Berkovich Indenter Research Articles

Effect of surface detection error due to elastic–plastic deformation on nanoindentation measurements of elastic modulus and hardness

Elastic modulus and hardness are commonly measured using nanoindentation. Calculating these properties from measured force–displacement curves typically requires knowledge of the contact depth of the indenter into the specimen. However, surface detection methods in many nanoindentation experiments can lead to an error in the contact depth measurement and, subsequently, the measured properties. Here, the contributions of elastic and plastic deformations to surface detection errors in nanoindentation experiments are examined through experiments and modeling. The model is used to quantify errors in elastic modulus and hardness measurements due to elastic–plastic deformation during surface detection as a function of the specimen properties, indenter geometry, preload, and contact depth. Nanoindentation measurements on polystyrene, an aluminum alloy, and fused silica specimens with a Berkovich indenter are used to illustrate the effects of surface detection error and are compared to the model. The experiments and model both demonstrate that surface detection error can lead to measurement of apparent depth-dependent properties in homogenous materials.

Analysis of mechanical properties of copper thin film in ambient, DI water and slurry environment by nanoindentation

ABSTRACT The nanomechanical properties of chemically altered wafer surface are critical for modelling the material removal in the chemical mechanical planarization (CMP). This paper investigates the nanomechanical properties of copper thin film on the silicon wafer and the reacted passivation layer in different environmental conditions by nanoindentation. The environmental conditions are ambient air, DI water and slurry environment at 45°C temperature. Nanoindentation test is performed on Hysitron TI980 triboindenter using standard Berkovich indenter. Experimental results show that the nanohardness and Young’s modulus of the copper thin film in the ambient environment are 1.72 GPa and 118.03 GPa, respectively. The passivation in DI water results in a slight increase in nano-hardness of copper thin film, on the other hand, a significant decrease in nano-hardness is observed after passivation in the slurry environment. The reduced values of hardness and young’s modulus in the slurry environment are in line with the chemical action of slurry in CMP. The estimated nano-hardness and modulus of the wafer contact surface after the chemical action of slurry are critical process parameters for the analysis and modelling of the advanced node (CMP) process.

Determination of the Elastic Modulus of the Coating Using a Spherical Indenter

In this work, we investigate the nanoindentation of the surface of powder paint and varnish coatings on an epoxy-polyester base, applied to steel substrates. The study of the influence of the test method on the identified mechanical properties has been carried out. A comparison is made of the measurement results obtained using a spherical indenter and a Berkovich indenter. Estimates of the reduced modulus of elasticity, Young's modulus and hardness of coatings are obtained. The obtained experimental data indicate a significant dependence of the determined mechanical properties of paint and varnish coatings depending on the type of indenter used. In the case of using the Berkovich indenter, the found Young's modulus of the coatings (0,6 GPa) turns out to be underestimated in relation to the properties of coatings known from macro experiments (3 GPa). When using a spherical indenter, Young's modulus turns out to be overestimated (6,3 GPa).

Effects of particle distribution and calculation method on results of nano-indentation technique in heterogeneous nanocomposites-experimental and numerical approaches

This study aims to investigate the effects of two testing parameters on the results of the nano-indentation experiment in the heterogeneous particle reinforced composites: (1) the particle distribution pattern, and (2) the methods for calculating the residual projected contact area of the sample under the indenter. For this purpose, several nano-indentation experiments were performed by using Berkovich indenter on the specimens prepared from Filtek Z350 XT dental nanocomposite as a particle reinforced composite with a volume fraction of 63.3 percent. Then, the nano-indentation procedure on the dental nanocomposite was simulated using the finite element (FE) method. In the FE simulation, several representative volume elements (RVEs) of the nanocomposite were modeled by modifying the Lubachevsky-Stillinger algorithm to distribute particles randomly with a volume fraction of more than 50 percent in a cubic volume. The hardness and elastic modulus of the nanocomposite were calculated from the results of the nano-indentation experiment and the simulation. In these calculations, the projected contact area of the indenter on the specimen was obtained using two different approaches of the Oliver-Pharr method and direct measurement of the area. The results indicated that the distribution of particles around the indenter has significant effects on the nano-indentation results. According to the simulation results, the heterogeneity of the material causes the projected contact area of the indenter on the sample to distort from its equilateral triangle shape, which is assumed in the Oliver-Pharr method. Therefore, the method of direct measurement of the indenter projected contact area on the specimen is proposed to obtain more precise results from the nano-indentation test on heterogeneous materials.

Strain rate shift for constitutive behaviour of sintered silver nanoparticles under nanoindentation

As one of the promising packaging materials, the paste of silver nanoparticles (AgNPs) reinforced by SiC particles is investigated in this study for microstructure, thermal stability and constitutive behaviour. As a common challenge in the integrated circuit industry, it is difficult to reveal the strain rate-dependent mechanical properties of thin-film materials in such a large number of sandwich-like electronic devices. In this paper, to enable finite element analysis for mechanical reliability of packaging structure, the stress-strain relationships of the sintered AgNP material at different strain rates are evaluated analytically using the nanoindentation approach with the Berkovich type of indenter. Based on dimensionless analysis, the work done and contact stiffness are identified as the critical variables from nanoindentation responses. The proposed rate factors for the representative stress and the hardening exponent attempts to bridge the strain rate gap between nanoindentation and uniaxial tests. The proposed rate factors are calibrated by a typical lead-free packaging material Sn-3.0Ag-0.5Cu based on tensile tests under the uniaxial strain rate between 10−4 s−1 and 10−3 s−1 and nanoindentation tests under the indentation strain rate between 0.01 s−1 and 0.10 s−1. This makes it possible that the proposed approach is capable of shifting the indentation strain rate by a factor of 100 with regard to the uniaxial strain rate. In this manner, the constitutive responses of sintered AgNP materials at different uniaxial strain rates are achieved and compared with the predictions by using a spherical indenter, which reveals the advantages of assessing the strain rate sensitivity of sintered AgNP by using a Berkovich indenter.

The research of tool wear criterion in micro cutting using the elastic recovery ratio of high-strength elastic alloy 3J33B

In this study, indentation experiments were conducted on high-strength elastic alloy 3J33B material with a Berkovich indenter to study the elastic recovery of material. The experimental data showed that the load and material properties influence elastic recovery ratio of material. The functional expressions of elastic recovery ratio and load were established by regression analysis of experimental data. Therefore, the depths of elastic recovery of 3J33B can be controlled by adjusting the indentation load. Alloy 3J33B has the property of high elastic energy, so it is easy to produce large elastic recovery in the machining. Based on the functional expressions of elastic recovery ratio and load, it can be obtained that the relationships among the elastic recovery ratio of the machined surface, the yield strength of the material, the clearance angle, the average sliding friction coefficient between the tool and the workpiece, the wear width of the flank face and the cutting width. Then, the critical values of tool wear at different clearance angles can be obtained when the yield strength of material, the average sliding friction coefficient between the tool and the workpiece and the cutting width are known. Then, a group of micro milling experiments were conducted on alloy 3J33B using several single-edge micro milling cutters. Finally, it can be obtained that the clearance angle of cutting tool should not be more than 34° in micro cutting in order to reduce the tool wear.

The Strain Rate Sensitivity and Creep Behavior for the Tripler Plane of Potassium Dihydrogen Phosphate Crystal by Nanoindentation.

As an excellent multifunctional single crystal, potassium dihydrogen phosphate (KDP) is a well-known, difficult-to-process material for its soft-brittle and deliquescent nature. The surface mechanical properties are critical to the machining process; however, the characteristics of deformation behavior for KDP crystals have not been well studied. In this work, the strain rate effect on hardness was investigated on the mechanically polished tripler plane of a KDP crystal relying on nanoindentation technology. By increasing the strain rate from 0.001 to 0.1 s−1, hardness increased from 1.67 to 2.07 GPa. Hence, the strain rate sensitivity was determined as 0.053, and the activation volume of dislocation nucleation was 169 Å3. Based on the constant load-holding method, creep deformation was studied at various holding depths at room temperature. Under the spherical tip, creep deformation could be greatly enhanced with increasing holding depth, which was mainly due to the enlarged holding strain. Under the self-similar Berkovich indenter, creep strain could be reduced at a deeper location. Such an indentation size effect on creep deformation was firstly reported for KDP crystals. The strain rate sensitivity of the steady-state creep flow was estimated, and the creep mechanism was qualitatively discussed.

Estimate of theoretical shear strength of C60 single crystal by nanoindentation

The onset of plasticity in a single crystal C60 fullerite was investigated by nanoindentation on the (111) crystallographic plane. The transition from elastic to plastic deformation in a contact was observed as pop-in events on loading curves. The respective resolved shear stresses were computed for the octahedral slip systems langle{01}overline{1}rangleleft{ {{111}} right}, supposing that their activation resulted in the onset of plasticity. A finite element analysis was applied, which reproduced the elastic loading until the first pop-in, using a realistic geometry of the Berkovich indenter blunt tip. The obtained estimate of the C60 theoretical shear strength was about {1}/{11} of the shear modulus on {111} planes.Graphical abstract

Evolution of high-pressure metastable phase Si-XIII during silicon nanoindentation: A molecular dynamics study

Berkovich indenters are widely employed in nanoindentation experiments of single-crystal silicon, in molecular dynamic simulations of silicon nanoindentation, however, spherical indenters are generally employed. To close this gap, in this paper, a series of molecular dynamic simulations are conducted on (001), (101), and (111) silicon surfaces to explore the evolution of high-pressure phases. Several possible silicon phases are tracked by coordination number (CN), radial distribution function (RDF), and angular distribution function (ADF). Results show that the metastable phases and the high-pressure phases present different symmetrical patterns along different crystallographic orientations. A large amount of high-pressure phase Si-XIII, which is seldomly observed in nanoindentation using a spherical indenter, is first discovered under the Berkovich indenter, and the evolution mechanism is characterized by tracking the position transition of labeled silicon atoms. As a transition phase for high-pressure phase Si-II and Si-XIII, bct5 phase is found in the {111} [110] slip systems, which is related with slipping flatten lattice structures. Different from the phase transformation criterion for Si-II, the transformation from Si-I to Si-XIII companies with the local elastic deformation of (001) surface. The atoms in the three neighboring unit cells are compressed into a uniform long-distance ordered crystal structure. Upon indenter extraction and rapid stress releasing, the elastic deformation of the crystal surface resumes incompletely. A part of Si-XIII recovers to pristine Si-I and the rest changes into amorphous phase. The distribution of local hydrostatic pressure and von Mises stress in the phase transformation regions indicates that the concentrated hydrostatic pressure and specific stress induce this high-pressure silicon phase. This research clarifies the evolutionary process of Si-XIII phase generation and enriches fundamental understanding on the mechanisms of silicon phase transformations in nanoindentation.

An investigation on the friction, wear and deformation of potassium dihydrogen phosphate

This paper investigates the friction, wear and deformation of potassium dihydrogen phosphate (KDP) using the nano-scratching technique with both Berkovich and conical indenters. It was found that the indenter tip radius significantly affected the tribological properties of the material. Under a smaller tip radius (Berkovich indenter), the pill-ups were higher at the end of the wear/scratching tracks and friction fluctuation during nano-scratching was greater. The ploughing and brittle deformation dominated the wear mode under a larger tip radius (conical indenter). The KDP deformed in a ductile, ploughing or ploughing and brittle mode depending on the magnitude of the scratching load. The variation in friction coefficient was related to the wear mode and brittle deformation brought about a greater friction fluctuation. The crystal orientation (plane) also affected the behaviour of friction and wear of the material. The softer plane of KDP experienced more brittle deformation under both indenter types. The indenter tip radius had a significant influence on the surface morphology of KDP.

Structure, morphology and mechanical properties of arrays of zirconia nanofibers at different heat treatment modes

Mats of yttria-stabilized tetragonal zirconia nanofibers were prepared in the present research. The effect of the mats calcination temperatures (600, 900, and 1200 °C) on their structure and morphology was investigated. It was found that phase composition of the fibers did not change in all range of the calcination temperatures, while the average grain size in fiber increased from 8 to 39 nm. Multi-cyclic and single loading-unloading nanoindentation testing of the ceramic mats showed that the hysteresis loop energy in samples decreases with higher calcination temperature. Hardness and the elastic modulus measured by spherical (with 10 and 250 μm radii) and sharp Berkovich indenters were the highest in the mats calcined at 900 °C. This calcination temperature can be considered an optimal one for preparation of nanofibers mats which mechanical properties are of importance for their application.

Effect of Strain Rate on the Deformation Characteristic of AlN Ceramics under Scratching.

To clarify the influence mechanism of strain rate effect on deformation characteristics of aluminum nitride (AlN) ceramics, some varied-velocity nanoscratching tests were carried out using a Berkovich indenter in this paper. The deformation characteristics of the scratched grooves were observed using the scanning electron microscope. The experimental results showed higher scratch speed would lead to shallower penetration depth, fewer cracks, and indenter fewer slipping, which was more conducive to the plastic deformation of AlN ceramics. Considering the strain rate effect and the elastic recovery of material, a model for predicting the Berkovich indenter penetration depth under edge-forward mode was established. The prediction results were consistent with the experimental data, and the error was less than 5%, indicating that the model is effective. Based on the Boussinesq field, the Cerruti field, and the Sliding bubble field, a strain rate dependent scratch stress field model was established. The stress field revealed higher scratch speed may significantly reduce the maximum principal stress in the stress field under the indenter, which is the fundamental reason for reducing the crack damage and promoting the plastic deformation. The above study can provide theoretical guidance for reducing the processing damage of AlN ceramics.

STUDY ON FRACTURE TOUGHNESS OF SEMICONDUCTOR MATERIAL USING VICKERS AND BERKOVICH INDENTERS

The indentation method is one of the commonly used methods to determine fracture toughness ($K_{\rm IC})$ of brittle materials. One of the challenges is to obtain a suitable equation of the materials from various equations according to different materials and indenters. Therefore, fracture toughness tests with pyramid indenters (Vickers indenter and Berkovich indenter) were conducted on Si (111) and 4H-SiC (0001) under various loads. The crack length $c$ generated in the Vickers indentation experiments were statistically analyzed, and thirteen equations were selected to calculate the fracture toughness of semiconductor materials at room temperature. The applicability of the indentation test was evaluated, based on a comparative analysis with the results of the scratch test. The results show that to eliminate the inherent discreteness of crack length $c$ generated in the Vickers indentation experiment, multiple indentation tests (at least thirty tests) need to be conducted. The ratio of crack length $c$ over the indentation diagonal length $a$ increases with an increase in the applied load $P$. The crack types of the materials depend on $P$: Palmqvist crack system appears for low loads and Median crack system appears for high loads. Compared with the average fracture toughness (0.96~MPa,$\cdot$,$\sqrt{\rm m}$ and 2.89~MPa,$\cdot$,$\sqrt{\rm m}$, respectively) of Si (111) and 4H-SiC (0001) obtained by micro scratch test, based on linear elastic fracture mechanics (LEFM), the appropriate equations was obtained for both Vickers and Berkovich indenters for the same as material, but which can not be obtained for both Si (111) and 4H-SiC (0001) under the same as indenter from thirteen equations. The fracture toughness of semiconductor materials are best calculated by an expression develope from the Median crack system, and the relationship between fracture toughness being obtained with Vickers indenter and that of with Berkovich indenter is not theoretically 1.073 times, which should be 1.13$\pm $0.01.

Challenges to Accurate Evaluation of Bulk Hardness from Nanoindentation Testing at Low Indent Depths

Estimations of bulk hardness from nanoindentation data are frequently subject to considerable uncertainties, due to indentation size effects, potential pileup effects, and potential influence of surface quality or test methods. In this study, we examined materials science principles of nanoindentation test methods to enable accurate prediction of bulk hardness for a series of high purity Fe and Fe alloys containing 3-25 wt. %Cr. These materials were tested in as-annealed and thermally aged (100-900 hours at 475 oC for 14-25 wt. %Cr) conditions to produce Cr-rich a’ precipitates of varying size and density (bulk Vickers hardness values of ~50 to 350 VHN). Nanoindentation performed with a Berkovich indenter using constant strain rate (0.05 to 0.5 /s) and constant loading rate test methods provided comparable bulk equivalent hardness (H0) extracted by Nix-Gao model, indicating a weak strain rate sensitivity of the investigated materials at room temperature. Results from electropolished and fine mechanically polished samples were found to give comparable measured hardness. Conversely, material pileup adjacent to the indented area produced a 7-20% correction to the indent contact area. The Nix-Gao fitted nanoindentation H0 after pileup corrections agreed quantitatively better with the bulk Vickers hardness than the uncorrected H0 values. The model-predicted (dispersed barrier hardening superposition) and measured strength values agreed for aged Fe18Cr, indicating that Nix-Gao model combined with pileup corrections significantly improved the accuracy of hardness evaluation by nanoindentation. Analytic and experimental analyses demonstrate that inappropriate methods such as hardness ratios or changes at a reference depth (applied in many prior nanoindentation studies) can cause quantitative errors in bulk hardness estimates as large as 60% due to indentation size effects.

Volume, Side-Area, and Force Direction of Berkovich and Cubecorner Indenters, Novel Important Insights

The iteration-free physical description of pyramidal indentations with closed mathematical equations is comprehensively described and extended for creating new insights in this important field of research and applications. All calculations are easily repeatable and should be programmed by instrument builders for even easier general use. Formulas for the volumes and side-areas of Berkovich and cubecorner as a function of depth are deduced and provided, as are the resulting forces and force directions. All of these allow for the detailed comparison of the different indenters on the mathematical reality. The pyramidal values differ remarkably from the ones of so-called “equivalent cones”. The worldwide use of such pseudo-cones is in severe error. The earlier claimed and used 3 times higher displaced volume with cube corner than with Berkovich is disproved. Both displace the same amount at the same applied force. The unprecedented mathematical results are experimentally confirmed for the physical indentation hardness and for the sharp-onset phase-transi- tions with calculated transition energy. The comparison of both indenters provides novel basic insights. Isotropic materials exhibit the same phase transition onset force, but the transition energy is larger with the cube corner, due to higher force and flatter force direction. This qualifies the cube corner for fracture toughness studies. Pile-up is not from the claimed “friction with the indenter”. Anisotropic materials with cleavage planes and channels undergo sliding along these under pressure, both to the surface and internally. Their volumes add to the depression volume. These volumes are essential for the exemplified pile-up management. Phase-transitions produce polymorph interfaces that are nucleation sites for cracks. Technical materials must be developed with onset forces higher than the highest thinkable stresses (at airliners, bridges, etc.). This requires urgent revision of ISO 14577-ASTM standards.

Effect of plasticity on the experimental characterization of the creep property of a cement paste: Spherical vs. conical microindentation

Microindentation is today a powerful tool for rapidly characterizing the elastic modulus and the logarithmic basic creep of a cement paste. However, a theoretical work proved that a microindentation test with a sharp indenter shape involves stress concentration and delayed plasticity which can cause an overestimation of the estimated creep property. This work aims at experimentally investigating the effect of the shape indenter on the identification of the visco-elastic property of a cement paste by microindentation.First, several microindentation grids were carried out on a cement paste with both a Berkovich indenter and a spherical indenter at different penetration depths or load levels for load control (creep) tests or displacement control (relaxation) tests, respectively. As for a visco-elastic material the duality principle between creep and relaxation holds, a numerical method was developed for predicting the relaxation response from the assumed logarithmic creep compliance. The present results show that only spherical microindentation satisfy the duality principle for which creep and relaxation response can be predicted by a unique logarithmic creep compliance function. Finally, spherical microindentation creep tests at low load as well as spherical microindentation relaxation tests provide a greater indentation modulus M and contact creep modulus Cv as likely less affected by possible plasticity effects.

Characterization and mechanical properties of TiO2 nanotubes formed on titanium by anodic oxidation

The well-ordered titanium dioxide (TiO2) nanotube array surfaces were formed at different voltages such as 20 V, 40 V, 60 V, 80 V and 100 V for 1 h on cp-Ti by anodic oxidation (AO) technique. And then, to improve crystallinity of the surface, heat treatment was applied at 450 °C for 1 h to all surfaces without any morphological changing. The surface and cross sectional morphology, elemental structure, phase composition, functional groups, roughness and thickness, wettability and mechanical results were investigated by SEM, EDX, XRD, FT-IR, AFM, contact angle measurement device and nanoindentation tester, respectively. Mainly, anatase- and rutile-TiO2 phases were obtained at post-heat treatment whereas only, Ti phase was detected on AO surfaces at pre-heat treatment. All nanotube structures and the elements of Ti and O were uniformly distributed through the whole surface. The roughness and thickness of tube structures usually increased with increasing voltage values and measured. The roughness and thickness values were measured as 10.67–111.97 nm and 0.21–1.92 μm, respectively. TiO2 nanotube surfaces exhibited hydrophobic behaviors with respect to plain Ti surface. Furthermore, mechanical properties such as hardness and elastic modulus of the coating produced at minimum voltage were great compared to ones at higher voltage and plain Ti surface under a Berkovich indenter due to phase structure, homogeneity and density of nanotube structures.

Nano mechanical property analysis of single crystal copper using Berkovich nano indenter and molecular dynamic simulation

Nanoindentation analysis of FCC single crystal copper with different crystal orientations under Berkovich indenter was carried out by molecular dynamics simulation. The influence of crystal orientation on load distribution under Berkovich indenter was studied and compared with the experiment. Simultaneously, by establishing the relationship between the load–displacement curve and the instantaneous defect structure, the defect formation and slip processes under different crystal orientations were analyzed. Finally, the dislocation density of different orientations was calculated. Meantime, the relationship between the dislocation density and the hardness was explored. The results show that the 〈100〉 orientation shows a slightly different anisotropy difference, and the load value is lower than the 〈110〉 and 〈111〉 orientations. The 〈111〉 load value is slightly greater than 〈110〉 and the hardness values also show the same trend as the load value. The launch time of the initial dislocation loop of 〈100〉 orientation is earlier than 〈110〉, 〈111〉. The crystallographic orientation has a great influence on the change of dislocation morphology during the indentation process. With different orientations, the main plastic deformation is incomplete dislocation nucleation. Under different orientations, different forms of dislocation proliferation, such as quadruple, double and triple symmetry, and different stacking slip directions activated during indentation are observed. The 〈110〉 orientation has a relatively small dislocation density value, the dislocation density ρ0.5 is proportional to the hardness, and the coefficient values are different with different orientations.

Investigation of the superelastic behavior of a Ti-16Zr-13Nb-2Sn sputtered film by nanoindentation

A new Ti-16Zr-13Nb-2Sn superelastic film incorporating β-stabilizing and highly biocompatible elements was elaborated by magnetron sputtering. The morphological, crystallographic and microstructural characteristics of the obtained films were studied by scanning electron microscopy, atomic force microscopy, X-ray diffraction, and transmission electron microscopy. Superelastic response of the film was investigated at local scale by nanoindentation using both spherical and Berkovich indenters. The sputter-deposited film revealed nanograined β microstructure with preferential growth orientation along [110] direction and excellent superelastic recovery at room temperature. Special attention was paid to the indenter geometry influencing reliable evaluation of the superelastic nature of the film. Evolution of the deformation mechanisms during nanoindentation at increasing depths was rationalized by the calculated representative strain beneath the indenting tips and is discussed in this work.

Microstructures generated in AISI 316L stainless steel by Vickers and Berkovich indentations

Abstract The work aimes for studying the specifics of deformation of AISI 316L stainless austenitic steel under the conditions of micro severe plastic deformation (mSPD) created locally at the submicro and micro levels using Berkovich and Vickers indenters. The deformation was carried out by instrumented (depth-sensing), quasi-static indentation and microscratching methods in the load interval P = 10–2000 mN. Studies have shown that various mSPD methods (submicro-, microindentation and microscratching) create similar patterns of plastic deformation in thin surface layers of the material. The stick-slip nature of the scratching process has been demonstrated. It has been established that in the region of loads below 50 mN, the intragranular deformation mechanism has the main contribution to the formation of indentations, while at loads above 50 mN, intragranular and intergranular mechanisms participate in the process, and the role of the latter becomes greater with P increase. Load growth leads to a decrease in hardness under submicro-, microindentation and microscratching for all applied mSPD methods. The type of mSPD method, as well as the type of indenter and the magnitude of the applied load are the factors affecting the mechanical characteristics that should be taken into account depending on the practical purpose of the AISI 316L austenitic steel products.