An Instrumented Indentation Method for Young’s Modulus Measurement with Accuracy Estimation

The relationships between indentation responses and Young’s modulus of an indented material were investigated by employing dimensional analysis and finite element method. Three representative tip bluntness geometries were introduced to describe the shape of a real Berkovich indenter. It was demonstrated that for each of these bluntness geometries, a set of approximate indentation relationships correlating the ratio of nominal hardness/reduced Young’s modulus H _n /E _r and the ratio of elastic work/total work W _e/W can be derived. Consequently, a method for Young’s modulus measurement combined with its accuracy estimation was established on basis of these relationships. The effectiveness of this approach was verified by performing nanoindentation tests on S45C carbon steel and 6061 aluminum alloy and microindentation tests on aluminum single crystal, GCr15 bearing steel and fused silica.     

Determination of mechanical properties by instrumented indentation

The paper reviews the current state of the depth-sensing indentation (sometimes called nanoindentation), where the information on material behaviour and properties is obtained from the indenter load and depth, measured continuously during loading and unloading. It is shown how the contact parameters and principal characteristics are determined using pointed or spherical indenters. Indentation tests can be used for the measurement of hardness and elastic modulus, and also of the yield stress and for the construction of stress–strain diagrams, for the determination of the work of indentation and its components. Most devices use monotonic loading and unloading, but some also enable measurement under a small harmonic signal added to the basic monotonously increasing load. This makes possible continuous measurement of contact stiffness and the study of dynamic properties and the determination of properties of coatings. One section is devoted to the measurement on viscoelastic-plastic materials, where the delayed deforming must be considered during the measurement as well as in data evaluation. Instrumented indentation can also be used for the study of creep under high temperatures. The paper also discusses the errors arising in depth-sensing measurements and informs briefly about some other possibilities of the method.     

Determination of Mechanical Properties of Sand Grains by Nanoindentation

Determination of the mechanical properties of individual sand grains by conventional material testing methods at the macroscale is somewhat difficult due to the sizes of the individual sand particles (a few μm to mm). In this paper, we used the nanoindentation technique with a Berkovich tip to measure the Young’s modulus, hardness, and fracture toughness. An inverse problem solving approach was adopted to determine the stress-strain relationship of sand at the granular level using the finite element method. A cube-corner indenter tip was used to generate radial cracks, the lengths of which were used to determine the fracture toughness. Scatter in the data was observed, as is common with most brittle materials. In order to consider the overall mechanical behavior of the sand grains, statistical analysis of the mechanical properties data (including the variability in the properties) was conducted using the Weibull distribution function. This data can be used in the mesoscale simulations.     

A Load-Based Multiple-Partial Unloading Micro-Indentation Technique for Mechanical Property Evaluation

A load-based multiple-partial unloading micro-indentation technique has been developed for evaluating mechanical properties of materials. Comparing to the current prevailing nano/micro-indentation methods, which require precise measurements of the indentation depth and load, the proposed technique only measures indentation load and the overall indentation displacement (i.e. including displacement of the loading apparatus). Coupled with a multiple-partial unloading procedure during the indentation process, this technique results in a load-depth sensing indentation system capable of determining Young’s modulus of metallic alloys with flat, tubular, or curved architectures. Test results show consistent and correct elastic modulus values when performing indentation tests on standard alloys such as steel, aluminum, bronze, and single crystal superalloys. The proposed micro-indentation technique has led to the development of a portable load-depth sensing indentation system capable of on-site, in-situ material property measurement.     

Full-Field Strain Measurement and Identification of Composites Moduli at High Strain Rate with the Virtual Fields Method

The present paper deals with full-field strain measurement on glass/epoxy composite tensile specimens submitted to high strain rate loading through a split Hopkinson pressure bar (SHPB) device and with the identification of their mechanical properties. First, the adopted methodology is presented: the device, including an Ultra-High Speed camera, and the experimental procedure to obtain relevant displacement maps are described. The different full-field results including displacement, strain and acceleration maps for two mechanical tests are then addressed. The last part of the paper deals with an original procedure to identify stiffnesses on this dynamic case only using the actual strain and acceleration maps (without the applied force) by using the Virtual Fields Method. The results provide very promising values of Young’s modulus and Poisson’s ratio on a quasi-isotropic glass-epoxy laminate. The load reconstructed from the moduli and strains compares favourably with that from the readings.     

Young’s Modulus Measurement Using a Simplified Transparent Indenter Measurement Technique

In material nano- and micro-indentation research, it is well accepted to use the initial unloading stiffness of the load-depth curve to determine the material’s Young’s modulus. This approach requires the use of high-precision displacement sensors in order to calibrate the loading apparatus system compliance and thus obtain the load-depth curve accurately. In this research, using a transparent spherical indenter coupled with a multi-partial unloading technique, we present a simpler approach to measure the material’s Young’s modulus. Experimental results of several metallic alloys and related discussions are presented.     

Identification of Dynamic (Young’s and Shear) Moduli of a Structural Adhesive Using Modal Based Direct Model Updating Method

In this paper, mechanical characteristics (Young’s modulus and shear modulus) of an adhesive are identified using modal based direct model updating method and experimental modal data. The results show that both Young’s and shear moduli of adhesive are frequency dependent. Also, it is demonstrated that the thickness and length of the adhesive-line have influence on these properties. All experiments and subsequent identifications are conducted both in bending and shear modes, and it has been shown that the shear modulus of adhesive is more sensitive to length and thickness variations. The repeatability and consistency of method is proved through repeating the process several times and with different adherends.     

纳米硬度技术的发展和应用

近二十年来,主要用于检测材料表面微米和亚微米尺度力学性质的纳米硬度技术发展迅速.首先,概述硬度的定义、分类及其适用范围.然后,系统地总结纳米硬度技术的发展,重点介绍纳米压痕硬度的测量原理及其影响因素,连续刚度测量原理,高分辨率的载荷位移测量原理,几种常用压头的几何形状,试样表面的准备和确定,相关的测试方法,仪器校准和显微观察等问题.通过压痕实验可获得硬度、弹性模量、断裂韧性、存储模量和损耗模量、蠕变应力指数等.最后,简要介绍纳米划痕硬度测量技术的发展和应用.      

Characterization of viscoelastic properties of polymeric materials through nanoindentation

Nanoindentation testing was used to determine the dynamic viscoelastic properties of eight polymer materials, which include three high-performance polymers and five densities of high-density polyethylene. It was determined that varying the harmonic frequency of nanoindentation does not have a significant effect on the measured storage and loss moduli of the polymers. Agreement was found between these nanoindentation results and data from bulk dynamic mechanical testing of the same materials. Varying the harmonic amplitude of the nanoindentation had a limited effect on the measured viscoelastic properties of the resins. However, storage and loss moduli from nanoindentation were shown to be sensitive to changes in the density of the polyethylene.     

Influence of Vickers tip imperfection on depth sensing indentation tests

In the last decade, the development of depth sensing indentation equipment has permitted two of the most conventional mechanical properties of materials to be easily determined: hardness and Young’s modulus. Some care is needed to accurate results from the experimental determination of the aforementioned mechanical properties. In this study, numerical simulations were performed on two well-known materials (Bk7 glass, AISI M2 steel) and on fictitious materials with a wide range of mechanical properties, using Vickers indenters with different sizes of tip imperfections. The purpose is to estimate the influence of the size of the defect on the hardness and Young’s modulus results obtained by ultramicro and nanoindentation tests.     

Numerical simulation of debonding of adhesively bonded joint

This paper describes a numerical method to simulate the debonding of adhesively bonded joints. Assuming that the adhesive thickness and the adhesive Young’s modulus are small with respect to the characteristic length of the joint and to the Young’s modulus of the adherents, a simplified model is derived in the case of large displacements using the asymptotic expansion technique. Then, the problem of the crack growth is stated, in the case of a stable growth, as the search of the local minima of the total energy of the joint, sum of the mechanical energy and the Griffith’s fracture energy. This is made using the Newton’s method. To this end, the expressions of the first and second derivatives of the mechanical energy with respect to a crack front displacement are derived analytically. Finally, numerical examples are presented, highlighting the unstable character of the crack growth at initiation.     

High Temperature Nanoindentation of PMR-15 Polyimide

This paper presents the high temperature nanoindentation experiments performed on an aerospace polymer resin–PMR-15 polyimide. The sharp-tipped Berkovich nanoindenter equipped with a hot-stage heating system was used. The indentation experiments were performed using the “hold-at-the-peak” method at various indenter holding times and unloading rates. The creep effect was seen to decrease with increasing holding time and/or unloading rate. Procedures used to minimize the creep effect are investigated at both ambient and elevated temperatures so that the correct contact depth (together with modulus and hardness) can be determined from nanoindentation load-depth curve. The temperature dependent mechanical properties of PMR-15 are measured through the current nanoindenter and results are consistent with those obtained from macroscopic tests.     

Measurements of Two Independent Viscoelastic Functions by Nanoindentation

Current nanoindentation measurement techniques normally assume that one material function (such as the Poisson's function) is a constant, and measures just one material function, such as the creep compliance in shear. For materials with significant viscoelastic effects and unknown viscoelastic functions, assuming a constant for one material function is not satisfactory. Accurate measurements require simultaneously determining two independent material functions. This paper provides a method to use nanoindentation to measure both bulk and shear relaxation functions. Two different nanoindenter tips, namely Berkovich and spherical indenters, are used for nanoindentation on polymers. Any two independent viscoelastic functions, such as bulk relaxation modulus and shear relaxation modulus, have different representations in the load–displacement curves obtained with these two indenters so that the two independent viscoelastic functions can be separated and determined. Two polymers, poly(vinyl acetate) (PVAc) and poly(methyl methacrylate) (PMMA) were used in nanoindentation. Nanoindentation measurements were conducted on PVAc above glass transition temperature (Tg) and on PMMA below Tg. Both shear and bulk relaxation functions determined from nanoindentation were found in a reasonably good agreement with data obtained from conventional tests, providing validation of the method presented. The new method can be applied in measurements of two independent viscoelastic functions at sub-micron scale of very small amounts of materials such as polymeric films on a substrate, heterogeneous materials such as bones, tissues, and nanocomposites.     

A Multi-step Method for <Emphasis Type="Italic">In Situ</Emphasis> Mechanical Characterization of 1-D Nanostructures Using a Novel Micromechanical Device

A novel micromechanical device was developed to convert the compressive force applied by a nanoindenter into pure tensile loading at the sample stages inside a scanning electron microscope or a transmission electron microscope, in order to mechanically deform a one-dimensional nanostructure, such as a nanotube or a nanowire. Force vs. displacement curves for samples with Young’s modulus above a threshold value can be obtained independently from readings of a quantitative high resolution nanoindenter with considerable accuracy, using a simple conversion relationship. However, in-depth finite element analysis revealed the existence of limitations for the device when testing samples with relatively low Young’s modulus, where forces applied on samples derived from nanoindenter readings using a predetermined force conversion factor will no longer be accurate. In this paper, we will demonstrate a multi-step method which can alleviate this problem and make the device capable of testing a wide range of samples with considerable accuracy.     

New Double Indentation Technique for Measurement of the Elasticity Modulus of Thin Objects

In this paper we introduce a new method to determine the Young’s modulus of thin (biological) samples. The method is especially suitable for small objects with a thickness of a few hundred micrometers. Such specimens cannot be examined with existing tests: compression and tensile tests need well-known geometry and boundary conditions while classic indentation tests need relatively thick pieces of material. In order to determine the elastic modulus we use the indentation theory as proposed by Sneddon and correct it with a finite element calculated κ factor to compensate for the small thickness. In order to avoid material deformations at the contact zone between the sample bottom and the sample stage, we replace the sample stage by a second indentation needle. In this way the sample can be clamped between two identical needles and a virtual mirror plane is introduced. The new method was used on four test-materials and results agreed well with the outcome of a standard compression method applied on large samples of the same materials. As an application example the technique was applied on thin biological samples, namely middle ear ossicles of rabbits.     

On the determination of the Young’s modulus of thin films using indentation tests

The main difficulty with the characterization of thin coatings using depth-sensing indentation tests is related to the determination of the contributions of the substrate and the film to the measured properties. In this study, three-dimensional numerical simulations of the Vickers hardness test are used in order to examine the influence of the elastic and plastic properties of the substrate and the film on the composite’s Young’s modulus results. The hardness of the film is equal to or higher than the substrate hardness. A study of the stress distributions and the indentation geometry of composites, film/substrate, was performed, taking into account the relative mechanical properties of the film and substrate. In addition, stress evolution during indentation was studied, in order to quantify the critical indentation depth under which the substrate is not elastically deformed. The accurate evaluation of the Young’s modulus of the films using weight functions is also examined: some of these have previously been proposed and one was introduced for this study. Two different fitting procedures were used to compare the results obtained from eight fictive film/substrate combinations using six weight functions. The first procedure, commonly used, considers the substrate’s modulus as a known parameter in the fitting process. In the second, the film and the substrate’s modulus are considered as unknown variables that are calculated simultaneously during the fitting process. The validity of the conclusions obtained using the fictive materials was checked by applying the weight functions to four real composites.     

Identification of Damping and Dynamic Young’s Modulus of a Structural Adhesive Using Radial Basis Function Neural Networks and Modal Data

In this paper, the radial basis function neural networks (RBFNN) was applied to the problem of identifying dynamic Young’s modulus and damping characteristic of a structural adhesive, using modal data. To identify Young’s modulus from undamped model, an appropriate RBFNN using modal data (mode shape and natural frequency) in each mode is developed. Based on a previous work, in order to identify loss factor, two approaches adopted in the identification process. In the first one, a two stage RBFNN is developed. In stage I, Young’s modulus is identified from undamped model and in stage II using the results of stage I an appropriate RBFNN is developed in each mode for identification of loss factor by implementing real parts of eigenvalues of damped model. In the second approach, a one stage RBFNN is developed using real and imaginary parts of eigenvalues of damped model to identify Young’s moduli and loss factors simultaneously. The repeatability and consistency of the method is proved by repeating the identification process for several times. The validity of results is proved by comparing the results with those identified in a previous work.     

Bending analysis of thin functionally graded plates using generalized differential quadrature method

In this paper, the differential quadrature (DQ) method is presented for easy and effective analysis of isotropic functionally graded (FG) and functionally graded coated (FGC) thin plates with constant Poisson’s ratio and varying Young’s modulus in the thickness direction. The bending of FG and FGC plates under transverse loading has been studied using the polynomial differential quadrature (PDQ) and the harmonic differential quadrature (HDQ) methods. A three-dimensional elasticity solution for a moderately thick FG plate with exponential Young’s modulus is used as the benchmark. Two examples, including a thin FG rectangular plate and a thin FGC rectangular plate with sigmoidal Young’s modulus, are investigated. The numerical results of PDQ and HDQ methods reveal good agreement with other solutions. Also, it is shown that the formulations for thin FG plates and homogeneous plates are similar, except that the plane strain components of the middle surface in FG plates are not zero.     

Investigation of Near-Surface Mechanical Properties of Materials Using Atomic Force Microscopy

As ultra-thin films or small-scale structures become widely used in electronics and biology, knowledge concerning their near-surface mechanical properties of the materials is increasingly important. Atomic force microscopy (AFM) is employed to determine near-surface elastic modulus via force-penetration curves acquired during indentation. Samples include polydimethylsiloxane (PDMS), parylene, mica, and single-crystal silicon, and indentations are performed with single-crystal silicon and silicon nitride AFM tips. An analysis algorithm based on the secant modulus method is proposed to extract the true penetration curves from the experimental displacement curves. The penetration data is then analyzed in terms of Hertzian model to estimate the elastic modulus. Three concerns in applying nanoscale AFM indentation to the measurement of the elastic modulus of an ultra-thin material are addressed. First, the effect of the lateral force caused by the inclined angle of the cantilevered probe is investigated theoretically and by numerical simulation. A second concern is local plastic deformation induced by a sharp probe tip. In this case, numerical results show a relatively small effect on the force-penetration curves if the plastic deformation is limited to the central area below the probe tip. The deviation of the elastic-plastic simulation from the elastic estimation depends on the yield strength of the material. Finally, the effect of stiffness matching between the AFM probe and the sample is a key issue that is studied numerically, and appropriate stiffness matching criteria are suggested.     

Characterization of the Damping Behavior of a Nanoindentation Instrument for Carrying Out Dynamic Experiments

A new displacement modulation based dynamic indentation method is demonstrated and shown to be effective for viscoelastic characterization of a glassy polymer. The analysis of dynamic experiments requires a complete understanding of the measuring system’s dynamic characteristics especially the damping. Accordingly, an improved method, based on the use of a wire spring, is developed for determining the damping characteristics. In general, damping in an indentation instrument is contributed by two elements: the eddy current damping from the electromagnetic loading coil and the squeeze film damping from the capacitive displacement transducer. Therefore, a method to determine the relative contribution from the different damping elements present in the system is demonstrated and the results are compared with the calibration obtained from the wire spring method. Finally, dynamic indentation tests are carried out on a glassy polymer to obtain the complex modulus; the values of which are compared with those obtained from bulk dynamic mechanical analysis (DMA) tests. Storage modulus values are found to be in good agreement with bulk data but some divergence in the case of loss modulus is observed. The calibration procedure of the measuring instrument is critically examined in view of these observations. Overall, displacement modulation based dynamic indentation is shown to be a promising method for viscoelastic characterization at the micron length scales. An erratum to this article can be found at