Evaluation the effect of aspect ratio for Young’s modulus of nanobelt using finite element method

The traditional nanoindentation method provides experimental data for the calibrating mechanical parameters of nanobelt through semi-empirical formulae. In this paper, a technique to identify Young’s modulus of nanobelts with different aspect ratios is introduced combining finite element method (FEM) and nanoindentation test. For the nanobelt on the substrate, the power function relationship is used to describe the loading curve of the nanobelt indentation behavior. The loading curve exponent of the power function which is the fitting parameter can reflect the influence of aspect ratio of nanobelt on Young’s modulus of nanobelts as well as the maximum indentation load. In the forward analysis, considering the substrate effect and the size effect, the numerical loading responses are simulated at the appropriate penetration depth, and then the dimensionless equations between the parameters characterizing the indentation loading curve and the properties of nanobelt/substrate system can be established via extensive FEM simulation. In the reverse analysis, the nanoindentation tests were performed on ZnO and ZnS nanobelts, and the experimental indentation loading curves can be fitted as power function. The maximum indentation loads and the loading curve exponents are extracted from two experimental loading curves, and then they are substituted into the dimensionless equations to solve the Young’s moduli of ZnO and ZnS nanobelts. The results show the Young’s moduli solved are close to previous values, indicating that the Young’s moduli are reasonable. This developed method is effective to identify the Young’s modulus of nanobelt and it can be applied to identify the Young’s modulus of other nanobelts in practice.     

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.     

Tip-radius effect in finite element modeling of sub-50 nm shallow nanoindentation

An accurate representation of the indenter geometry is essential for correct finite element simulations of shallow indentations of less than 50 nm using a 90° cube-corner indenter. A nonlinear regression method for estimating the tip radius of an indenter is presented, which takes into account that initially the contact is only with the spherical surface of the tip and subsequently also includes contact with the equivalent conical surface. The tip radius of a Berkovich indenter is estimated by a finite element modeling (FEM) best-fitting method. Using the estimates of tip radii, the yield strength of gold in the film of a gold/silicon system was estimated from the best fit between FEM simulations and nanoindentation experiments using the 90° cube corner indenter, which compared favorably with an FEM simulation and nanoindentation data using a Berkovich indenter.     

Effect of surface roughness on nanoindentation test of thin films

By using the two-dimensional quasicontinuum method, the nanoindentation process on a single crystal copper thin film with surface roughness is simulated to study the effect of surface morphology on the measurements of mechanical parameters. The nanohardness and elastic modulus are calculated according to Oliver-Pharr’s method. The obtained results show a good agreement with relevant theoretical and experimental results. It is found that surface roughness has a significant influence on both the nanohardness and elastic modulus of thin films determined from nanoindentation tests. The effect of such factors as the indenter size, indentation depth and surface morphology are also examined. To rule out the influence of surface morphology, the indentation depth should be much greater than the characteristic size of surface roughness and a reasonable indenter size should be chosen. This study is helpful for identifying the mechanical parameters of rough thin films by nanoindentation test and designing nanoindentation experiments.     

Thin film hardness determination using indentation loading curve modelling

A methodology for determining the thin film hardness from a microindentation loading curve is proposed. The loading curve is modelled to compute the dynamic Martens hardness using the indentation depth reached during the test. Moreover, the indentation size effect is taken into account by applying the strain gradient plasticity theory. Then, the dynamic Martens hardness and the hardness length-scale factor are used to express the applied load as a function of the indentation depth. The proposed model involves three parameters: (i) the dynamic Martens macro-hardness, equivalent to the hardness obtained for an infinite applied load, (ii) the hardness length-scale factor, which represents the material resistance to plastic deformation under indentation and (iii) a corrective load, considering the rounded tip effect of the indenter and the zero shift. The model is validated on a 316L stainless steel which subsequently is used as a substrate material for two different Diamond Like-Carbon thin films. The coated systems involved both a hydrogen-free mostly amorphous carbon-chromium (a-C) film of ∼ 2.6 μm in thickness and a hydrogenated, amorphous carbon (a-C:H) solid lubricant of ∼ 2 μm.     

Adsorbed multilayer effects on the mechanical properties in nanometer indentation depth

Nanoindentation is a powerful technique for determining the mechanical properties of a material at the nanometer scale. In this study, the changes induced in the mechanical properties of a thin film by the presence of adsorbed multilayers are examined by performing nanoindentation tests with ultra-low indentation depths. The current findings suggest that the results obtained for the mechanical properties of thin films under nanoindentation will be overestimated if the effects of the adsorbed multilayers on reducing elastic recovery between the indenter and the substrate are not taken into consideration.     

平头压头下基体对压痕规律的影响研究

本文通过对软薄膜/硬基体两相材料体系的平头压痕弹塑性模拟.重点研究了平压头压入过程中,不同屈服强度比(软薄膜屈服强度与硬基体屈服强度之比)以及不同压头尺寸下硬基体对压痕规律的影响.研究发现硬基体对压痕规律的影响与屈服强度比近似满足线性关系,且这种线性关系不随压头尺寸的改变而改变,相同压头半径下,屈服强度比越大,影响就越明显;相同屈服强度比下,压头半径越大,影响就越小.研究还发现压头压入过程中,材料的堆积对压入深度没有影响.     

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.     

Finite element analysis on nanoindentation with friction contact at the film/substrate interface

Finite elements (FE) provide a numerical method to calculate complex nanoindentation problems. Correlation of FE analysis with experimental data on nanoindentation may lead to improved characterization of the mechanical properties of thin films and coating systems. In this study, a model of the friction contact at the interface of thin films and substrates is established using FE analysis about a cone indenter, which imitates a Berkovich nanoindenter. Finite element nanoindentation simulations were performed at three different interface friction contact conditions. The following conclusions were depicted through the study of the simulation data. First, for increasing values of the friction coefficient, the indenter’s force versus displacement response of the film/substrate-friction-contact (F/SFC) model coincides with the response of the film/substrate-perfectly-bonded (F/SPB) model. Second, when the indenter’s maximum displacement is less than 10% of the film thickness the deformed nanoindentation area is concentrated under the indenter tip for both F/SFC and F/SPB models. Third, a mechanical response is generated along the F/SFC interface while the mechanical response along the F/SPB interface is negligible. Finally, the nanoindentation simulation data indicate that the calculated mechanical properties intrinsically depend on the interfacial contact conditions of the film/substrate even when the maximum displacement of the indenter is controlled within the 10% of the thin-film thickness.     

The influence of indenter bluntness on the apparent contact stiffness of thin coatings

In the present paper, the influence of punch tip sharpness on the interpretation of indentation measurements is considered.Firstly, in order to obtain analytical insight into the nature of the problem, closed form solutions are presented for the indentation of a homogeneous elastic half-space by an axisymmetric indenter of arbitrary shape, including Hertzian, conical, and conical indenter with a rounded tip.Next, a fast and efficient numerical implementation of a semi-analytical approach to the solution of problems about frictionless axisymmetric indentation of an elastic layer on a dissimilar substrate is described. The approach allows rapid determination of the load-displacement curves for an arbitrary punch shape.The aim of the study was to explore the implications of a finite indenter tip radius for the problem of property identification of thin films. The variation of the apparent substrate stiffness with indentation depth was established for several generic indenter shapes, namely for flat, conical and parabolic punches, and for a conical punch with a rounded tip. It is demonstrated that in each of these cases the depth variation can be described by a simple curve belonging to a family of two-parametric functions. On the basis of these findings we assess the efficiency of using different punch shapes for property determination. A procedure is proposed for this purpose which relies on the use of the depth variation profiles established here. Finally, the influence of imperfect punch shape on the accuracy of analysis is considered.     

Finite element analysis of the indentation stress characteristics of the thin film/substrate systems by flat cylindrical indenters

The indentation stress characteristics of thin film/substrate systems by the flat cylindrical indenters have been simulated by means of the finite element method (FEM). The emphasis was put on the stress distribution ahead of the indenters. The influences of the friction coefficient between the indenter and the thin film, the thickness and hardening modulus of the thin film have been considered. It is found that the stress distribution was not affected by the friction coefficient. But the influence of the thickness and hardening modulus of the thin film on the stress distribution was obvious. At small indentation depth, the plastic deformation occurs at the edge of the indenter only, and the zone will propagation both vertically and laterally with the indentation depth increasing. When the indentation depth reaches a certain value, the thin film at the interface will occur the deformation plastic zone for the case studied in this paper. At lager depths, the two plastic zones will connect, and then the plastic zone propagates along the lateral direction. Beside, it is also found that the maximum of the Mises stress and the shearing stress on the interface occur at 0.8r and r(r is the radius of the indenter), respectively.     

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.     

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.     

硅橡胶压磁复合材料力学性能纳米压痕实验研究

通过纳米压痕测试技术对非晶Fe_73.5Cu₁Nb₃Si_13.5B₉/硅橡胶压磁复合材料薄膜的力学性能进行了研究, 讨论了加载速率、 保载时间、 峰值载荷等试验参数对模量和硬度测试结果的影响。进一步分析了纳米压痕实验表征非晶Fe_73.5Cu₁Nb₃Si_13.5B₉/硅橡胶压磁复合材料薄膜蠕变行为的可行性, 通过合理确定压痕蠕变实验参数, 获得该材料的蠕变应力指数。结果表明: 相对峰值载荷, 加载速率对测试结果影响更为显著, 而保载时间对硬度和模量测试结果几乎没有影响。     

Indentation of an incompressible elastic film

The problem of impressing a rigid flat-ended cylindrical indenter onto an incompressible elastic film is considered. An integral transform solution is developed to reduce the solution of the problem to a Fredholm integral equation of the second kind with a symmetrical kernel depending on the boundary conditions (frictionless/bonded) in the areas of contact. The relationship between the applied load and the indentation depth is derived, which provides a guideline for measuring the elastic constants of thin films and determining the degree of adhesion between a thin film and a stiffer substrate.     

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.     

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.     

Numerical Study of Creep Damage Behavior of Thin Film/Substrate Systems under Indentation

A numerical study has been performed on the creep damage development of the thin film/substrate systems by the Kachanov‐Rabothov damage law. The emphasis was to study the influence of the modulus ratio of the substrate to the thin film, the size of the indenter and the indentation stress. Results show that two obvious damage zones are found ahead of the indenter. One is at the edge of the indenter, the other is at the interface ahead of the indenter edge. The influence of the modulus ratio of the substrate to the thin film on the indentation damage is not obvious before a certain creep time, and later, the greater modulus ratio of the substrate to the thin film has the smaller damage rate. And the indentation depth rate and the damage rate are also affected by the size of the indenter and indentation stress.     

Position effect of cylindrical indenter on nanoindentation into Cu thin film by multiscale analysis

The quasi-continuum multiscale method (QC) is applied to investigate position effect of cylindrical indenter on nanoindentation into Cu thin film. Load–displacement responses reflect that indenter position influences the critical load and critical displacement distinctly. The microscopic deformation mechanism shows that it is the retarding of dislocation nucleation beneath the indenter that actually leads to a relative lower critical load. Once the plastic deformation is retarded, the load–displacement curve will undulate several times until dislocations nucleate at the retarded region. It is found that the critical loads periodically change with indenter positions. The period equals to the distance between two adjacent atomic planes in [1 1 1] direction. An improved elastic model is proposed to predict the critical load in consideration of the effect of indenter position. The agreement between QC simulation and the present model has shown the effectiveness of the improved model.     

An investigation on the onset of plastic deformation of nanocrystalline solid solution Ti-Al-N films

The nanoscale deformation behavior of the solid solution Ti_0.5Al_0.5N thin film was systematically investigated by nanoindentation measurements. The effect of the tip radius of the indenter on the behavior of elastic-plastic deformation was also evaluated. The Hertzian stress analysis was used to determine the distribution of resolved shear stress at the initiate plastic deformation, and the obtained critical resolved shear stress was compared to the theoretical shear strength to establish correlations and differences. Comparison of the calculated critical shear stress and theoretical shear strength also indicated that new complete dislocation nucleation during nanoindentation was not the prerequisite of the onset of plastic deformation, even at very shallow indentation depth.