Indentation Theory Research Articles

Dependence of adhesion and friction on porosity in porous anodic alumina films

We explore, using atomic force microscopy, adhesion and friction characteristics of porous anodic alumina (PAA) films as the porosity varies. Pore formation greatly reduces the adhesive force, by as much as 30 times, but the porosity of PAA films has little influence on its adhesion properties, showing good agreement with the relative contact area estimated by the Hertzian model and indentation theory. Frictional coefficients vary nonlinearly with the porosity of the PAA films due to intrinsic characteristics of the surface morphology of PAA films.

Interfacial mechanical properties of TiN coating on steels by indentation

The elastic theory of indentation on nitride films/steel systems showed distribution of stresses (shear stress, radial stress and circumferential stress) near the interface and in the film. The difference in values for each stress along the distance to the load center increased with increasing Poisson’s ratios of steels. The shear stresses (σrz) had the maximum value at a distance to the load center and the difference became more significant with increasing Poisson’s ratios of steel substrates (from 0.2–0.3 of Poisson’s ratio for high-speed steels to 0.3–0.35 for stainless steels), which accounted for the large amount of cracks inside the indent cavity of nitride films/stainless steel in spite of the smoothness outside the cavity. The calculation of σr and σz showed that the differences in nitride films/steel stress increased with increasing Poisson’s ratios of steels, which also facilitated the formation of ring cracks in the film of nitride films/stainless steel composite. Indentation examination revealed the large amount of cracks inside the indent cavity of nitride film/stainless steel but smooth surface outside the cavity. These were formed under the high sinusoidal shear stress and circumferential radial stress due to the higher Poisson’s ratio of stainless steel and the plastic deformation due to the lower yield stress of stainless steel (SS), which induced more local residual stresses, whereas some cracks or spalling observed around the cavity and no cracks inside the cavity were attributed to the edge effect when the conical indenter strained the surface downward for nitride film/high-speed steel (HSS) system.

박막 물성평가 압입시험의 수치접근법

In this work, the prior indentation theory for a bulk material is extended to an indentation theory for evaluation of thin-film material properties. We first select the optimal data acquisition location, where the strain gradient is the least and the effect of friction is negligible. A new numerical approach to the thin-film indentation technique is then proposed by examining the finite element solutions at the optimal point. With this new approach, from the load-depth curve, we obtain the values of Young's modulus, yield strength, strainhardening exponent. The average errors of those values are less than 3, 5, 8% respectively.

The contact problem of a circular rigid punch on piezomagnetic materials

In this project, a general theory for the axisymmetric indentation of piezomagnetic solids by a flat rigid punch is presented within the context of fully coupled linear model, in the absence of friction or adhesion. It is shown that the coupling has a significant effect on the indentation force and the magnetic flux through the contact area. In addition, an experiment on the material Terfenol-D was carried out to confirm the theoretical results.

Indentation of elastic solids with a rigid Vickers pyramidal indenter

Experimental investigations of the normal loading of a rigid Vickers pyramidal indenter on to several blocks of elastic solids, namely neoprene, rubber, and optically clear polydimethylsiloxane (PDMS) containing 10%, 5%, and 2.5% by volume of the curing agent have been described. An instrumented indentation machine was used and several types of measurement were made. These included (1) indentation load versus indenter penetration behaviour, (2) in situ photography of the contact area between the indenter and the substrate, (3) the depth of the points of contact where a plane going through an indenter diagonal and containing the indenter tip intersects the surface of the specimen, and the depth of the contact points lying along a direction at an angle of 45° to the planes containing the diagonals. The measurements were compared with the predictions of the theory of a rigid cone indenting an elastic half space and by assuming that the rigid pyramid could be likened to a cone of a semi-included angle of 70.3°. It is shown that in all cases there were significant discrepancies between the predictions of the theory and the experimental measurements. It is concluded that a rigid pyramidal indenter normally loading on to an elastic solid cannot be likened to a conical indenter for such studies. It is suggested that it is the high friction at the ridges of the indenting pyramid, which gives rise to the discrepancies between the experimental data and the theory for a frictionless indentation with a rigid cone. This conclusion has very significant implications for a commonly used method of nanoindentation data analysis. These implications are also discussed.

High speed impact behaviors of Al alloy particle onto mild steel substrate during kinetic deposition

During kinetic spraying or cold spraying process, high speed impact occurs between feedstock and substrate. The deformation in this production causes high strain rates, which are higher than in the normal metal-working operation. In this study in order to investigate the deformation at kinetic spraying process individual Al–Si particle deposition onto mild steel substrate was obtained from a low feeding rate and high gun scanning speed spraying experiment. Flattening ratios and particle strains were measured and calculated from 3D analysis of the attached particles. The indentation theories were used for analyzing deformation and impact behavior. The contact pressure during the impact process was expatiated as increasing with the particle velocity, but it could not rise at a notable rate because of the effect of the particle velocity on the impact particle deformation. The calculations showed that the impinging process had a contact time less than 0.1 ms and a mean particle strain rate exceeding 10 7 s −1.

A numerical approach to spherical indentation techniques for material property evaluation

In this work, some inaccuracies and limitations of prior indentation theories, which are based on experimental observations and the deformation theory of plasticity, are investigated. Effects of major material properties on the indentation load-deflection curve are examined via finite element (FE) analyses based on incremental plasticity theory. It is confirmed that subindenter deformation and stress–strain distribution from deformation plasticity theory are quite dissimilar to those obtained from incremental plasticity theory. We suggest an optimal data acquisition location, where the strain gradient is the least and the effect of friction is negligible. A new numerical approach to indentation techniques is then proposed by examining the FE solutions at the optimal point. Numerical regressions of obtained data exhibit that the strain-hardening exponent and yield strain are the two key parameters which govern the subindenter deformation characteristics. The new indentation theory successfully provides a stress–strain curve and material properties with an average error of less than 3%.

Indentation of metals by a flat-ended cylindrical punch

The paper reviews the fundamentals of indentation theory for punches with cylindrical geometry, presents a deep-indentation finite element (FE) simulation and discusses an experimental technique for flat-ended cylindrical indentation. This technique is based on the use of cylindrical punches with diameters up to 1 mm and allows pressure–penetration curves to be drawn from which yield stress and elasticity modulus can be determined. Several materials have been tested including pure metals, steels and refractory alloys; yield stress has been determined and compared with literature values. By testing at different temperatures it was also possible to determine the ductile-to-brittle transition temperature (DBTT) for some alloys that show such phenomenon.

416 しゃ熱コーティング材の押込み試験方式によるヤング率評価(OS コーティング・溶射)

Thermal Barrier Coatings (TBCs) are essential technique for increasing gas temperature on the gas turbines, but evaluation method for Young's modulus of top-coating has not established until now. On the other hand, indentation hardness tests are useful to evaluate materials properties, not only hardness value but also Young's modulus, tensile strength, and so on. In addition, indentation hardness tests have a lot of advantages, compared with another material testing - its simplicity, swiftness, and it is able to experiment with various materials such as composite or coating materials. Therefore, indentation hardness tests are suitable to evaluate Young's modulus of top-coating. In this paper, indentation hardness tests with a truncated conical indenter were carried out to evaluate Young's modulus of top-coating. As the results, effectiveness of the indentation theory for a truncated conical indenter was demonstrated from 4.9 to 9.8 N of testing load. Furthermore, load dependency of calculated Young's modulus was discussed.

Marble cutting with single point cutting tool and diamond segments

An investigation has been undertaken into the frame sawing with diamond blades. The kinematic behaviour of the frame sawing process is discussed. Under different cutting conditions, cutting and indenting-cutting tests are carried out by single point cutting tools and single diamond segments. The results indicate that the depth of cut per diamond grit increases as the blades move forward. Only a few grits per segment can remove the material in the cutting process. When the direction of the stroke changes, the cutting forces do not decrease to zero because of the residual plastic deformation beneath the diamond grits. The plastic deformation and fracture chipping of material are the dominant removal processes, which can be explained by the fracture theory of brittle material indentation.

On the reliability of the measurements of mechanical properties of superhard coatings

Conditions which have to be satisfied in order to assure the reliability of the measurements of mechanical properties of superhard coatings are briefly summarized with references to earlier papers which provide insight into the relevant problems of fracture physics. It is shown that our published data on coatings with hardness in the range of 100 GPa have been, in contrast to the statement of Musil et al. (Mater. Sci. Eng. (in press)) done in the load independent regime and carefully verified by comparison with the Vickers hardness calculated from the size of the remaining indentation measured by SEM. The self-consistency of the measured mechanical properties was demonstrated by the analysis of the measured indentation curves in terms of Hertzian indentation theory.

Subsurface deformations induced by a Vickers indenter in GaAs/AlGaAs superlattice

During the past century, indentation mechanics has been extensively explored. This effort led to the development of instrumented microand nanoindentation techniques that have proved to be of first importance in materials science research. As reviewed recently by Tabor [1], indentation mechanics straightforwardly used today was developed mainly in view of experimental results found on metals [2–4]. Therefore, the use of indentation theory for other materials (for instance ceramics) assumes that plastic-flow characteristics are not much affected. Furthermore, Chaudhri showed using pearlite grains as markers that the measured plastic strains in heavily work-hardened mild steel deformed by indenters of various geometries were much higher than previously thought [5]. In a more recent work, the same author used the hardness-strain relation to map the strain field in high-conductivity copper deformed by spherical indenters [6]. He showed then that the strain-contour geometry was more complex than what had been observed previously in other metals [2]. Determination of the strain field under a Vickers indenter in semiconductors was studied recently in a GaAs/AlAs superlattice where interfaces were used as markers [7]. However, severe delamination occurred at the interfaces. In this paper, we have deformed a GaAs/AlGaAs superlattice by a Vickers indenter and have used focused-ion beam (FIB) technique to prepare cross-sectional thin foils through the center of the indent site for transmission electron microscopy (TEM) observation. These techniques let us get information on the plastic and brittle deformations underneath the indent site and allow us to determine the strain-field map. Superlattices were grown on (001) surfaces of GaAs single crystals by metal-organic vapor-phase epitaxy at 650 ◦C. GaAs and AlGaAs layers (30 of each) were grown alternatively to form a structure about 7.6 μm thick (period 254 nm). The composition of the Alx Ga1−x As (x = 0.85) alloy was chosen so that the misfit with GaAs was only e = 0.13% and the structure was almost lattice matched. The samples were deformed by a Vickers diamond pyramid at room temperature under 500 mN for 30 s. They were set in the indenting machine in such a way that the diagonals of the indentations were along a 〈110〉 direction. The central zone of the indent site was protected from the gallium FIB by a tungsten thin film. Two trenches were milled with a 30 kV FIB in such a way that a thin wall was left containing the selected zone that was transparent to the electron beam as described elsewhere [8]. The periodical structure of the superlattice can be observed in Fig. 1. AlGaAs layers appear in clear contrast while GaAs layers appear in dark contrast. At the bottom of the superlattice, the structure was started by an AlGaAs layer and a GaAs layer about 510 and 235 nm thick respectively. It should be noted that during the milling two layers on top of the structure on the left-hand side of the indent were lost despite the tungsten protection. The indent site is situated on the top of the median crack (observed perpendicularly to the indented surface). Curvature of the surface at the indent site and of layers underneath is obvious and is the result of the plastic deformation generated by the indenter. The curvature of the layers was observed to decrease with depth. For instance, it is about 158◦ for the third GaAs layer and about 176◦ for the 41st layer below. Interestingly the value found in the vicinity of the indent site (158◦) differs from the Vickers pyramid angle (148◦) because of the elastic recovery of the sample while the indenter was unloaded [8]. Using a higher-magnification image just beneath the indent site (Fig. 2), converging slip bands could be observed. They are inclined to the indented surface by about 54◦ and correspond to the gliding of dislocations in the {111} slip planes. On a higher contrast image (Fig. 3) slip bands in {111} planes diverging from the indent site could also be observed. Such a plastic-flow geometry is now well established for bulk semiconductors and was shown to operate here [8–11]. The slip bands correspond to the gliding of dislocations with Burgers vectors inclined to the indented surface that generates deformation of the layers on their path [8–10]. This finally results in the curvature of the superlattice that was described above. At the intersection of the converging slip bands (underneath the indent site and along the load axis direction), we observed a median crack that crossed the layers. This crack was propagated straight into the GaAs substrate on 4 μm. A median-radial crack system is commonly observed in brittle material under sharp contact [12]. Here the crack was initiated at

Impact of a planar flexible bar with geometrical discontinuities of the first kind

A model is presented for the impact of a multiple-angled flexible bar in planar motion. The model consists of a system of nonlinear differential equations that considers the multiple collisions as well as frictional effects at the contacting end, and allows one to predict the rigid and elastic body motion after the impact. The mode functions are selected such that the method can be made computationally as simple as possible, without compromising accuracy. To describe the impact between the elastic bar and the rigid surface, the classical Hertzian contact theory and elasto-plastic indentation theory are used. Particular emphasis is placed on the geometry of the bar because the unit tangent vector and the unit normal vector have first-order discontinuities. Analytical and experimental results are compared to establish the accuracy of the model.

Mechanical properties of arc-evaporated CrN coatings.: Part II: intrinsic film hardness and composite hardness

A systematic experimental investigation of the composite hardness of CrN coatings with different thickness on metal substrates with different hardness was carried out. The hardness response of the samples was studied over a range of applied loads between 100 and 2000 gf in Vickers tests. The measured hardness was analyzed as the function of the film thickness, the indentation size, and the substrate hardness based on the composite hardness models derived from the volume fraction law. The intrinsic hardness of CrN films, which was separate from the measured composite hardness, was independent of the coating thickness and given as a function of the indentation diagonal length. The ‘1/10th rule’, which is considered the critical ratio of indentation depth to film thickness to evaluate the film hardness of coating systems has been analyzed from the plastic deformation theory for indentation, and it was analytically expressed by the functions of hardness and elastic modulus.

An Indentation Theory Based on FEA Solutions for Property Evaluation

A novel indentation theory is proposed by examining the data from the incremental plasticity theory based finite element analyses. First the optimal data acquisition location is selected, where the strain gradient is the least and the effect of friction is negligible. This data acquisition point increases the strain range by a factor of five. Numerical regressions of obtained data exhibit that strain hardening exponent and yield strain are the two main parameters which govern the subindenter deformation characteristics. The new indentation theory successfully provides the stress-strain curve with an average error less than 5%.

142 小球衝突によるセラミックスの表面損傷及び強度低下に関する研究(OS5-2 異物衝突損傷)(OS5 材料の衝撃強度・損傷に関する最近の知見)

In order to clarify the effect of the size of sphere and the thickness of specimen on the surface damage and residual strength, Al_2O_3 sphere impact tests and indentation tests were carried out for Al_2O_3+TiC specimen. The diameter of sphere was 1.5mm, and thicknesses of the specimen were 2.0mm, 3.6mm and 9.0mm. The residual strengths were measured by flexural test after impact tests or indentation tests. As a result, it was seen that the residual strength decreased with the increase in impact speed. Also, the residual strengths of indentation test were somewhat smaller than those of impact test. Therefore, the possibility was shown that the residual strength due to impact test would be evaluated using the method based on the elastic indentation theory.

Some Remarks on the Spherical Indentation Theory

Some Remarks on the Spherical Indentation Theory

What is indentation hardness?

Using dimensional analysis and finite element calculations, we derive simple scaling relationships for loading and unloading curve, contact depth, and hardness. The relationship between hardness and the basic mechanical properties of solids, such as Young's modulus, initial yield strength, and work-hardening exponent, is then obtained. The conditions for ‘piling-up’ and ‘sinking-in’ of surface profiles during indentation are determined. A method for estimating contact depth from initial unloading slope is examined. The work done during indentation is also studied. A relationship between the ratio of hardness to elastic modulus and the ratio of irreversible work to total work is discovered. This relationship offers a new method for obtaining hardness and elastic modulus. Finally, a scaling theory for indentation in power-law creep solids using self-similar indenters is developed. A connection between creep and ‘indentation size effect’ is established.

Spherical indentation of elastic–plastic solids

The finite–element method is used to perform an accurate numerical study of the normal indentation of an elastic–plastic half–space by a rigid sphere. The effects of elasticity and strain–hardening rate of the half–space are explored, and the role of friction is assessed by analysing the limiting cases of frictionless contact and sticking friction. Indentation maps are constructed with axes of contact radius a (normalized by the indenter radius R and the yield strain of the half–space. Competing regimes of deformation mode are determined and are plotted on the indentation map: (i) elastic Hertzian contact; (ii) elastic–plastic deformation; (iii) plastic similarity regime; (iv) finite–deformation elastic contact; and (v) finite–deformation plastic contact. The locations of the boundaries between deformation regimes change only slightly with the degree of strain–hardening rate and of interfacial friction. It is found that the domain of validity of the rigid–strain–hardening similarity solution is rather restricted: it is relevant only for solids with a yield strain of less than 2 x 10 −4 and a / R

Evaluation of Surface Damage and Residual Strength in Ceramics due to Sphere Impact. 1st Report, Si3N4 Sphere Impact to Si3N4 Specimen-Experinrental Results.

In order to clarify mechanisms of surface damage and to establish methods for evaluating strength degradation in ceramics subjected to impact of solid particles, testings of silicon nitride sphere impact to silicon nitride specimens were carried out. The residual strengths of specimens were measured by flexural tests, in which the damaged surfaces were the tensile sides. Fractures were classified to several types depending on their own impact damages. Influences of specimen thickness on the impact damage and the residual strength were also examined. From the comparison of test results of indentation and impact, the possibility was shown that the residual strength due to sphere impact would be evaluated using a method based on the elastic indentation theory.