like glass to an utmost precision level for ultra-sophisticated applications ranging from mobile devices to aerospace as well as space shuttle components to biomedical appliances pose a big challenge today. Looking simplistically, the grinding and polishing processes are basically material removal by multiple scratching at a given speed. Unfortunately however, the role of the scratching speed in affecting the material removal mechanism in soda–lime–silica (SLS) glass is yet to be comprehensively understood. Therefore, the present work explores the surface and subsurface deformation mechanisms of SLS glass scratched under a normal load of 5 N at various speeds in the range of 100–1000 μm?s^?1 with a diamond indenter of ～200 μm tip radius. The results show important roles of the time of contact, the tensile stress behind the indenter and the shear stress just beneath the indenter in governing the material removal mechanisms of the SLS glass.     

Tip‐heating‐assisted Raman spectroscopy at elevated temperatures

We demonstrate tip‐heating‐assisted enhanced Raman spectroscopy to investigate the temperature dependence of the carbon nanotube G‐band with nanoscale resolution. The controllable and nanoscale heat generated at the tip apex was used to thermally perturb and characterize a small volume in a carbon nanotube sample that is precisely positioned underneath the tip. The dependence of tip enhancement with temperature was also experimentally examined, which is in good agreement with the enhancement calculated from the electromagnetic model of isolated spheroids. The technique presented may open up opportunities in the study of controlled heat‐assisted biochemical reactions and physical transformations of nanostructures. It can also be used for thermal characterization of various materials requiring site‐selective and controllable nanoscale heat source and could enable the realization of new photothermal devices. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical simulation of micro-scratch tests for coating/substrate composites

In this paper the micro-scratch test is simulated by ANSYS finite element code for thin hard coating on substrate composite material system. Coulomb friction between indenter and material surface is considered. The material elastic-plastic properties are taken into account. Contact elements are used to simulate the frictional contact between indenter and material surfaces, as well as the frictional contact after the detachment of coating/substrate interfaces has taken place. In the case of coating/substrate interfaces being perfectly bonded, the distributions of interfacial normal stress and shear stress are obtained for the material system subjected to normal and tangential loading. In the case of considering the detachment of interfaces, the length of interfacial detachment and the redistribution of stresses because of interfacial detachments are obtained. The influences of different frictional coefficients and different indenter moving distances on the distributions of stresses and displacements are studied. In the simulation, the interfacial adhesion shear strength is considered as a main adhesion parameter of coating/substrate interfaces. The critical normal loading from scratch tests are directly related to interfacial adhesion shear strengths. Using the critical normal loading known from experiments, the interfacial adhesion shear strength is obtained from the calculation. When the interfacial adhesion shear strength is known, the critical normal loading is obtained for different coating thicknesses. The numerical results are compared with the experimental values for composite materials of thin TiN coating on stainless steel substrate.     

Size effects and stochastic behavior of nanoindentation pop in

A statistical model for pop in initiated at preexisting dislocations during nanoindentation is developed to explain size-dependent pop-in stresses. To verify theoretical predictions of this model, experiments were performed on single-crystal Mo, utilizing indenter radii that vary by over 3 orders of magnitude. The stress where plastic deformation begins ranges from the theoretical strength in small volumes, to 1 order of magnitude lower in larger volumes. An intermediate regime shows wide variability in the stress to initiate plastic deformation. Our theory accurately reproduces the experimental cumulative probability distributions, and predicts a scaling behavior that matches experimental behavior.     

Indenter size effect on the reversible incipient plasticity of Al(001) surface:Quasicontinuum study

Indenter size effect on the reversible incipient plasticity of Al(001) surface is studied by quasicontinuum simulations.Results show that the incipient plasticity under small indenter, the radius of which is less than ten nanometers, is dominated by a simple planar fault defect that can be fully removed after withdrawal of the indenter; otherwise, irreversible incipient plastic deformation driven by a complex dislocation activity is preferred, and the debris of deformation twins, dislocations,and stacking fault ribbons still remain beneath the surface when the indenter has been completely retracted. Based on stress distributions calculated at an atomic level, the reason why the dislocation burst instead of a simple fault ribbon is observed under a large indenter is the release of the intensely accumulated shear stress. Finally, the critical load analysis implies that there exists a reversible-irreversible transition of incipient plasticity induced by indenter size. Our findings provide a further insight into the incipient surface plasticity of face-centered-cubic metals in nano-sized contact issues.     

Kinetic features of the deformation of solids in nano-and microscopic volumes

The deformation dynamics of nanovolumes in crystalline, quasicrystalline, and amorphous solids is studied experimentally using continuous nanoindentation with a resolution of 0.1 nm. The elastic limits of some materials are determined in a nanocontact region. A jumplike transition to a plastic flow (which is equivalent to a drop in yield in uniaxial macroscopic tests) is revealed and studied. The dynamics and statistics of an unstable plastic flow in strain-aging alloys are analyzed. The specific features of a local stress-strain curve associated with a phase transformation under an indenter and with microcrack nucleation are revealed. The load-carrying ability of a material upon nanocontact loading is shown to be many times its macroscopic yield strength and to approach the theoretical ultimate strength even in plastic materials. The relaxation processes occurring in submicrovolumes after unloading are found to induce an elastic aftereffect that is much larger than that in macroscopic tests. In Si and Ge single crystals, the effect of a jumplike increase in the cracking resistance with the strain rate is detected.     

Deformation and fracture of TiN coating on a Si(1 1 1) substrate during nanoindentation

The deformation mechanisms and fracture behavior of TiN coating on a Si(111) substrate, deposited using magnetron sputtering Ti target, is characterized by nanoindentation experiments. The morphologies of the indentations are revealed by scanning electron microscopy, coupled with in situ atomic force microscopy in nanoindentation experiments. The results show that permanent trigonal impressions and radial plastic grooves are confined within the contact regions even though the peak indenter displacement increases to 1500 nm. Local cracks of TiN appear around the indent marks making the edges of the indentations irregular. The cracks increase with an increase of the indenter displacement until the indenter arrives at (or approaches) the Si(1 1 1) substrate at a critical displacement. As the peak indenter displacement increases to 2500 nm, an interfacial fracture between the TiN coating and the Si(1 1 1) substrate is observed using both scanning electron microscopy micrograph and in situ atomic force microscopy images. The diameter of the interfacial fracture determined by scanning electron microscopy micrographs is more accurate than that determined by in situ atomic force microscopy images in nanoindentation experiments. The failure mechanism of the TiN coating is also investigated by means of a standard nanoscratch test.     

Nondislocation plasticity and its role in the mass transfer and formation of the indentation under dynamic conditions

The share of nondislocation plasticity in the process of mass transfer from under the indenter is determined by a novel method of dynamical indentation for a number of ionic, semiconducting, and metallic materials.     

A determination of the rate and heat of evaporation by measuring the radius variations of a metal tip

A new material loss technique for the experimental determination of the free evaporation rate of a metal is presented. This technique is based on the study of tip profile changes. The tip radius variation is a consequence of the simultaneous action of free evaporation and surface self-diffusion. The rate of free evaporation is related to the tip radius evolution, so the vapor pressure and heat of evaporation can be determined by measuring in situ the radius changes with time. The method permits an easy control of the cleanliness of the surface by field electron microscopy, and should enable one to study the influence of adsorption on evaporation. The method is tested with molybdenum tips. The variation of the radius of the tips, heated in ultra-high vacuum, is determined by field electron and scanning microscope measurements. Vapor pressures and heat of evaporation values obtained are in agreement with values obtained by other techniques.     

光学元件亚表层裂纹成核临界条件研究

基于压痕实验和连续刚度测量法得到了熔石英材料硬度和弹性模量随压入深度的变化曲线, 系统分析了材料由延性到脆性转变的过程, 确定了熔石英晶体在静态/准静态印压和动态刻划时产生裂纹的临界载荷和临界深度。渐变载荷刻划实验结果表明, 划痕过程诱发的裂纹对法向载荷有很强的依赖性, 载荷较小时材料去除方式为延性域去除。随着法向载荷的增加, 首先产生垂直于试件表面的中位裂纹和平行于试件表面方向扩展的侧向裂纹, 而在试件表面上并没有产生明显的特征。载荷进一步增加后, 侧向裂纹扩展并形成了明亮区域, 最终诱发了沿垂直于或近似垂直于压头运动方向扩展的径向裂纹, 实现了材料的脆性去除。     

Phase transitions in a nonuniformly stressed state of matter

The nucleation of a new phase of a substance in a nonuniform stress field created during measurements of rigidity is considered. The phase diagram of silicon containing the Si I, II, and V phases are considered. The high-pressure boundaries of the phases formed near the indenter are found using the finite elements method.     

Ion current generation in the field ion microscope: I. dynamic approach

The numbers of gas particles arriving at unit tip surface in unit time from a field free region are derived as functions of velocity components for a spherical tip. It is shown that a considerable fraction of the gas particles arrives at the tip having large tangential velocities. The simple model of collision of a particle with a metal surface is used and the trajectories and rebounds of particles are tracked. The principal method to calculate the total ion current is shown. The capture probability of particles by the dipole attraction potential is shown to increase when the tip temperature is lowered, the field strength is increased, the mass ratio of the gas atom to the metal atom increases and the gas temperature is lowered.