Spherical Indentation Tests Research Articles

Mechanical characterization of carbonitrided steel with spherical indentation using the average representative strain

This paper investigates the identification of mechanical properties of carbonitrided steels using the spherical indentation test. The proposed procedure consists in performing the Vickers microindentation hardness test across the carbonitrided steel in order to obtain the thickness of the hardened layers. Thus, with the assumption of a linear variation of the plastic properties in the intermediate layers between surface and substrate, two spherical macroindentation tests, performed on the substrate and on the surface of the carbonitrided steel, are necessary to identify the work hardening laws' variation through the thickness of the carbonitrided steel. The proposed method does not call for inverse analysis but is based on the use of a database of finite element simulation F–h curves obtained by simulating indentation tests on the surface of various pseudo-carbonitrided materials. The advantage of this method compared to those based on inverse analysis is that it allows a representative strain and a confidence domain of the solution to be determined. The confidence domain of the identified solution takes into account the experimental imprecision of the indentation test and of the case depth variability often encountered in carbonitrided parts.

Local Mechanical Characterization of Metal Foams by Nanoindentation

This paper deals with microstructure and micromechanical properties of two commercially available aluminium foams (Alporas and Aluhab). Since none of the materials is available in a bulk and standard mechanical testing at macro-scale is not possible the materials need to be tested at micro-scale. To obtain both elastic and plastic properties quasi-static indentation was performed with two different indenter geometries (Berkovich and spherical tips). The material phase properties were analyzed with statistical grid indentation method and micromechanical homogenization was applied to obtain effective elastic wall properties. In addition, effective inelastic properties of cell walls were identified with spherical indentation. Constitutive parameters related to elasto-plastic material with linear isotropic hardening (the yield point and tangent modulus) were directly deduced from the load–depth curves of spherical indentation tests using formulations of the representative strain and stress introduced by Tabor.

Surface residual stress in soda-lime glass evaluated using instrumented spherical indentation testing

Instrumented spherical indentation testing is proposed as a non-destructive way to evaluate surface residual stress in soda-lime glass. 10 μm-deep indentations with a spherical indenter of 250 μm radius do not reduce the strength of 3.5-mm-thick soda-lime glass as measured in four-point bending tests. We find good linearity between the compressive surface residual stress and the force difference at maximum indentation depth in the indentation force–depth curve, while hardness as measured by instrumented spherical indentation testing is independent of compressive surface residual stress introduced by bending and strengthening heat treatment.

Novel monitoring techniques for characterizing frictional interfaces in the laboratory.

A pressure-sensitive film was used to characterize the asperity contacts along a polymethyl methacrylate (PMMA) interface in the laboratory. The film has structural health monitoring (SHM) applications for flanges and other precision fittings and train rail condition monitoring. To calibrate the film, simple spherical indentation tests were performed and validated against a finite element model (FEM) to compare normal stress profiles. Experimental measurements of the normal stress profiles were within −7.7% to 6.6% of the numerical calculations between 12 and 50 MPa asperity normal stress. The film also possessed the capability of quantifying surface roughness, an important parameter when examining wear and attrition in SHM applications. A high definition video camera supplied data for photometric analysis (i.e., the measure of visible light) of asperities along the PMMA-PMMA interface in a direct shear configuration, taking advantage of the transparent nature of the sample material. Normal stress over individual asperities, calculated with the pressure-sensitive film, was compared to the light intensity transmitted through the interface. We found that the luminous intensity transmitted through individual asperities linearly increased 0.05643 ± 0.0012 candelas for an increase of 1 MPa in normal stress between normal stresses ranging from 23 to 33 MPa.

Toughness measurement and toughening mechanisms of arc ion plating Cr2O3 films treated by annealing

Abstract Chromium sesquioxide (Cr2O3) films were deposited on Ni-based high-temperature alloy substrates by an arc ion plating technique and then annealed at different temperatures and heating rates. The influence of annealing conditions on the toughness of Cr2O3 films was calculated according to spherical indentation tests. The increase in grain size and compressive stress, variety of microstructure and surface morphology, and atom diffusion that resulted from annealing caused toughness variations. The increase in grain size closed micro-cracks along the direction of film growth. Compressive stress and a multi-crystal plane led to cracks caused by indentation that required more energy to break through the film. In the process of indentation, turning, bifurcating, and bridging of cracks on film surface was also able to dissipate energy. Atom diffusion in the process of 1000 °C annealing also played a role in grain boundary toughening. The toughness improvement of Cr2O3 film significantly improved friction life.

Softening-induced plastic flow instability and indentation size effect in metallic glass

Despite the absence of microstructural features, metallic glasses (MGs) could display size-dependent hardness at the submicron scale. While most early studies attributed this size effect to Weibull statistics, here we propose a mechanism related to shear softening induced flow instability that can give rise to a deterministic indentation size effect in MGs. In line with this mechanism, an explicit relation is derived linking the size dependency of hardness to a critical length scale that governs the transition from a stable to unstable plastic flow in MGs. Through a series of carefully designed spherical indentation tests, this mechanism is experimentally justified, from which we are able to extract the critical transition length for a Zr-based MG at different indentation strain rates. On the basis of the combined theoretical/experimental efforts, our current work provides a quantitative insight into the indentation size effect in MGs.

Determination of Area Reduction Rate by Spherical Indentation Test

Rate of area reduction is an important mechanical characterization to appraise the plasticity of metals, which is always obtained from the uniaxial tensile test. A methodology is proposed to determine the area reduction rate by continuous ball indentation test technique. The continuum damage accumulation theory has been adopted in this work to identify the failure point in the indentation. According to this theory, the damage is accumulated in the material during the test with voids nucleating and growing, which can be divided into two stages due to the variation in the degree of constraint. The turning point between two stages can be identified as the failure point where the material beneath the indenter collapses. The corresponding indentation depth of this point can be obtained and used to estimate the area reduction rate. The local strain limit criterion proposed in the ASME VIII-2 2007 alternative rules is also adopted in this research to convert the multiaxial strain of indentation test to uniaxial strain of tensile test. This method can be useful in engineering practice to evaluate the material degradation under severe working condition due to the non-destructive nature of ball indentation test. In order to validate the method, spherical indentation test is performed on ferritic steel 16MnR and B16, then the results are compared with that got from the traditional uniaxial tensile test.

J0230104 肩こりのハンディタイプ押込試験システムを用いたYoung率による計測評価

Spherical indentation testing is studied to evaluate the muscle stiffness of human shoulder. Here, the Hertzian contact theory is functionally extended to evaluate indentations for the thin tissues on the human body. In the expansions, the technique used for evaluating the thickness of finite specimens is first explained by analyzing the experimental results of indentations. Then, the elasticity of soft materials with finite thickness is theoretically derived by defining an equivalent indentation strain for the analysis of the indentation process. The expansions are examined to evaluate its reliability by applying them to measure the stiffness of some soft materials. Furthermore, this technology is applied to the elasticity investigation of the human body. Especially, the measurement results of elastic characteristics of the body of human body are shown and the availability of developed device is discussed to reveal the deformation mechanics of human body in this report.

The Anvil Effect in the Spherical Indentation Testing on Sheet Metals

Spherical indentation hardness tests are widely used in manufacturing industry to obtain material property of the workpiece. For the indentation test on sheet metals, significant error can occur in measuring the penetration depth due to the anvil effect. This anvil effect is manifested with decreasing specimen thickness and increasing indentation depth. This paper critically reviews the experimental observations of the anvil effect, and studies the mechanism behind it. The experimental results and numerical simulations suggest that, when the thickness of the specimen is reduced, a change in deformation mode is experienced during the indentation process. A correction method for the anvil effect is proposed and an empirical equation is derived to determine the effective indentation depth. The experimental and numerical investigations have important implications for the interpretation of the indentation anvil effect; and the correction method for anvil effects can be used in hardness measurement to obtain accurate material property.

A Novel Method to Determine Material Properties and Residual Stresses Simultaneously Using Spherical Indentation

Abstract Spherical indentation is one of the non-destructive techniques that has gained great interest among researchers in recent years. Spherical indentation is inexpensive and quick and can provide a fairly accurate estimation of in-plane residual stresses. This method has typically been used to characterize material properties. However, the application of the technique to measure residual stresses has also been practiced. In this paper, the parameters of Hollomon’s equation and residual stresses were determined using the load–penetration (P–h) curve technique obtained from a single loading-unloading spherical indentation test. Artificial Neural Networks (ANN) were employed to achieve the best results from the data. Neural networks are trained using the data from a series of finite element analyses. An exponential equation is then fitted to the loading curve. Having the fitted equation and the trained neural networks, the residual stresses and the material characteristics were found simultaneously. An important benefit of this method was that it could be used with no requirement for a reference stress-free sample.

Damage Induced by a Spherical Indentation Test in Tool Steels Detected by Using Acoustic Emission Technique

The aim of this study is to monitor the subsurface damage mechanisms of commercial cold-work tool steel by observing acoustic emissions generated in a spherical indentation test. Monotonic loads are applied in the elastic and plastic ranges to damage the specimen. Two types of damage prior to the occurrence of cracking are found: carbide breakage and plastic deformation. The phenomena are confirmed by microscopic images and the good agreement between the estimated carbide fracture strength and previous results. The two types of damage gives rise to different acoustic emission signals: a burst-type, high-amplitude signal for the breakage of carbides and a continuous-type, low-amplitude signal for plastic deformation. It is thus possible to detect and differentiate the incipient damage mechanisms on the subsurface in real time in a spherical indentation test.

Understanding pop-ins in spherical nanoindentation

Pop-ins, or sudden displacement-bursts at constant load in a nanoindentation test, are typically attributed to the difficulty of setting up potent dislocation sources in the very small indentation zones in these experiments. Such displacement (and strain) bursts would intuitively indicate a sharp drop in stress during the pop-in event itself. However, spherical indentation stress-strain curves routinely exhibit a high and stable indentation stress value during the pop-in, and the indentation stresses decrease only after a further finite amount of additional indentation displacement has been applied. In order to understand this discrepancy, we utilize a combination of interrupted spherical indentation tests along with depth profiling of the residual indentation surfaces using in-situ atomic force microscopy (AFM) to study pop-ins. The AFM surface profile maps show that there is an asymmetric profile change over a limited region around the indentation contact area for a single pop-in; the asymmetry disappears upon further loading beyond the pop-in. A plausible sequence of physical processes (related to metal plasticity) occurring underneath the indenter during and immediately after the occurrence of the pop-in is proposed to explain these observations.

Evaluation of the material’s damage in gas turbine rotors by instrumented spherical indentation

Experimental indentations are carried out on items of two different materials, taken in several location of various components from high pressure gas turbine rotor which have seen an extensive service. The components object of investigation consisted in 1st and 2nd high pressure turbine wheels made in nickel-base superalloy (Inconel 718), the spacer ring (Inconel 718) and the compressor shaft made in CrMoV low alloy steel (ASTM A471 type10). Aim of the work is to set up the capability of the instrumented spherical indentation testing system to evaluate variations in the material properties due to damage, resulting from temperature field and stresses acting on components during service. To perform this task load-indentation depth curves will be acquired in various zones of the above mentioned components. The analysis of the results has allowed to identify an energy parameter which shows a linear evolution with the mean temperature acting on the components.

Digital Volume Correlation Applied to X‐ray Tomography Images from Spherical Indentation Tests on Lightweight Gypsum

ABSTRACTCylinders made of lightweight gypsum are extracted from industrial plasterboard and then indented in situ in an X‐ray tomograph. The results from the in situ experiment show that a compacted zone develops under the indenter, which is displaying a very sharp boundary with the undamaged material. Tomographic imaging during the mechanical load associated with digital volume correlation enables the displacement fields to be measured during the test. However, because of the inhomogeneous nature of the indentation test, a high spatial resolution for the displacement is called for, and because the range of displacement amplitudes is small, uncertainties on the measured displacement and strain fields are large. In this study, a new methodology is presented to address integrated digital volume correlation based on a library of fields computed from a commercial finite element software. It allows many fluctuations in the estimated displacement fields to be filtered out and the measurement to be much more robust and reliable. This opens new pathways for the identification of mechanical properties.

Experimental and numerical investigation on carbonitrided steel characterization with spherical indentation

This study investigates the mechanical behavior of a carbonitrided steel, plastically graded material, during a spherical indentation test. We demonstrate that the behavior of a carbonitrided steel can be simulated accurately with a seven layer sample, including the surface, five intermediate layers and the substrate. Moreover, for engineering design simulations which require a lot of calculation time, using three layers provides a good compromise for accuracy.A complete experimental procedure involving seven successive identifications with inverse analysis gave the same results as a simpler procedure proposed in a previous paper. It is shown that the assumption of a linear variation of the properties in the intermediate layers between surface and substrate is valid. This is the first time that an instrumented roller indentation test has demonstrated the reliability of the proposed method for the mechanical characterization of carbonitrided steels with spherical indentation.

Mechanical properties of WC coatings evaluated using instrumented indentation technique

Instrumented indentation tests have been conducted on the surface and cross-section of the two WC based coatings obtained by means of high velocity oxygen fuel thermal spray techniques in order to investigate their mechanical properties. The yield strength of the coatings has been determined by means of the Zeng and Chiu model. In addition, the absolute hardness of the coatings has been determined by means of the modified proportional specimen resistance model. Additionally, conventional spherical indentation tests were carried out on the surface of the coatings, aimed at determining the yield strength by means of the equations employed in classical elastic contact mechanics. The analysis indicates that the yield strength determined from the Zeng and Chiu model is of 3·5 and 3·1 GPa for the WC–10Co–4Cr and WC–12Co coatings respectively. The absolute hardness of the WC–10Co–4Cr coating was found to be of 11·1 GPa, whereas that of the WC–12Co was of 9·3 GPa.

Strain-dependent transition of time-dependent deformation mechanism in single-crystal ZnO evaluated by spherical nanoindentation

We have systematically explored the time-dependent plasticity of (0 0 0 1)-oriented ZnO single crystal through spherical indentation tests. Constant load indentation creep tests were performed in elastic strain and elastic–plastic strain regimes. In both regimes, creep indeed occurred at ambient temperature. With the observed quasi-steady-static strain rate, the stress exponent was found as ~1.361 for elastic contact regime and ~3.077 for elastic–plastic regime, suggesting predominant creep mechanism of diffusion and dislocation, respectively. This strain-dependent transition of creep mechanism is discussed in terms of possible factors affecting the creep in each regime.

Identification of the hardening law of materials with spherical indentation using the average representative strain for several penetration depths

The identification of plastic properties with spherical indentation has been the subject of many studies in the last decades. In the present work, a new method for the determination of the hardening law of materials using the load–displacement curve of a spherical indentation test is proposed. This method is based on the use of an average representative strain. The advantage of the proposed average representative strain is that it is strictly obtained from the material in response to the indentation test. By using various values of penetration depth, the proposed method gives the range of strain for which the hardening law is precisely identified and allows determining a confidence domain that takes into account experimental imprecision and material heterogeneity. The influence of penetration depth and the error formula on the identified Hollomon hardening law are discussed in the present study. The present study clarifies many problems that were observed in previous studies such as the uniqueness of solution and the sensitivity of the indentation test to the plastic parameters of the Hollomon hardening law.

Identification of Stress-Strain Relation of Aluminium Foam Cell Wall by Spherical Nanoindentation

The aim of this paper is to identify, in addition to elastic properties, inelastic properties of tiny aluminium foam cell walls that can be directly deduced from the loaddepth curves of spherical indentation tests using formulations of the representative strain and stress. Constitutive parameters related to plastic material with linear isotropic hardening, the yield point (122 ± 17 MPa) and tangent modulus (950 ± 377 MPa), were obtained in this work. Spherical indentation and uniaxial tension experiments have also been performed on a standard aluminium alloy EN AW 6060 to explore the accuracy of the analytical models used to predict the uniaxial stressstrain in wide strain ranges. Some deviations received from different tests arose and, therefore, their effect on the evaluation of inelastic properties was discussed.

Viscoelastic analysis of single-component and composite PEG and alginate hydrogels

Hydrogels, three-dimensional hydrophilic polymer networks, are appealing candidate materials for studying the cellular microenvironment as their substantial water content helps to better mimic soft tissue. However, hydrogels can lack mechanical stiffness, strength, and toughness. Composite hydrogel systems have been shown to improve upon mechanical properties compared to their singlecomponent counterparts. Poly (ethylene glycol) dimethacrylate (PEGDMA) and alginate are polymers that have been used to form hydrogels for biological applications. Singlecomponent and composite PEGDMA and alginate systems were fabricated with a range of total polymer concentrations. Bulk gels were mechanically characterized using spherical indentation testing and a viscoelastic analysis framework. An increase in shear modulus with increasing polymer concentration was demonstrated for all systems. Alginate hydrogels were shown to have a smaller viscoelastic ratio than the PEGDMA gels, indicating more extensive relaxation over time. Composite alginate and PEGDMA hydrogels exhibited a combination of the mechanical properties of the constituents, as well as a qualitative increase in toughness. Additionally, multiple hydrogel systems were produced that had similar shear moduli, but different viscoelastic behaviors. Accurate measurement of the mechanical properties of hydrogels is necessary in order to determine what parameters are key in modeling the cellular microenvironment. Open image in new window