Indenter Area Function Research Articles

High-Precision Calibration of Indenter Area Function and Instrument Compliance

High-Precision Calibration of Indenter Area Function and Instrument Compliance

Direct measurement of nanoindentation area function by metrological AFM

Abstract Both the hardness and modulus values obtained by nanoindentation depend on knowledge of the area of contact between the test material and the indenter. Significant errors can be introduced into the measurement if the projected area of the indentation contact is not known with sufficient accuracy. The state-of-the-art for user validation of indenter area function is to use materials of known Young’s modulus in the ‘two reference materials method’. However, the area function is best measured directly by traceably calibrated metrological atomic force microscopy. An area function for a standard Hysitron indenter was generated, using both atomic force microscopy and indentation. The results are compared, and the effect of data fitting techniques and measurement uncertainty are discussed.

Single-step calibration method for nano indentation testing machines

Nano indentation is an effective method for materials mechanical characterisation at grain scale. Literature underlined relevance of testing machine calibration to measurement uncertainty of the mechanical characterisation. ISO 14577-2 defines multi-step iterative methods for calibrating frame compliance and indenter area function that do not require high-resolution microscopes. Previous research demonstrated that standard's recommendations are unsatisfactory and result in high calibration uncertainty. This work defines an improved calibration method based on a single-step procedure that achieves, as proved by experimental tests, definite advantages in terms of implementation and measurement uncertainty of both calibration and mechanical characterisation with respect to current procedures.

Characterization of power-law creep in the solid-acid CsHSO4 via nanoindentation

Abstract

Instrumented Indentation Test in the Nano-range: Performances Comparison of Testing Machines Calibration Methods

In the modern manufacturing industry, dealing with innovative productions and advanced materials, technological surface characterisation is becoming crucial to qualify components and optimise processes. Instrumented indentation test is an effective method for characterising mechanical behaviour of materials through the analysis of the force–displacement curve obtained during the implementation of a predefined loading/unloading cycle. Instrumented indentation test allows for hardness test to be performed at different force ranges, thus enabling bulk to local material characterisation. To guarantee the characterisation accuracy, rigorous procedures for the calibration of testing machines are defined in ISO 14577-2. In particular, calibration of frame compliance and indenter area function may be addressed according to methods which do not require the indenter area function to be known a priori, thus avoiding the need of high-resolution microscopes. The present work aims at comparing performances and compatibility of these methodologies by considering tests performed in the nano-range.

High resolution lateral force-displacement measurements as a tool for the determination of lateral contact stiffness and Poisson's ratio

A Lateral Force Unit (LFU) as a second measuring head for nanoindenters is now available as a commercial tool with the necessary accuracy to investigate the elastic contact between a sphere and a flat surface with sub-nanometer resolution. The combination of normal and lateral load-displacement measurements at one and the same sample position gives two independent measurement results and can therefore be used to extract beside Young's modulus a second elastic constant. This can be shear modulus or Poisson's ratio for elastically isotropic materials. To realize that, it is necessary to determine all necessary corrections with high precision. This comprises normal and lateral instrument compliance, indenter area function, spring constant of the holding springs of the LFU and the surface slope. Two algorithms were developed and tested for the determination of the Poisson's ratio from fully elastic measurements with a spherical indenter. One is using the ratio of normal and lateral contact stiffness and the other the curvature of the lateral load-displacement curve at the turning points and the transition from sticking to sliding friction. By measuring six different materials it was shown that the ratio of normal and lateral contact stiffness results in relatively large errors for the Poisson's ratio of up to 50% against literature data while the other method had only an error (1σ) between 6% and 20%. The last method is restricted to hard and smooth materials to enable measurements in fully elastic regime but it can also be applied to coatings if they are about 2.5–4 times ticker than the contact radius during the measurement. This is nevertheless a progress against the current situation where the Poisson's ratio of coatings is mostly unknown.

Contact between traps and surfaces during contact sampling of explosives in security settings

Realistic descriptions of interfacial contact between rough, deformable surfaces under load are difficult to obtain; however, this contact is of great import in a wide range of applications. Here, we detail, through experiment and computational simulation, the interfacial contact between four common traps and five commonly investigated surfaces encountered in explosives detection applications associated with airport security. The Young's modulus and hardness of four traps and seven substrates were measured using nanoindentation. These properties determine how deformation occurs when traps are applied for contact sampling of explosives. The nanoindentation data were analyzed using the Oliver-Pharr method, and an indenter area function was created using silicon and gold as the reference materials. The Young's moduli of the traps ranged from 0.2 to 8GPa, while those of the surfaces ranged from 0.5 to 4GPa. The hardness values of the traps ranged from 0.005 to 0.22GPa, while those of the surfaces ranged from 0.02 to 0.2GPa. For each of 20 scenarios (4 traps, 5 surfaces), six contact simulations were performed. In these contact simulations, the Greenwood-Willliamson microcontact model was used to represent the behavior of the asperities on the traps, while the Timoshenko Beam model was used to describe the macroscopic behavior of the bulk trap materials spanning the space between asperities. This combination of feature- and trap-scale modeling provides a more realistic description of the interfacial contact than either model applied individually. The calculated distributions of separation distances between the traps and surfaces when the traps were contacted with the surfaces under a normal load were compared to estimate the relative effectiveness of the traps at interrogating the topography of the surfaces. This method is proposed as a tool to guide the development of trap materials for surface sampling and surface cleaning applications.

Relationship between Indenter Calibration and Measured Mechanical Properties of Elastic-Plastic Materials

Calibration of Berkovich indenter area function was performed on materials with different elastic-plastic behavior resulting in pile-up and sink-in, respectively. Experimentally obtained results were compared with the results obtained by the application of theoretical area function. The values of Young’s modulus and hardness were significantly affected by the calibration function used. Since the effects of pile-up and sink-in are already included in the used area function, this simple method can lead to more accurate results of Young’s modulus and hardness measurements.

Indenter Shape Characterization for the Nanoindentation Measurement of Nanostructured and Other Types of Materials

A review and comparison of different techniques for indenter shape characterization have been carried out. The techniques considered in this study are: a series of indentations in a reference material with known mechanical properties, a direct AFM observation of indenter apex and SPM imaging of calibration gratings supported with laser interferometer. All of the described techniques are analyzed in terms of the factors affecting the indenter shape characterization and the efficiency of obtaining the resulting indenter area function.

압입자 첨단마모에 따른 나노압입곡선의 변화 및 이의 보정기법

A force calibration of a nanoindenter and a 3D morphology observation of indenters were carried out in this study. A microbalance calibrated with standard weights was used for measuring the loads generated by a nanoindenter. The indentation load could be calibrated from the ratio of measured and generated loads and the first contact load also could be detected from the microbalance data. By analyzing atomic force microscopy images of two indenters, curvature radii of apexes were determined by 19.71±3.03 and 1043.94±50.91 nm, respectively, for the nearly new indenter A and the severly worn indenter B. Corresponding bluntness depths were estimated by 1.22 and 64.56 nm for the both indenters by overlapping their profiles on the perfect pyramidal shape. In addition, nanoindentation curves obtained from a fused silica reference material with the both indenters showed a depth difference corresponding to the bluntness depth difference along the indentation depth axis. By shifting amounts of the bluntness depths along the horizontal axis, whole nanoindentation curves overlapped on themselves and resulted in nanohardness values consistent within 1.11 % without considering the complex indenter area function of each indenter.

Two approaches for enhancing the accuracy of the Rockwell hardness test

Two approaches have been investigated in our study in order to develop indenter calibration methods with high accuracy. One approach is by establishing a group standard utilizing several indenters, which yields better statistical results than the calibration using only one indenter. The second approach is by correcting the hardness test values using the indenter's area function determined by a highly accurate stylus profilometer. In the stylus profilometer developed in this study, the indenter is scanned in 3D and is detected by a position stationary stylus probe. The 3D geometry of the indenter is thus derived from the displacements of the indenter which are measured by three homodyne laser interferometers, offering direct measurement traceability. In addition, for achieving a better measurement performance a special radial scan function is designed where the indenter is scanned radially over its apex. A data evaluation method has been established for calculating the indenter's area function from its measured 3D geometry. The correction method of hardness values based on the indenter's area function is described. In this paper, a group of three Rockwell indenters has been investigated. The mean deviation of HRC values measured by this group of Rockwell indenters has been reduced from 0.11 HRC to 0.06 HRC by using the proposed correction method.

Using the ratio: maximum load over unload stiffness squared, Pm/Su², on the evaluation of machine stiffness and area function of blunt indenters on depth-sensing indentation equipment

Depth sensing indentation study was conducted in a Fischerscope H100V machine, equipped with a Vickers indenter with a tip roundness of approximately 1330 nm. Tests were carried out on soda-lime glass, fused silica, sapphire, aluminum (1100 alloy), high alloyed steel, titanium and copper. The widely used iterative method of Oliver and Pharr was unsuccessful in the attempts to analyze machine compliance and indenter area function. Therefore, an alternative procedure was adopted. The alternative procedure is based on the ratio between maximum load and unload stiffness squared, Pm/Su². It was found that this procedure, which is not iterative, gives good results. A careful study of the Pm/Su² ratio, lead us to conclude that the Fischercope machine has a low compliance which depends on the sample mounting. This low compliance in conjunction with the recent discovery of the dependence of beta factor on the tip roundness/maximum depth ratio, which appears in the relation between contact stiffness and contact area, explains why the iterative method does not converge. However, variations in beta and machine compliance produces deviation on the hardness and elastic modulus lower that 6% with respect to expected values for the materials and the machine studied in this work.

Determination of the Load-Independent Hardness by Analyzing the Peak-Load-Dependence of the Unloading Slope in Nanoindentation

By assuming that the test material has a load-independent nanohardness number, a linear relationship was predicted to exist between the reciprocal of the initial unloading stiffness, 1/SM, and the inverse square root of the peak load, (1/Pmax)0.5, and the load-independent hardness can be obtained directly from the slope of the 1/SM−(1/Pmax)0.5 straight line. This prediction was then verified by analyzing the experimental data obtained on soda-lime glass and a tetragonal ZrO2 polycrystalline. The indenter area function established based on the resultant load-independent hardness was found to deviate from the perfect Berkovich indenter and such a deviation can be attributed to the indenter deformation occurring during indentation as well as the indenter tip rounding.

Direct measurement of nanoindentation area function by metrological AFM

Abstract Both the hardness and modulus values obtained by nanoindentation depend on knowledge of the area of contact between the test materaal and the indenter. Significant errors can be introduced into the measurement if the projected area of the indentation contact is not known with sufficient accuracy. The state-of-the-art for user validation of indenter area function is to use materaals of known Young's modulus in the ‘two reference materials method’. However, the area function is best measured directly by traceably calibrated metrological atomic force microscopy. An area function for a standard Hysitron indenter was generated, using both atomic force microscopy and indentation. The results are compared, and the effect of data fitting techniques and measurement uncertainty are discussed.

Simple method and critical comparison of frame compliance and indenter area function for nanoindentation

A simple method has been proposed for an independent determination of the frame compliance Cf and the area function of a Berkovich indenter. Cf was determined from the unloading compliance of very large indentations in four test materials (fused silica, silicon nitride, high-carbon steel, and copper-zinc alloy) with known elastic properties, following the Oliver–Pharr method by assuming the ideal shape of Berkovich indenter. For a specific value of Cf (= 0.3 nm/mN in our case) all the specimens showed an hc (contact depth)-independent modulus, which agreed well with the expected value when the pile-up effect was taken into account. The contact area A(hc) was then estimated using fused silica as the standard specimen, according to two different procedures, i.e., the Oliver–Pharr method and the Field–Swain method. Both methods gave almost identical area functions over the whole range of the measurement. It was also found that such area functions can be described by two separate equations: A = 2πRehc for hc < Δh and A = g(hc + Δh)2 for hc ⩾ Δh, where Re is the effective tip radius, Δh the truncation depth, and g the geometrical factor for a Berkovich indenter. Based on the spherically truncated cone model, a simple procedure is presented to determine all these parameters from the analysis of a multiple partial unloading P-h curve.

Progress in determination of the area function of indenters used for nanoindentation

It is generally accepted that the most significant source of uncertainty in nanoindentation measurement is the geometry of the indenter tip. In this paper results are presented on the determination of indenter area functions by two methods: (1) direct determination from co-ordinate measurements obtained using a scanning force microscope (SFM); (2) indentation into reference materials with known Young's modulus and Poisson ratio. The direct measurement of geometry of a Berkovich indenter was determined using a traceably calibrated Thermomicroscopes ‘Autoprobe CP’ SFM that of other mentioned indenters (Berkovich and ball shaped indenters) was determined with a modified SFM Veritekt-3. The modification of the latter is that the movement of the SFM scanner is directly calibrated by three laser interferometers fitted in the co-ordinate axes x, y and z, thus realizing directly traceable measurements. Recently, the original arrangement of the laser-interferometers was improved such that an Abbe error is minimized. The paper reports the results achieved with this arrangement and analyses the uncertainty of the area functions obtained. Good knowledge of the machine compliance is a second prerequisite for the accurate determination of the mechanical properties of thin films, in particular elastic modulus. Using the indenter area calculated from SFM measurements, an iterative procedure of high load indentation into a stiff reference material is assessed. In the alternative method, improvements in the determination of the area function by means of indentation into reference materials, based on the Oliver and Pharr method (J. Mater. Res. 7 (1992) 1564–1583), is reported. Due to the uncertainty of the thus determined area functions essentially depending on the uncertainty of the machine compliance, a combined iterative approach using two reference materials is described. The machine compliance again was determined by high load indentation into a stiff reference material (as in the first method). The indenter area function, however, is derived from another reference material allowing accurate stiffness measurements at shallow depths. This allows measurement of the area function near the indenter tip. Both methods are compared with assess the accuracy of the indentation method for determining the indenter area function and the machine compliance.

Depth Sensing Indentation of Thin Hard Films: A Study of Modulus Measurement Sensitivity to Indentation Parameters

The sensitivity of modulus measured by traceably calibrated Depth Sensing Indentation (DSI) is investigated as a function of the indentation parameters: maximum load; loading rate; hold time at maximum load; and single vs. repeated loading. Other issues, including instrument compliance, indenter area function and in-plane anisotropy are also discussed.

A comparison of three microindentation hardness scales at low and ultralow loads

Indentation hardness tests were performed on thick, fine-grained, electro-formed deposits of copper and nickel using Knoop, Vickers, and Berkovich indenters. The latter type of indenter was used for shallow penetrations (85–1750nm), and results are reported in terms of nanoscale hardness (NH) numbers. Knoop and Vickers indenters were used with applied loads of between 0.15 and 0.98 N, and at the lowest load, produced indentation depths comparable to the larger ones obtained with the Berkovich indenter. The NH numbers became very sensitive to penetration depth when the penetration depth was less than certain critical values. NH numbers for Cu and Ni were higher than those for Knoop and Vickers testing at comparable penetration depths. Applying indenter area function corrections to calculate hardness numbers (i.e., considering projected area versus facet contact area) resulted in a closer correlation between microhardness and nanohardness scales; however, changes in the tip shape because of wear or other imperfections can lead to inaccurate calculation of NH numbers at the lowest loads. Results also suggest that the interconversion of lowload hardness numbers from one scale to another can be material-dependent.