Indenter Shape Research Articles

Direct measurement of surface shape for validation of indentation deformation and plasticity length-scale effects: a comparison of methods

It is ironic that recent developments in instrumented indentation, such as the drive to obtain tensile properties from indentation data and to understand length-scale effects in plasticity, have seen a return to direct imaging of indentations. Significant uncertainties in contact size arise when using contact mechanics calculations that do not take into account the lateral dilation of elastic recovery (Hou et al 2008 J. Phys. D: Appl. Phys. 41 074006) and important sink-in and pile-up contributions to the contact response (Lim and Chaudhri 1999 Phil. Mag. A 79 2979–3000). High resolution, direct measurement avoids these problems. Accurate wear volume and coating thickness measurements obtained by cap grinding methods also depend on high accuracy and low uncertainty direct measurement methods. The use of metrological atomic force microscopy to measure and certify the shape of indenters is well established (Aldrich-Smith et al 2005 Z. Metallk. 96 1267–71) and is essential for valid mechanical property measurement by instrumented indentation. In this paper, we consider indent measurement and compare three direct measurement techniques: optical microscopy, metrological atomic force microscopy (AFM) and confocal laser scanning microscopy (CLSM). We compare the relative merits and uncertainties of various 2D and 3D analysis methods with a new analysis method of differentiating 3D data obtained from AFM and CLSM. This new method has the lowest uncertainty (2.8% for a 50 µm diameter indent at the 95% confidence level). Better still, it enables objective measurements of indent size that avoid the issues caused by difficult-to-standardize parameters (such as illumination angle, contrast and brightness settings), which strongly affect manual estimates of the edge position of an indentation/crater (Gee et al 2002 NPL Measurement Good Practice Guide No 57).

Nanoindentation response of nickel surface using molecular dynamics simulation

The mechanisms of dislocation nucleation on a nickel (Ni) (001) surface under nanoindentation behaviours are investigated using molecular dynamics simulation. The characteristic mechanisms include the molecular models of a thermal layer (TL) and thermal with a free layer (TFL), multi-step load/unload cycles, tilt angles and shapes of the indenter, and slip vectors. The model of a TL has higher reaction force than a TFL. The maximum forces of nanoindentation decrease with increasing time of the multi-step load/unload cycle. The indenter with the tilt angle has larger force to act on the molecular model than the indenter along the normal direction. The effect of the indentation shape is presented such that the conical tip has larger load force to act on the molecular model. The defects along Shockley partials on the (111) plane are produced during nanoindentation involving nucleation, glide and slip.

Mechanical Properties of Potassium Dihydrogen Phosphate Single Crystal by the Nanoindentation Technique

Mechanical properties of potassium dihydrogen phosphate single crystal (KH2PO4, KDP) at room temperature were investigated using nanoindentation approaches. This study was carried out for two crystallographic planes of KDP single crystal, (001) crystallographic plane and the tripler crystallographic plane. The hardness and the reduced modulus values were calculated by the most commonly used Oliver–Pharr method. It was found that hardness and reduced modulus exhibited significant peak load dependence. Furthermore, the strong anisotropy of the hardness and reduced modulus were observed on two tested surfaces. At the same time, the indentation anisotropy of hardness and reduced modulus on each crystallographic face along different directions were estimated in detail. The results showed that these two faces behave quite differently from each other. The variations of hardness and reduced modulus values for (001) face and the tripler face both were periodic due to the rotational symmetry of crystallographic face microstructure and the indenter shape, and the periods were 90 and 120 degrees, respectively.

Micro- and Nanopatterning of Inorganic and Polymeric Substrates by Indentation Lithography

This paper describes the use of a nanoindenter, equipped with a diamond tip, to form patterns of indentations on planar substrates (epoxy, silicon, and SiO(2)). The process is called "Indentation Lithography" (IndL). The indentations have the form of pits and furrows, whose cross-sectional profiles are determined by the shapes of the diamond indenters, and whose dimensions are determined by the applied load and hardness of the substrate. IndL makes it possible to indent hard materials, to produce patterns with multiple levels of relief by changing the loading force, and to control the profiles of the indentations by using indenters with different shapes. This paper also demonstrates the transfer of indented patterns to elastomeric PDMS stamps for soft lithography, and to thin films of evaporated gold or silver. Stripping an evaporated film from an indented template produces patterns of gold or silver pyramids, whose tips concentrate electric fields. Patterns produced by IndL can thus be used as substrates for surface-enhanced Raman scattering (SERS) and for other plasmonic applications.

Experimental and analytical study on the deformation response of closed-cell Al foam panels to local contact damage—Mechanical properties extraction

The present paper studies the deformation response of closed-cell aluminium foam panels (ALPORAS brand) to local contact damage, experimentally simulated by indentation tests with indenters of various shapes and sizes. The foam density varies between 0.184 g/cm 3 and 0.351 g/cm 3; panels of various thicknesses are also considered. Analytical models are developed to estimate the crushing force, the tearing resistance, and the shearing resistance in indentation with cylindrical and spherical indenters. Of particular interest are the failure mechanisms, the foam ligament tear energy and the foam shear strength in all indentation types. The tear energy, as well as the shear strength, is deduced by fitting the experimental load–displacement curves and using the developed analytical models. The influence of the panel thickness, indenter shape and size, and foam microstructure on the deformation mechanisms and material properties is also discussed.

Strength of self-organized TiO 2 nanotube arrays

Self-organized titanium oxide (TiO 2) nanotube arrays were formed by an anodic oxidization technique. Nanoindentation experiments were conducted using three different indenters (i.e. flat punch, cone and triangular pyramid) to explore the mechanics governing the strength of the TiO 2 nanotubes. The force–displacement responses were strongly dependent on the tip geometry and size of the nanotubes. A stress-based fracture model considering graded, porous and discrete structures of the nanotube arrays is proposed, and fracture stress was estimated based on the model. The experimental fracture stresses obtained using different indenters were almost the same, regardless of the indenter shape, which indicates the validity of the model. The evaluated compressive strength of the TiO 2 ligament was approximately 3 GPa, and no clear size effects were observed for the 55–110 nm diameter nanotubes.

The sharpness of a Berkovich indenter

Precise calibration of the indenter shape is an important procedure in nanoindentation analysis since the indenter geometry enters directly into the most common methods of data analysis in this type of testing. Not only is the geometry required to be known with some precision, but also the sharpness of the tip, especially in the case of pyramidal indenters, is important for the use of indenters for testing hardness in thin film specimens—the most common application of nanoindentation. In this paper, a method of determining the area function and tip radius for a Berkovich indenter is described. It is shown that the tip radius estimated from the area function data is in reasonable agreement with a direct measurement using a calibrated atomic force microscope. It is shown that subjective decisions about tip radius may lead to unjustified rejection of a tip for hardness measurement. A new criterion for tip quality is presented in terms of tip radius and specimen material properties.

Indentation into polymeric foams

The effects of the nose shape of rigid indenters on the indentation behaviour of polymethacrylimide (PMI) and polyetherimide (PEI) foams with different densities are investigated. Experimental results show that indentation resistance depends on the geometry of the indenter and the density of the foam. Analytical models based on the deformation mechanisms observed in experiments are developed to predict the indentation resistance. It shows that the analytical predictions are in good agreement with experimental measurements for a range of polymeric foams. This study presents a complete and systematic experimental data on the indentation behaviours of a range of polymeric foams and demonstrates the capability of the analytical model to predict the indentation behaviours of PMI and PEI foams.

A physically based model for indenter tip shape calibration for nanoindentation

A new function that describes the shape of three-sided pyramidal indenters is introduced. This function differs from the polynomial tip shape function conventionally used in nanoindentation tip shape calibration in that the new function includes fewer fitting parameters with clearer physical meaning. Specifically, two of the fitting parameters integrated into the new function are the indenter’s tip radius and the slope of the indenter’s equivalent cone. Tip shape calibration data were collected with four different diamond indenter tips, and both the new function and the standard polynomial function were fit to the data. It is found that the new function can fit calibration data nearly as well as the standard polynomial function and better than existing physically based functions. Although the tip radius parameter obtained by fitting the new model to data deviates from the tip radius determined from Hertzian elastic contact, the two values are correlated.

Use of quasi-static nanoindentation data to obtain stress–strain characteristics for metallic materials

This paper concerns optimization of procedures and algorithms for extraction of stress–strain relationships from quasi-static nanoindentation experiments, using finite element method modelling. Several issues are highlighted, including the usefulness of incorporating residual indent shape in the comparisons, as well as load–displacement–time data, and the significance of creep and interfacial friction. The study is focused on extruded copper bar, using a spherical indenter and assuming transverse isotropy throughout. It is shown that, using the methodology presented here, experimental nanoindentation data could be used to estimate the yield stress and work-hardening rate, with good accuracy, i.e. the yield stress could have been obtained to a precision of about ±10%, and the work-hardening rate to about ±25%. Such inferred constitutive relations are more likely to be reliable if the comparisons are made in regimes within which creep does not significantly influence the behaviour, and in general the timescale of measurement is important.

Impact indentation of a rigid body into an elastic layer. Analytical and numerical approaches

A plane contact-impact problem is considered for an elastic layer subjected to indentation of a rigid body moving with given velocity. An exact analytical solution is obtained in the case of a blunt contour of the indenter shape. Results of the solution are presented for stresses developed with time in a layer of finite thickness. The stress pattern under multiple reflections is analyzed. A numerical solution of the problem is obtained on the basis of a simplified model of elasticity theory having a single displacement. The explicit finite difference algorithm is developed on the basis of the mesh dispersion minimization technique, resulting in precise calculations of discontinuities. Calculated stresses and force of resistance to pressing are presented in the cases of irregular shapes of the indenter contour (rectangle, wedge, and their combination).

Acousto-plasmonic Hot Spots in Metallic Nano-Objects

We investigate the acousto-plasmonic dynamics of metallic nano-objects by means of resonant Raman scattering and time-resolved femtosecond transient absorption. We observe an unexpectedly strong acoustic vibration band in the Raman scattering of silver nanocolumns, usually not found in isolated nano-objects. The frequency and the polarization of this unexpected Raman band allow us to assign it to breathing-like acoustic vibration modes. On the basis of full electromagnetic near-field calculations coupled to the elasticity theory, we introduce a new concept of "acousto-plasmonic hot spots" which arise here because of the indented shape of the nanocolumns. These hot spots combine both highly localized surface plasmons and strong shape deformation by the acoustic vibrations at specific sites of the nano-objects. We show that the coupling between breathing-like acoustic vibrations and surface plasmons at the "acousto-plasmonic hot spots" is strongly enhanced, turning almost silent vibration modes into efficient Raman scatterers.

AN APPROXIMATE FORMULATION OF THE EFFECTIVE INDENTATION MODULUS OF ELASTICALLY ANISOTROPIC FILM-ON-SUBSTRATE SYSTEMS

Frictionless contact between an arbitrarily-shaped rigid indenter and an elastically anisotropic film-on-substrate system can be regarded as being superposed incrementally by a flat-ended punch contact, the shape and size of which are determined by the indenter shape, indentation depth (or applied load) and elastic properties of film and substrate. For typical nanoindentation applications, the indentation modulus can thus be approximated from the response of a circular contact with pressure of the form of [1 - (r/a)2]-1/2, where r is the radial coordinate and a is the contact radius. The surface-displacement Green's function for elastically anisotropic film-on-substrate system is derived in closed-form by using the Stroh formalism and the two-dimensional Fourier transform. The predicted dependence of the effective modulus on the ratio of film thickness to contact radius agrees well with detailed finite element simulations. Implications in evaluating film modulus by nanoindentation technique are also discussed.

Effect of indenter shapes on inverse materials characterization based on the dual indenters method

Abstract The indentation method is a useful tool for studying the onset of plastic flow and work hardening in small volumes. Several approaches based on either single and dual indenters have been reported to characterise a wide range of materials. In this work, the single and dual indenters approaches, with different indenter types, have been comparatively studied using an inverse finite element modelling program developed based on the Kalman filter method. The effect of indenter shapes on the accuracy and uniqueness of the predicted results, as well as convergence time of the program are systematically analysed by automatically mapping the results with a wide range of initial values.

Molecular dynamics simulation of effect of indenter shape on nanoscratch of Ni

Thin films of Ni and Ni alloy have been widely used in microelectromechanical systems (MEMS) and magnetic storage systems. As the dimensions of components in these systems decrease to the micro-scale, even the nano-scale, the interfacial phenomena significantly differ to the counterparts on the macro-scale. A better understanding of micro-/nano-tribology will benefit the fabrication of the small components. In this manuscript parallel molecular dynamics (MD) simulations have been conducted to investigate the nanoscratch behavior of nickel. The simulations are performed for two cases with different indenter shapes. Case I has a sharp indenter, while the indenter in Case II is blunt. It has been found that the indenter shape significantly influences the nanoscratch deformation. The sharp indenter only generates a small deformation area under the indenter, while the blunt one produces more dislocations and larger deformation area in the substrate. The simulation results show that the vertical forces during scratch in Case I are larger than those in Case II, while the scratching forces are similar in both cases during scratch. In addition, the sharp indenter has smaller indentation hardness than the blunt indenter. However, the blunt indenter exhibits smaller scratch hardness and smaller ratio of the scratching force to the vertical force. In order to improve the thermal stability, an algorithm has been proposed to dynamically determine the time-step of MD simulation, by which the system temperature can be maintained within a small range without thermostat layers.

Atomistic simulation of nanoindentation of iron with different indenter shapes

In this article molecular dynamics (MD) simulations have been conducted to investigate the effect of the indenter shape on the nanoindentation behaviours of iron with body centred cubic structure. Two types of indenters (hemispherical indenter and pyramidal indenter) with dimensions of several nanometres have been modelled. The simulation results have shown that the indenter shape significantly influences the nanoindentation behaviours at such small scale. The indentation force increases with indentation depth during loading for the hemispheri-cal indenter, while the indentation force is low in values for the pyramidal indenter. To validate the MD model nanoindentation experiments have been carried out. The calculated indentation hardness of the hemispherical indenter is in reasonable agreement with the experimental value.

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.

Nanoindentation of yttria-doped zirconia: Effect of crystallographic structure on deformation mechanisms

This article presents a nanoindentation study of polycrystalline and single crystals of yttria-doped zirconia with both tetragonal and cubic phases. Analysis of the deformation mechanisms is performed by both atomic force microscopy (AFM) and micro-Raman spectroscopy. Phase transformation from tetragonal to monoclinic phase is clearly distinguished on tetragonal crystals, whereas in cubic crystals the plastic deformation seems to be controlled by dislocation nucleation and interactions. AFM observations in tetragonal zirconia grains have shown that both grain size and autocatalytic transformation strongly influence the size of the transformed zone. Furthermore, the martensitic phase transformation seems to be also strongly dependent of the indenter shape. Experimental results suggest that a critical contact pressure is necessary to induce the phase transformation.

S0302-1-4 微小押込み試験による純チタン結晶方位評価法の提案(実験力学における計測・解析法の新展開(1))

Most characteristics of metallic materials are influenced by crystallographic orientation of grains. Measurement of crystal orientation is therefore important for effective use of metallic materials. However, the most methods employed for orientation measurement require expensive apparatus and technical skills. Meanwhile, indentation testing is easy to perform and the imposed micro-indentation geometry on a grain is possible to reflect its crystallographic orientation. The present study aims to establish the method to evaluate crystallographic orientation of grain in polycrystalline metal, based on the indentation geometry. The indentation tests with triangular pyramidal indenter were carried out on pure titanium grains, of which crystal orientations were premeasured by electron backscattered diffraction method. Thus, the relationship between the crystallographic orientation and the indentation geometry was discussed. The results indicated that the directions of <0001> axis and <21^^-1^^-0> axis projected on sample surface were well-correlated with the deviation of te indentation shape from the ideal one. This fact suggests the possibility to evaluate crystallographic orientation by the imposed indentation geometry.

Pyramidal indentation into fcc single crystals and quasi‐isotropic polycrystals: similar phenomena, different driving mechanisms

AbstractPyramidal microindentation into the (001) surface of an fcc single crystal made of the Ni–base superalloy CMSX‐4 has shown indent shapes which strongly depend on the azimuthal orientation of the pyramid. This observation is experimentally elucidated by digital surface models obtained from high resolution electron back–scatter diffraction (EBSD) technique along with digital image processing. Predictions of crystal plasticity finite element simulations agree with the experimental observations; the observed surface deformation patterns are due to pile–up formation, which is invariantly maximum in &lt;110&gt; directions thus being independent of the azimuthal orientation of the pyramid. The material pile–up is locally accommodated to the indenter faces leading to a convex, a concave contact rim at the faces of the indenter depending on the orientation. The result of maximum pile–up in &lt;110&gt; directions suggests that the driving mechanism for pile–up is purely crystallographic in that the influence of stress concentrations due to different indenter orientations and indenter shapes is negligible. The present findings for fcc single crystals are contrasted to well known observations for quasi–isotropic polycrystals. The different driving mechanisms resulting in phenomenologically similar material response are identified for both materials. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)