Depth-sensing Indentation Research Articles

Measuring elastic–plastic properties of thin films on elastic–plastic substrates by sharp indentation

A new technique has been proposed to measure the elastic–plastic properties of thin film materials on elastic–plastic substrates from the force–displacement curve of the sharp indentation. With the assistance of the substrate effect, explicit relationships between the indentation parameters and the elastic–plastic properties of film–substrate materials are established through extensive finite element analysis. The forward analysis predicts an indentation response from a given set of elastic–plastic properties of film/substrate systems considering the substrate effect, whereas the reverse analysis seeks to extract film elastic–plastic properties from depth-sensing indentation response with a moderate penetration depth. Numerical indentation tests are carried out to examine the effectiveness of the proposed method. Both nanoindentation and uniaxial tensile tests are also carried out on Ni films coated on mild steel substrates and the good agreement shows that the proposed film indentation technique can be applied in practice.

Surface detection errors cause overestimation of the modulus in nanoindentation on soft materials

The accuracy of mechanical properties from depth-sensing indentation, or nanoindentation, depends on the accuracy of the displacement measurement used to calculate these properties. Here, current nanoindentation techniques and analysis methods for accurate displacement measurements are reviewed. First, the ability of a commercial instrument to sense the surface of soft materials is examined. Second, methods of sample surface detection are reviewed. Finally, a case of overestimation of the elastic modulus of a compliant material using nanoindentation with incorrect displacement values is presented.

The use of flat punch indentation to determine the viscoelastic properties in the time and frequency domains of a soft layer bonded to a rigid substrate

This paper reports a computational study of the indentation of a flat punch into a compressible elastic layer (with Poisson’s ratio varying from 0 to 0.49) bonded to a rigid substrate. Based on the computational results and using Sneddon’s solution [Sneddon IN. The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int J Eng Sci 1965;3:47] and the asymptotic solution [Jaffar MJ. A general solution to the axisymmetric frictional contact problem of a thin bonded elastic layer. Proc Inst Mech Eng C 1997;211:549; Yang FQ. Asymptotic solution to axisymmetric indentation of a compressible elastic thin film. Thin Solid Films 2006;515:2274] as the two limits, a simple expression of the load–depth curve valid for an arbitrary ratio of the indenter radius to the thickness of the layer is obtained. Further, a correlation between indentation load and depth for a rigid flat punch indenting into linearly viscoelastic layers bonded to a rigid substrate is proposed by using the correspondence principle. Several procedures are suggested based on the results reported in this study to determine the viscoelastic properties of the layer in the time or frequency domains. The findings are verified by numerical examples. The results may facilitate the use of depth-sensing indentation tests to characterize the mechanical properties of polymeric films or functional coatings on hard substrates, and some biological materials, e.g. articular cartilage.

Non-direct estimations of adhesive and elastic properties of materials by depth-sensing indentation

Using the connection between depth-sensing indentation by spherical indenters and mechanics of adhesive contact, a new method for non-direct determination of adhesive and elastic properties of contacting materials is proposed. At low loads, the force–displacement curves reflect not only elastic properties but also adhesive properties of the contact, and therefore one can try to extract from experiments both the elastic characteristics of contacting materials (such as the reduced elastic modulus) and characteristics of molecular adhesion (such as the work of adhesion and the pull-off force) using a non-direct approach. The direct methods of estimations of the adhesive characteristics of materials currently used in experiments are rather complicated due to the instability of the experimental force–displacement diagrams for ultra-low tensile forces. The proposed method is based on the use of the stable experimental data for the elastic stage of the force–displacement curve and the mechanics of adhesive contact for spherical indenters. Since the experimental data always have some measurement errors, mathematical techniques for solving ill-posed problems are employed.

Determining the viscoelastic parameters of thin elastomer based materials using continuous microindentation

Depth-sensing indentation (DSI) was used to evaluate the viscoelastic properties of three proprietary silicone-based coatings and four butyl-based rubber sheets. The coatings are used as layers in silicone bilayer coatings. The elastic indentation modulus, E ∗, irrecoverable deformation energy and elastic energy were determined in an earlier study using the unloading data of DSI tests and applying a creep correction method proposed by Ngan et al. The model used in this study to characterize the coatings was the standard four parameter Maxwell–Voigt viscoelastic model combined with the elastic indentation load-depth model for a Berkovich indenter as proposed by Fischer-Cripps. This model fits the data quite well. The parameters E 1 ∗, E 2 ∗, η 1, and η 2 were found by curve fitting this model with the indentation depth versus time data while held at a constant maximum load. The parameter E 1 ∗ is equivalent to E ∗; values of E 1 ∗ obtained using the Fischer-Cripps technique were 6.8 ± 0.9 MPa, 109 ± 7 MPa, and 4.2 ± 0.5 MPa for bond coat A, bond coat B, and the top coat, respectively. One purpose of this paper is to demonstrate a technique to determine viscoelastic parameters of silicone-based elastomers. It is hoped that these parameters may then be used in the evaluation and development of more durable silicone-based foul release coatings. Another purpose is to apply this technique to other elastomer-based materials such as butyl-based rubbers.

Monolithic Carbon-based Nanocomposites with Hierarchical Porosity: Novel Anode Materials for Li Ion Batteries

This study compares the effects of meso- and macroporosity and the influence of nanocomposite structure on textural, electronic, and mechanical properties of monolithic carbon samples. Glassy carbon monoliths with three-dimensionally ordered macropores and walls containing mesopores (3DOM/m C) were synthesized by nanocasting from monolithic silica with hierarchical pore structure. Subsequent introduction of more graphitic, nitrogen-doped carbon into the mesopores by chemical vapor deposition produced a monolithic 3DOM/m carbon-graphitic carbon nanocomposite material (3DOM/m C/C). The materials were characterized in detail by powder X-ray diffraction, scanning electron microscopy, transmission electron microscopy, nitrogen- adsorption measurements, depth-sensing indentation, and electrochemical measurements.

Fracture toughness, hardness, and elastic modulus of kyanite investigated by a depth-sensing indentation technique

Macroscopically bladed kyanite crystals of blue and glassy luster were cleaved along two planes, and the mechanical properties were measured through depth-sensing indentation (DSI). The conventional method to determine fracture toughness (KIC) from indentation is based on radial crack lengths measurements, which is difficult to estimate owing to the ease with which kyanite cleaves. An alternative method is proposed to determine the KIC for the perfect cleavage plane (100) of kyanite based on the estimation of the crack nucleation threshold load from a discontinuity or “pop-in” in the DSI load-unload curve. The toughness value for kyanite in the plane of perfect cleavage (100) determined by the proposed method is KIC =2.1 MPa·m1/2. The hardness of 10.7 ± 1.6 GPa for the perfect cleavage plane is lower than the one measured in a plane (010), 18.0 ± 2.9 GPa. The measured elastic modulus for the perfect cleavage plane (100) and for the plane (010) are 297 ± 11 and 405 ± 31 GPa, respectively. These values are in agreement with the published mechanical properties of kyanite, obtained by other techniques. The mechanical behavior is discussed and correlated to fracture patterns during indentation for both crystallographic directions of this mineral.

Denitrogenation prior to hydrodesulfurization

The review covers the understanding of the nanostructure development in glassy and semicrystalline polymers as revealed by indentation hardness methods. The microhardness of polymer glasses is discussed emphasizing the influence of thermal history and physical ageing. The correlation between hardness and glass transition temperature is brought in. Furthermore, the role played by the lamellar morphology in the case of amorphous blends of a block copolymer and a glassy homopolymer is highlighted. A discussion on the influence of filler structure on the microhardness of polymer glasses is introduced. Indentation hardness is presented as a valuable tool to study the kinetics of crystallization from the glassy state. As an example, distinct results on polymer systems under different confinement conditions are shown. The nanostructure–microindentation hardness correlation in the case of semicrystalline polymers and the influence of degree of crystallinity and crystal thickness for various flexible and semirigid polymer systems are recalled. A comprehensive discussion of the creep properties of polymer materials is offered. Concerning deformation mechanisms, experimental results show that for polymers with low degree of crystallinity and Tg below room temperature, a large deviation from the microhardness additivity law is always found. This is due to a different deformation mechanism with respect to that envisaged for polymer materials with Tg above room temperature. The assumption that microhardness approaches zero for amorphous materials above Tg is experimentally confirmed. In the case of an oriented material, it is shown that indentation hardness is capable to detect the gradual appearance of phases of intermediate order. In addition, the study of the creep properties also yields valuable information on the internal degree of order of the oriented system. Finally, an overview of the future perspectives of the application of depth-sensing indentation to the study of polymer materials is offered.

Microstructure and mechanical properties of Cr–Si–N coatings prepared by pulsed reactive dual magnetron sputtering

Cr–Si–N thin films were deposited by pulsed DC reactive dual-magnetron sputtering using Cr and Si targets, while various currents applied to the Si target allowed one to vary the Si content ( C Si) in the films. Microstructure, composition and mechanical properties were studied as a function of C Si using XRD, ERD-TOF and depth-sensing indentation. Three regions of C Si were distinguished: (i) C Si < 2.3 at.%, where the grain size ( D) does not significantly change with increasing C Si; (ii) 2.3 < C Si < 6.7 at.%, where D decreases as C Si increases; and (iii) 6.7 ≤ C Si ≤ 11.6 at.%, where a relatively rapid decrease of D is observed with increasing C Si. We found that the hardness ( H) and the reduced Young's modulus ( E r) of the films reached maximum values of H ~ 24 GPa and E r ~ 240 GPa for C Si ~ 2.3 at.%. Based on the evolution of the microstructural and mechanical properties of the Cr–Si–N films, we propose to explain the hardening observed for C Si < 2.3 at.% in terms of the solid solution mechanism rather than the nanocomposite formation.

Cyclic Depth-Sensing Indentation of Gold Wire

Conventional depth-sending indentation and novel cyclic indentation were performed to study the mechanical properties and strengthening mechanism of pure gold and Ca-doped gold of up to 90 ppm. The system was chosen because it is popular materials for microelectronics interconnection, yet the strengthening mechanism is not well-understood. Conventional depthsensing indentation showed an increase in hardness and modulus of gold with increasing Ca content of up to 90 ppm, which remained significantly higher after annealing. Cyclic depth sensing indentation, where the specimen is loaded to a specific value, unloaded and immediately reloaded, produced a cyclic loop between unloading and reloading curves. The path of the unloading and reloading curves tell the story of the different response of the dislocations generated under the indentation, in different materials, pure gold and Ca-doped gold at different level. Thus their dislocation movement and deformation behavior could be studied by cyclic depth-sensing indentation method. This paper reports cyclic indentation study performed in calcium doped gold widely used in wire bonding and shows that a few ppm level of calcium could result in dislocationssolute interactions, leading to significant strengthening of the materials. TEM micrographs of the material shows that it consists of elongated grains parallel to the drawing direction about 200 nanometers in diameter and a few micrometers in length. It is concluded that cyclic nanoindentation could be used as an extended technique to extract sensitive material information that are not reflected in the conventional test.

Indentation variability of natural nanocomposite materials

Small-scale depth-sensing indentation (nanoindentation) is a popular technique for measuring the mechanical properties of a wide range of materials. Contact mechanics solutions used in data analysis are based on the indentation of a homogeneous half-space, but the experiments are frequently conducted on mineralized biological tissues—biocomposite materials with nanometer-scale features—such as bone and dentin. The current study examines the experimental indentation response of bone across orders of magnitude in contact dimension length-scale, from nanometers to micrometers. Scaling arguments are used to establish the need for nanoscale simulations of mineralized tissue indentation. A finite element model of an inhomogeneous contact problem is developed and used to interpret experimental indentation data on bone and dentin. Both experimental data and modeling results demonstrate a convergence in apparent elastic modulus at increasing contact length-scales. Models results are used to estimate a feature size associated with inhomogeneity of the indentation response; for experiments conducted here the characteristic feature size is found to be substantially larger for bone than for dentin, and in both cases larger than for individual nanometer-scale mineral platelets.

Reverse analysis in depth-sensing indentation for evaluation of the Young's modulus of thin films

This paper presents an approach to reverse analysis in depth-sensing indentation of composite film/substrate materials, which makes use of numerical simulation. This methodology allows the results of experimental hardness tests, acquired with pyramidal indenter geometry, to be used to determine the Young's modulus of thin film materials. Forward and reverse analyses were performing using three-dimensional numerical simulations of pyramidal and flat punch indentation tests to determine the Young's modulus of the thin films. The pyramidal indenter used in the numerical simulations takes into account the presence of the most common imperfection of the tip, so-called offset. The contact friction between the Vickers indenter and the deformable body is also considered. The forward analysis uses fictitious composite materials with different relationships between the values of the Young's modulus of the film and substrate. The proposed reverse analysis procedure provides a unique value for the film's Young's modulus. Depending on material properties, the value of the Young's modulus of the film can be more or less sensitive to the scatter of the experimental results obtained using the depth-sensing equipment. The validity of the proposed reverse analysis method is checked using four real cases of composite materials.

Deformation mechanisms of TiN multilayer coatings alternated by ductile or stiff interlayers

TiN multilayers that alternate with either titanium (ductile) or nanocomposite TiSiN (hard) interlayers were surface coated by filtered arc deposition onto stainless steel substrates. Hardness and deformation mechanisms of these multilayer coatings were investigated using depth-sensing indentation in comparison with traditional monolithic TiN coatings. A dual ion/electron beam microscope was used to analyse subsurface indentation damage. It was found that microstructural layering and the presence of interlayers in TiN multilayers jointly provided resistance to deformation by intercolumnar shear sliding, observed more evidently in the monolithic TiN coatings. This resulted in an increase in hardness, which also increased with both the number of layers and the presence of interlayers. Calculations based upon a mechanistic-based model revealed that the resistance by interlayers played a more important role than an increase in intergranular shear area due to the layered structure in resisting deformation. Compared with the titanium interlayer, the use of a hard nanocomposite interlayer increased the resistance to deformation; however, cracking occurred within both the TiN layers and the nanocomposite interlayers.

Nanotribology, nanomechanics and nanomaterials characterization

Nanotribology and nanomechanics studies are needed to develop fundamental understanding of interfacial phenomena on a small scale and to study interfacial phenomena in magnetic storage devices, nanotechnology and other applications. Friction and wear of lightly loaded micro/nanocomponents are highly dependent on the surface interactions (a few atomic layers). These structures are generally coated with molecularly thin films. Nanotribology and nanomechanics studies are also valuable in the fundamental understanding of interfacial phenomena in macrostructures and provide a bridge between science and engineering. An atomic force microscope (AFM) tip is used to simulate a single-asperity contact with a solid or lubricated surface. AFMs are used to study the various tribological phenomena that include surface roughness, adhesion, friction, scratching, wear and boundary lubrication. In situ surface characterization of local deformation of materials and thin coatings can be carried out using a tensile stage inside an AFM. Mechanical properties such as hardness, Young's modulus of elasticity and creep/relaxation behaviour can be determined on micro- to picoscales using a depth-sensing indentation system in an AFM.

Mechanical characterization of composites prepared from WC powders coated with Ni rich binders

In this study composite powders of WC and Ni/Fe/Cr were prepared in an innovative way, which consists of the sputter-deposition of the metallic binder onto the tungsten carbide particles. Compacts of coated powders were sintered by conventional vacuum sintering followed by hot isostatic pressing (HIP) to reach almost full densities. In order to evaluate the mechanical properties of reduced specimens size (microcomponents), depth-sensing indentation equipment was used. This method enabled the evaluation of the hardness, H , Young’s modulus, E , and the yield stress, σ y , in a non-destructive way, using only one sample. For the composites of sputter-coated WC–Ni/Fe/Cr the results showed an effective reduction of H and E due to the properties of Ni and the binder characteristics of the coated powders, such as uniform distribution and nanometer structure.

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.

Dynamic hardness and elastic modulus calculation of porous SiAlON ceramics using depth-sensing indentation technique

Interest in characterizing the mechanical properties of porous materials at micro-/nanometer scales has increased due to recent development of micro-/nanosystems. Depth-sensing indentation (DSI) systems, also referred to as nanoindentation, are strong tools for performing indentation measurements. The load-displacement curves of SiAlON-based porous ceramics were measured under different peak load (200–1800 mN). The most commonly used Oliver–Pharr method was used to analyze the unloading segments of these curves. The experimental results revealed that the dynamic hardness ( H d) and reduced elastic modulus ( E r) exhibit peak-load dependence, i.e., indentation size effect (ISE). Such peak-load dependence requires calculation of the load-independent hardness ( H LI) and elastic modulus ( E r). The experimental hardness data were analyzed using Meyer's law, Hays–Kendall's model, the proportional specimen resistance (PSR) model, and the modified PSR (MPSR) model. As a result, the modified PSR model is found to be the most effective one for H d determination of these SiAlON ceramics.

Indentation Load Effect on Young's Modulus and Hardness ofPorous Sialon Ceramic by Depth Sensing Indentation Tests

Depth sensing indentation (DSI) tests at the range of 200–1800 mN areperformed on porous sialon ceramic to determine the indentation load onYoung's modulus and hardness values. The Young modulus and hardness(Dynamic and Martens) values are deduced by analysing the unloadingsegments of the DSI test load-displacement curves using theOliver–Pharr method. It is found that Young's modulus Er,the dynamic hardness HD and the Martens hardness HM exhibitsignificant indentation load dependences. The values of Young's modulusand hardness decrease with the increasing indentation load, as a resultof indentation load effect. The experimental hf/hm ratios lower thanthe critical value 0.7, with hm being the maximum penetration depthduring loading and hf the final unloading depth, indicate that oursample shows the work hardening behaviour.

Analysis of data from various indentation techniques for thin films intrinsic hardness modelling

Due to the influence of the substrate, direct measurement of the hardness of thin films by standard micro-indentation tests is not always possible. In such situation, determination of the intrinsic film hardness requires the analysis of a set of experimental apparent hardness values obtained for different indentation loads. A number of mathematical equations based on various assumptions were proposed in literature for that purpose. Most of the models were established on the basis of standard Vickers indentation. Using these models to process the data obtained by Knoop indentation does not provide the same intrinsic hardness value, even after Knoop/Vickers standard conversion, than the one obtained from Vickers indentation. The same problem arises when processing the data coming from depth-sensing indentation. A method to obtain comparable hardness values is proposed in the present work by considering an “equivalent” Vickers hardness in the case of Knoop indentations and the corresponding Martens hardness for depth-sensing indentation. This method has been used to determine the intrinsic hardness of titanium nitride film.

Nondestructive evaluation of material strength using depth-sensing indentation

Successful application of any structural repair or strengthening method requires knowledge of strength and stiffness properties of the materials used in the construction. Depth-sensing indentation is a relatively new material testing method that significantly expands the capabilities of conventional hardness tests. Due to the mathematical complexity of the indentation problem, an analytical solution of the load–penetration depth ( P – h ) behavior is not available for most indenters. This study derives the P – h equations for a truncated cone indenter with arbitrary tip radius and included angle, which covers a wide range of geometries including the cylinder and the cone. A step by step procedure for material strength evaluation is introduced and validated using recorded indentation data. The analytical approach described in this paper can be used in evaluating the modulus of elasticity, stiffness and hardness of common construction materials without resorting to empirical equations.