Evaluation of the Effectiveness of Representative Methods for Determining Young's Modulus and Hardness from Instrumented Indentation Data

The effectiveness of Oliver & Pharr's (O&P's) method, Cheng & Cheng's (C&C's) method, and a new method developed by our group for estimating Young's modulus and hardness based on instrumented indentation was evaluated for the case of yield stress to reduced Young's modulus ratio (sigma(y)/E-r) >= 4.55 x 10(-4) and hardening coefficient (n) <= 0.45. Dimensional theorem and finite element simulations were applied to produce reference results for this purpose. Both O&P's and C&C's methods overestimated the Young's modulus under some conditions, whereas the error can be controlled within +/- 16% if the formulation was modified with appropriate correction functions. Similar modification was not introduced to our method for determining Young's modulus, while the maximum error of results was around +/- 13%. The errors of hardness values obtained from all the three methods could be even larger and were irreducible with any correction scheme. It is therefore suggested that when hardness values of different materials are concerned, relative comparison of the data obtained from a single standard measurement technique would be more practically useful. It is noted that the ranges of error derived from the analysis could be different if different ranges of material parameters sigma(y)/E-r and n are considered.

Effects of 'sinking in' and 'piling up' on estimating the contact area under load in indentation

The phenomena of the 'piling up' and 'sinking-in' of surface profiles in conical indentation in elastic-plastic solids with work hardening are studied using dimensional and finite-element analysis. The degree of sinking in and piling up is shown to depend on the ratio of the initial yield strength Y to Young's modulus E and on the work-hardening exponent n. The widely used procedure proposed by Oliver and Pharr for estimating contact depth is then evaluated systematically. By comparing the contact depth obtained directly from finite-element calculations with that obtained from the initial unloading slope using the Oliver-Pharr procedure, the applicability of the procedure is discussed.

Investigation of the Mechanical Properties of Thin Films by Nanoindentation, Considering the Effects of Thickness and Different Coating-Substrate Combinations

In order to further investigate nanoindentation data of film-substrate systems and to learn more about the mechanical properties of nanometer film-substrate systems, two kinds of films on different substrate systems have been tested with a systematic variation in film thickness and substrate characteristics. The two kinds of films are aluminum and tungsten, which have been sputtered on to glass and silicon substrates, respectively. Indentation experiments were performed with a Nano Indent XP II with indenter displacements typically about two times the nominal film thicknesses. The resulting data are analyzed in terms of load-displacement curves and various comparative parameters, such as hardness, Young's modulus, unloading stiffness and elastic recovery. Hardness and Young's modulus are investigated when the substrate effects are considered. The results show how the composite hardness and Young's modulus are different for different substrates, different films and different film thicknesses. An assumption of constant Young's modulus is used for the film-substrate system, in which the film and substrate have similar Young's moduli. Composite hardness obtained by the Joslin and Oliver method is compared with the directly measured hardness obtained by the Oliver and Pharr method.

压痕投影接触面积标定方法的研究

基于Oliver与Pharr方法的纳米压痕实验以其简单方便获得广泛的应用,但众多因素对压痕实验结果的影响范围并无明确的结论.其中压痕接触面积的确定是一个重要环节,该因素对实验结果,特别是小深度下的实验结果具有重要影响.仔细分析了Oliver与Pharr方法并进行了几种材料的纳米压痕实验,针对该方法在接触深度确定、不同深度范围下方法的适用性进行了说明.分析结果表明,对所有的材料使用统一的面积公式,只有在大压痕深度时才是适用的,而在小压痕深度时可能带来较大的误差.因此,应慎重使用由Oliver与Pharr方法得到的小压痕深度的硬度数据.

An New Area Function for Sharp indenter Tips in Nanoindentation

A new area function is introduced and applied to a Berkovich tip in order to characterize the contact projected area between an indenter and indented material. The function can be related directly to tip-rounding, thereby having obviously physical meaning. Nanoindentation experiments are performed on a commercial Nano Indenter XPsystem. The other two area functions introduced by Oliver and Pharr and by Thurn and Cook respectively are involved in this paper for comparison. By comparison from experimental results among different area functions, the indenter tip described by the proposed area function here is very close to the experimental indenter.

Relationships Between Initial Unloading Slope, Contact Depth, and Mechanical Properties for Conical Indentation in Linear Viscoelastic Solids

Using analytical and finite element modeling, we examine the relationships between initial unloading slope, contact depth, and mechanical properties for spherical indentation in viscoelastic solids with either displacement or load as the independent variable. We then investigate whether the Oliver-Pharr method for determining the contact depth and contact radius, originally proposed for indentation in elastic and elastic-plastic solids, is applicable to spherical indentation in viscoelastic solids. Finally, the analytical and numerical results are used to answer questions raised in recent literature about measuring viscoelastic properties from instrumented spherical indentation experiments.

Revelation of a Functional Dependence of the Sum of Two Uniaxial Strengths/Hardness on Elastic Work/Total Work of Indentation

Dimensional and finite element analyses were used to analyze the relationship between the mechanical properties and instrumented indentation response of materials. Results revealed the existence of a functional dependence of (engineering yield strength sigma(E,y) + engineering tensile strength sigma(E,b))/Oliver & Pharr hardness on the ratio of reversible elastic work to total work obtained from an indentation test. The relationship links up the Oliver & Pharr hardness with the material strengths, although the Oliver & Pharr hardness may deviate from the true hardness when sinking in or piling up occurs. The functional relationship can further be used to estimate the SUM sigma(E,y) + sigma(E,b) according to the data of an instrumented indentation test. The sigma(E,y) + sigma(E,b) value better reflects the strength of a material compared to the hardness value alone. The method was shown to be effective when applied to aluminum alloys. The relationship can further be used to estimate the fatigue limits, which are usually obtained from macroscopic fatigue tests in different modes.

Influence of Indenter Tip Roundness on Hardness Behavior in Nanoindentation

In this paper. the effect of indenter tip roundness on hardness behavior for two typical elastic perfectly plastic materials is studied by means of finite element simulation. A rigid conical indenter of semi apex angle 70.3 degrees fitted smoothly with a spherical tip is employed. It is shown that as the indentation depth increases hardness first rises from zero, reaches a maximum and then decreases slowly approaching asymptotically the limiting value equal to that due to a conical indenter of ideally sharp tip. The range within which hardness varies appreciably is comparable to the radius of the indenter tip. The difference between the maximum value and the limiting value depends on the yield stress over the Young's modulus ratio. The smaller this ratio the greater the difference is. Numerical simulation also provides an opportunity for checking the accuracy and limitations of the widely used Oliver-Pharr method.

Nanoindentation of thin-film-substrate system: Determination of film hardness and Young's modulus

In the present paper, the hardness and Young's modulus of film-substrate systems are determined by means of nanoindentation experiments and modified models. Aluminum film and two kinds of substrates; i.e. glass and silicon, are studied. Nanoindentation XP II and continuous stiffness mode are used during the experiments. In order to avoid the influence of the Oliver and Pharr method used in the experiments, the experiment data are analyzed with the constant Young's modulus assumption and the equal hardness assumption. The volume fraction model (CZ model) proposed by Fabes et al. (1992) is used and modified to analyze the measured hardness. The method proposed by Doerner and Nix (DN formula) (1986) is modified to analyze the measured Young's modulus. Two kinds of modified empirical formula are used to predict the present experiment results and those in the literature, which include the results of two kinds of systems, i.e., a soft film on a hard substrate and a hard film on a soft substrate. In the modified CZ model, the indentation influence angle, phi, is considered as a relevant physical parameter, which embodies the effects of the indenter tip radius, pile-up or sink-in phenomena and deformation of film and substrate.

Simple phenomenological determination of contact stiffness and elastic modulus of Ce-based bulk metallic glasses through nanoindentation

The viscoelastic deformation of Ce-based bulk metallic glasses (BMGs) with low glass transition temperature is investigated at room temperature. Contact stiffness and elastic modulus of Ce-based BMGs cannot be derived using the conventional Oliver-Pharr method [W. C. Oliver and G. M. Pharr, J. Mater. Res. 7, 1564 (1992)]. The present work shows that the time dependent displacement of unloading segments can be described well by a generalized Kelvin model. Thus, a modified Oliver-Pharr method is proposed to evaluate the contact stiffness and elastic modulus, which does, in fact, reproduce the values obtained via uniaxial compression tests. (c) 2007 American Institute of Physics.

宏观深度测量压入仪器的研制

基于深度测量压入方法,以材料试验机Instron 5848 Microtester作为加载平台,外接高分辨力位移传感器,设计专用夹具,开发出该材料试验机的宏观压入功能.研究发现:对于机架柔度,无需再进行修正;对于压针接触面积,可用相关的方法计算.采用Oliver-Pharr方法处理测试数据,可获得材料的硬度和弹性模量.为了验证试验的可靠性,选用5种典型金属材料,将宏观压入测试结果与MTS Nano Indenter(R) XP测试结果进行对比,二者基本一致,其分散性均在10%以内.显示了开发传统材料试验机宏观压入测试功能的可行性

纳米压痕仪接触投影面积标定方法的研究

基于Oliver与Pharr方法的纳米压痕实验以其简单方便获得广泛的应用,但众多因素对压痕实验结果的影响范围并无明确的结论.其中压痕接触面积的确定是一个重要环节,该因素对实验结果,特别是小深度下的实验结果具有重要影响.仔细分析了Oliver与Pharr方法并进行了几种材料的纳米压痕实验,针对该方法在接触深度确定、不同深度范围下方法的适用性进行了说明.分析结果表明,对所有的材料使用统一的面积公式,只有在大压痕深度时才是适用的,而在小压痕深度时可能带来较大的误差.因此,应慎重使用由Oliver与Pharr方法得到的小压痕深度的硬度数据.

Relationships between Initial Unloading Slope, Contact Depth, and Mechanical Properties for Spherical Indentation in Linear Viscoelastic Solids

Using analytical and finite element modeling, we examine the relationships between initial unloading slope, contact depth, and mechanical properties for spherical indentation in viscoelastic solids with either displacement or load as the independent variable. We then investigate whether the Oliver-Pharr method for determining the contact depth and contact radius, originally proposed for indentation in elastic and elastic-plastic solids, is applicable to spherical indentation in viscoelastic solids. Finally, the analytical and numerical results are used to answer questions raised in recent literature about measuring viscoelastic properties from instrumented spherical indentation experiments.

微尺度压痕实验的数值模拟及相关问题研究

目前国际上占主导地位的纳米压痕技术是由Oliver与Pharr提出并发展,目前的纳米压痕可以给出整个加、卸载过程的载荷—位移曲线以及硬度与弹性模量随压痕深度变化的曲线,从而提供了丰富的、比较精确的信息,为利用它探索材料比较完整的力学特性提供了可能.为达到该目的,就必须对压痕实验的加、卸过程进行较为深入的研究.作为主要的研究工具,有限元方法模拟微压痕过程在探讨通过实验数据得到更多、更准确的材料表层力学性能参数以及解释实验现象等方面发挥着重要作用.基于计算机速度与容量的原因,较早进行微压痕过程有限元模拟的BhattacharyaandNix、LaursenandSino都使用圆锥压头模拟维氏显微硬度标准正四棱锥Vicker压头与纳米压痕仪标准正三棱锥Berkovich压头,因为圆锥压头具有旋转对称性,可用二维旋转对称单元(二维实体单元)进行计算从而降低计算规模.即便如此,以当时大型计算机的水平,对规模为400~2000个四节点矩形单元的有限元模型进行一次完整的加、卸载过程也需要1~2天.到目前为止,微尺度压痕实验的数值模拟沿用二维模型.事实上,由于加工工艺的限制,微尺度压痕仪的压头如Berkovich与Vicker压头均不个旋转对称性;就微观尺度而言,实际的表层材料都是非均匀的.这些特征均不能由二维模拟体现,所以该文首先建立三维有限元模型,模拟带滑动接触的微尺度压痕加、卸载过程.在此基础上重点讨论了压头几何效应的问题,如二维模拟与三维模拟的关系、显微硬度与纳米的压痕硬度的关系、不同压头下材料的应力应变场、压痕间距与压痕边界的效应等,最后针对微尺度压痕实验中出现的压痕硬度随压痕深度减小而升高的现象,讨论了影响不同压痕深度硬度值的因素.

沿阶草族的染色体研究及系统学问题的探讨

本论文对沿阶草族Ophiopogoneae(Endl.)Kunth的研究历史作了回顾，从染色体、形态学和解剖学角度对此族作了研究，并作了数值分类和分支 系统学分析的尝试，在此基础上探讨了这个族的系统学问题． 1)本论文对此族三属37种123居群的染色体数目、基数及核型不对称性作了研究，其中19种的染色体为首次报道．它们是：P．macrostegiaHance， P.yunnanensis Wang et Tang，P.ophiopogonoides Wang et Tang,O. sarmentosus Wang et Dai,O.tienensis Wang et Tang, O.sylvicola Wang et Tang, O.fooningensis Wang et Dai, O.mairei L6vl.，O.szechuanensis Wang et Tang, O.angustiatus (Wang et Tang) S.C.Chen, O.amblyphyllus Wang et Dai,O.clavatus Wright ex Oliver,O.clivioidesD.M.Zhang et Hong, O.longiscaposus D.M.Zhang et Hong,O.umbraticola Hance,O.fuiD.M.Zhang ntHong,O.zingiberaceus Wang et Dai,O.gangxiensisd.M.Zhang et Hong,O. lo fouense L6vl. 2)在此族中首次报道了2n = 2x = 34的异基数二倍体，同时在O.umbraticola，O.japonicus,O.cLarkei中报道了2n=68的异基数二倍体，过核型和减数分裂等证明异基数是在二倍体水平上形成，并发展成倍性系列的． 3)在此族中首次报道了B染色体的存在，已确证了两种(P.macrostegia和D.tienensis)．一种尚需进一步确证(O.Larkei)． 4)通过对随体位置的系统研究，发现在此族中随体位置具有分类价值． 5)通过对8个种内多倍体、4个多倍体种的研究，表明多倍体分布于较北、海拔较高的地方，而亚洲热带地区的种，则无多倍体，同时在具异基数种类和核型较不对称种类上亦有这种分布特征;在确定了分布的多度中心的基础上，提出喜马拉雅_横断山脉到川西、川南一带是沿阶草属和山麦冬属的近代分化中心． 6)通过染色体结构和数目几个角度的研究，表明球子草属与其他两属在。染色体水平上已发生很大分化，但其属内的分化则不表现在染色体上．其他二属内部则有基数、倍性和核型不对称方面的分化．综观此族，染色体具有由核 型对称向不对称、由二倍体向多倍体、由种内多倍体向多倍体种，由单一基数向种内异基数几个方向进化的趋势． 7)通过对此族的形态观察和分析，提出茎或根状茎分枝方式是属下分类的重要依据;认为本族植物的花序是由圆锥花序简化而来，但残留着圆锥花序特征;并提出了本族花、茎、叶、根几个方面的形态演化趋势． 8)通过对此族二属21种的子房解剖，发现三属均有半下位子房，因而认为子房半下位作为分属检索性状是不合适的．此外还观察到子房着生位置在种内亦有变异，对这种变异的意义进行了探讨． 9)通过此族三属46种2变种的数值分类处理，表明本族由球子草群和沿阶草一山麦冬群两大类群组成，山麦冬属仅是与沿阶草属一个组（葶花组）并列的分类单元，其内部分化较小，而沿阶草属则较大． 10)通过46个性状计算了山麦冬属和沿阶草属共6个广布的“群内总体相 似度”(IOS)，表明山麦冬属3个种种内个体之间、种间个体之间的分化很小，且可能有杂交现象，结合染色体资料和分布特征，认为这个属的发生是个相当晚近的事件． 11)本文从形态和染色体角度，认为沿阶草族是一个自然类群;由分支系 统学分析表明，此族由二个单系类群（球子草属和沿阶草属）组成，沿阶草属含两个单系的组，其中各含3个系，山麦冬属为其中一个系．这一结果与数值 分类结果和染色体资料相符． 12)为避免单一分类方法可能导致的不合理结果，本文以自拟的一种综合分类方法，把谱系、进化、分化诸因素均予考虑，得出一个三维图象，以图象 上相对等径的球作为分类依据，得出的结果与分支系统学和数值分类结果基本一致．因此，山麦冬属作为与沿阶草属等阶的分类地位，应予重新考虑． 13）本文最后对这个族的全面修订提出几点建议. 14）此外，本文还描述了沿阶草属4个新种.