Indentation Hardness Research Articles

Model for predicting temperature-dependent indentation yield strength and hardness considering size effects

The development of theoretical models to facilitate access to the mechanical properties of materials has been a long-standing pursuit of scholars. In this study, temperature-dependent yield strength models and temperature-dependent hardness models considering indentation size effects were developed under different loading modes (loading to the same displacement or the same load at different temperatures), respectively. Based on the Force-Heat Equivalence Energy Density Principle, the proposed models are free of any adjustable fitting parameters, and the quantitative relationships among temperature, yield strength/hardness, Young's modulus, and indentation load/displacement were successfully captured. All the available 36 groups of experimental data validate the accuracy of the proposed models over a wide temperature range. The yield strength and hardness of metallic materials over a wide temperature range can be easily predicted by using the developed models. Based on the parametric analysis of the models, it has been theoretically clarified for the first time that the two loading modes have opposite indentation size effects for the same material. Although the indentation size effect all decreases gradually with increasing temperature for different loading modes. The influence of loading modes should be noted in future studies where temperature-dependent indentation size effects need to be considered. This work systematically considers the effects of temperature, loading mode, indentation load/displacement, and Young's modulus on the indentation yield strength and hardness, which is important to facilitate the study of the deformation behavior of materials at different temperatures by indentation methods.

Wedge indentation of elastoplastic solids — from single indentation to interaction between indenters

Wedge indentation of elastoplastic solids — from single indentation to interaction between indenters

Effective characterization for the dynamic indentation and plastic parameters acquisition of metals

As a fundamental test technique for the mechanical properties of materials, indentation shows broad application prospects. Compared to the well-studied quasi-static indentation, relatively few and incomplete studies on the dynamic indentation test and characterization have been performed. In this work, a dynamic indentation test technique based on the split Hopkinson pressure bar system is developed, and the corresponding “three-wave method” is proposed to effectively acquire the time-resolved dynamic indentation load and depth. Systematic indentation tests under different loading rates and indenter cone angles are conducted on typical metal materials such as Cu, α-Fe, and α-Ti. Based on the dynamic indentation contact stiffness analysis and indentation theory the indentation hardness under different loading conditions are determined. A procedure for plastic parameter inversion of metal materials, including strain hardening and strain rate strengthening terms based on dynamic indentation, is provided. The effectiveness is verified by the traditional compression test results, providing a new method for characterizing the dynamic mechanical properties of metal materials.

Investigation of microfriction properties of graphene/AlCoCrFeNi high entropy alloy

Applying graphene (Gr) coatings to high-entropy alloys (HEA) is anticipated to enhance their tribological characteristics. The current understanding of the mechanism by which the Gr/HEA is enhanced at the atomic level is still limited. Molecular dynamics simulations revealed the mechanical behavior and strengthening mechanism of the Gr/AlCoCrFeNi HEA during nanoindentation and nanoscratch. The results demonstrate a substantial increase in the indentation hardness of the Gr/AlCoCrFeNi HEA by about 2.4 times. When Gr changed from a single layer to three layers, it further improved (3.2 times for a double layer and 3.9 times for three layers). At the same time, the friction coefficient is effectively reduced. Furthermore, the elevated in-plane stiffness of the Gr coating leads to an expansion of the effective loading area, resulting in increased Shockley dislocation and stair-rod dislocation density within the Gr/AlCoCrFeNi HEA, thereby amplifying the strain hardening effect and reducing subsurface damage. Qualitative experiments confirmed the excellent wear resistance of the Gr/HEA, and coating Gr increased the width of scratches, effectively confirming our simulation results. These findings provide valuable insights for the development and design of Gr/HEA composite coatings with enhanced mechanical properties.

Experimental studies on mechanical properties of Al-7075/TiO2 metal matrix composite and its tribological behaviour

This study explores the fabrication and characterization of an Al-7075/TiO2 metal matrix composites (MMCs) through stir casting, varying TiO2 contents from 2% to 10%. Various tests, including tensile, hardness, and elastic indentation modulus testing, dynamic mechanical analysis, microstructural evaluation, and XRD, were conducted. Tribological analysis involved tribo-pairs of an EN31 disc and a smooth MMCs pin, using a high-temperature Pin-on-disc setup. Microstructural analysis of Al-7075/TiO2 MMCs revealed uniform TiO2 distribution, grain refinement, and enhanced mechanical properties, with XRD confirming structural changes. Tensile tests showed improved ultimate force and stress with increasing TiO2 content, indicating potential for high-strength applications. Hardness assessments demonstrated progressive improvements in Martens, Elastic Indentation, and Vickers Hardness, highlighting the material's suitability for critical wear and tribology applications. The composites exhibited enhanced damping flexural characteristics, especially with 8% TiO2. Maximum and minimum modulus values are reported as 98.9 GPa at 25 °C and 77.3 GPa at 350 °C for 8% TiO2 mix MMC. Tribological performance was improved with lower COF values and wear rates. At elevated temperatures, the wear behavior varied with TiO2 content, influenced by factors such as heat generation and localized welding.

Effect of a subsurface void on the micromechanics of ductile metal indentation using remeshing

Near-surface voids and pores are generated in metal processing operations as diverse as additive manufacturing and powder processing, but their effect on indentation hardness has not been explored outside homogenized frameworks. Here we model the micromechanics of near-surface void deformation up to closure in a wedge-indentation field in ductile metal, and reveal the considerable softening effect of voids on the indentation hardness. Both symmetrically and eccentrically located voids, at various depths below the free surface, are studied. Notably, the extent of apparent reduction in the elastic modulus due to a void is much smaller than its effect on apparent hardness, e.g. 6.5% against 55% for the same void. Critical to the simulations is an adaptive remeshing finite element (FE) framework that allows accurate capture of processes like void closure and void-wall self-contact. The simulations reveal the subsurface plastic strain, strain-rate, and velocity fields with high fidelity, and their radical differences from the radial indentation field in a void-free specimen. These differences include the presence of localized pockets of high and low strain, and the initial accommodation of material displaced by the indenter by a corresponding reduction in void area. Unlike voids under uniform compression, the void-area evolution in indentation shows a characteristic sigmoidal pattern of reduction with indentation depth for all but the smallest voids. Interestingly, the indented surface profile can exhibit a one-sided pile-up feature which is diagnostic of the presence of an eccentrically located sub-surface void. Our remeshing scheme is versatile, as exemplified by its ability to model the extreme deformation associated with two nearly closed-spaced voids under an indenter. Our work shows that void-closure simulations in related applications like forming could benefit from the adoption of a remeshing framework.

Influence of Cr + Si content variation on cutting behavior of TiAlCrSiN HPPMS coatings

As high power pulse magnetron sputtering (HPPMS) technology is becoming popular in cutting tool industry, the development of nanocomposite coating systems such as TiAlCrSiN with this technology presents a new research avenue. Here, the combined effect of Cr and Si contents on properties and cutting behavior of high Al content TiAlCrSiN HPPMS coatings needs further investigation. For this purpose, three HPPMS coatings with Al/Ti ratio x = 1.4–1.5 and varying Cr + Si content, namely (Ti28Al40Cr16Si16)N, (Ti30Al43Cr17Si10)N and (Ti36Al54Cr5Si5)N, were deposited on cemented carbide substrates. In addition to basic characterization, the fracture behavior of the coatings was characterized by scratch tests. The cutting behavior of the coated inserts was exemplarily investigated during dry cutting of normalized medium carbon steel C45 with cutting speed vc = 80 m/min, feed rate f = 0.12 mm and cutting depth ap = 0.8 mm. The tool damage over the cutting time of tc = 35–40 min, as per the tool condition, was observed using light microscopy. Moreover, the damage mechanisms were analyzed in detail at the end of the cutting test using scanning electron microscopy. All coatings showed comparable indentation hardness HIT and indentation modulus EIT. However, an increased Cr + Si content amplified the brittle fracture of the coating under sliding load of scratch test. Moreover, the workpiece material C45 showed a higher adhesion tendency to cutting insert with high Cr + Si content TiAlCrSiN coatings during cutting tests. The tool wear and built-up edge formation increased due to the combined effect of workpiece adhesions and amplified brittle fracture of the coating at considered cutting speed. On the other hand, the inserts with low Cr + Si content coating exhibited better cutting performance and reduced built-up edge formation based on the improved fracture behavior of the coating and lower adhesion tendency of workpiece material to the corresponding coated insert.

Hardness and scratch resistance of chemically strengthened alkali‐borosilicate thin glass

AbstractChemical strengthening of glass represents a standard technology for fabricating damage‐resistant protective covers. Still, little attention has been paid to modifications in the tribological properties of ion‐exchanged glass surfaces. This work reports on scratch testing of a chemically strengthened alkali‐borosilicate thin glass. Diffusive Na+/K+‐ion exchange produces a residual surface compressive layer with compressive stress of 200–340 MPa and layers depths between 16 and 50 µm, depending on exchange temperature and treatment time. This leads to notable changes in the surface mechanical properties, such as an increase in surface Young's modulus, indentation, and scratch hardness. Surprisingly, the Na+/K+‐ion exchange is shifting the onsets of scratch‐induced microcracking and microcracking to lower normal loads. The accelerated buildup of lateral indentation stress in glasses with high scratch hardness was found to be responsible for the lower threshold loads of microcracking and abrasive wear in chemically strengthened alkali‐borosilicate thin glass.

A Novel Viscoelastic Deformation Mechanism Uncovered during Vickers Hardness Study of Bone.

This study investigates the viscoelastic deformation mechanisms of bone as a response to Vickers hardness indentation. We utilized advanced high-resolution scanning electron microscopy (SEM) to investigate a distinct deformation pattern that originates from the indentation site within the bone matrix. The focus of our research was to analyze a unique deformation mechanism observed in bone tissue, which has been colloquially termed as "screw-like" due to its resemblance to a screw thread when viewed under an optical microscope. The primary goals of this research are to investigate the distinctive characteristics of the "screw-like" deformation pattern and to determine how the microstructure of bone influences the initiation and control of this mechanism. These patterns, emerging during the dwell period of indentation, underscore the viscoelastic nature of bone, indicating its propensity for energy dissipation and microstructural reconfiguration under load. This study uncovered a direct correlation between the length of the "screw-like" deformation and the duration of the indentation dwell time, providing quantifiable evidence of the bone's viscoelastic behavior. This finding is pivotal in understanding the mechanical properties of bone, including its fracture toughness, as it relates to the complex interplay of factors such as energy dissipation, microstructural reinforcement, and stress distribution. Furthermore, this study discusses the implications of viscoelastic properties on the bone's ability to resist mechanical challenges, underscoring the significance of viscoelasticity in bone research.

Structure and physicochemical characteristics of the glasses in the system Na2O/BaO/ZrO2/TiO2/SiO2/B2O3/Al2O3 – Influence of the ZrO2 addition on the physico-chemical and mechanical properties

Glasses with the compositions 20.1Na2O∙(23.1-y)BaO∙yZrO2∙23TiO2∙9.8B2O3∙21SiO2∙3Al2O3 with y = 0, 0.5, 1, 2, 3 and 6 mol% were prepared using a traditional melt-quenching technique. The thermophysical properties, i.e. glass transition temperature, Tg and crystallization peak maximum temperature, Tc were determined for the obtained glasses by differential scanning calorimetry and showed that increasing zirconium oxide concentrations resulted in an increasing Tc and an initial decrease followed by an increase of Tg values. The difference Tc-Tg, used as glass stability criterium, increases for ZrO2 concentrations up to 2 mol% and then starts to decrease for the compositions with higher zirconium oxide concentration. The densities were measured by using a helium pycnometer and served to determine main physico-chemical characteristics of the prepared glasses such as molar volume, oxygen packing density and refractive index. The obtained results reveal that the values of the density and of all estimated physico-chemical characteristics increase with increasing ZrO2 concentrations. X-ray photoelectron spectroscopy showed that all elements from the glass composition are present in oxide states with Zr4+ ions being only in octahedral coordination while Ti4+ ions are of 6-, 5- and 4-fold coordination to oxygen. The structure of the glasses was studied by Fourier Transformed Infrared Spectroscopy on powdered samples and the existence of Si–O–Si/O–B–O bending, Si–O–Si rocking, B–O–B bending and B–O–B/B–O–Si stretching vibrations was observed. The presence of BO3, BO4 and SiO4 polyhedra as interconnected as well as isolated structural units and the occurrence of some TiO62− and a larger number of TiO4 and mainly of TiO5− units is suggested. At 570-580 cm−1, a peak typical for the compound BaTiO3 is also registered for all samples. The conducted depth-sensing indentation on the obtained glasses allowed to determine mechanical properties such as universal and indentation hardness, elastic modulus and elastic part of indentation work. Increasing the ZrO2 concentration resulted in increasing elastic moduli which together with the DSC data implies that the addition of ZrO2 leads to structural changes in the glass network and enhanced mechanical properties which results in increased hardness.

The Advanced Assessment of Nanoindentation-Based Mechanical Properties of a Refractory MoTaNbWV High-Entropy Alloy: Metallurgical Considerations and Extensive Variable Correlation Analysis

In the present study, a thorough examination of nanoindentation-based mechanical properties of a refractory MoTaNbVW high-entropy alloy (RHEA) was conducted. Basic mechanical properties, such as the indentation modulus of elasticity, indentation hardness, and indentation-absorbed elastic energy, were assessed by means of different input testing variables, such as the loading speed and indentation depth. The obtained results were discussed in terms of the elasto-plastic behavior of the affected material by the indentation process and material volume. Detailed analysis of the RHEA alloy’s nanoindentation creep behavior was also assessed. The effect of testing parameters such as preset indentation depth, loading speed, and holding—at the creep stage—time were selected for their impact. The results were explained in terms of the availability of mobile dislocations to accommodate creep deformation. Crucial parameters, such as maximum shear stress developed during testing (τmax), critical volume for dislocation nucleation (Vcr), and creep deformation stress exponent n, were taken into consideration to explain the observed behavior. Additionally, in all cases of mechanical property examination and in order to identify those input testing parameters—in case—that have the most severe effect, an extensive statistical analysis was conducted using four different methods, namely ANOVA, correlation matrix analysis, Random Forest analysis, and Partial Dependence Plots. It was observed that in most of the cases, the statistical treatment of the obtained testing data was in agreement with the microstructural and metallurgical observations and postulates.

Selective growth of recrystallizing grains into well-characterized deformed aluminum at hardness indentation

The selective 3D growth of multiple recrystallization nuclei/grains around a hardness indentation into a deformed Al grain has been quantified through a new approach that combines two synchrotron techniques: 3D X-ray Laue micro-diffraction and diffraction contrast tomography. The former is used to characterize the deformed microstructure and nucleation, while the latter to track the nuclei's growth during interrupted in situ annealing. The combined 4D (x,y,z,t) datasets enable a detailed quantification of the local deformed microstructure consumed by the nuclei/grains and the boundary characteristics between them, including the stored energy and anisotropy of the orientation distribution of the deformation matrix, as well as the misorientation of the moving and non-moving boundary segments. It is found that only certain nuclei can grow into large sizes, and the growth is heterogeneous both among recrystallizing grains and along different directions. Neither the local stored energy nor the boundary misorientation, whether considered individually or in combination, can fully account for the observed growing and shrinking behavior. The growth difference along different directions is related to the deformation microstructure, specifically the geometrical alignment of dislocation boundaries. Furthermore, the effects of impingement of other recrystallizing grains, recovery of the matrix, and elastic strain/stress, on the growth heterogeneities are discussed in detail with a view towards developing advanced modeling with improved predictability of local recrystallization phenomena. The present study demonstrates the effectiveness of the new approach in enabling 3D analysis of recrystallization in complex materials, with potential applications in the development of advanced engineering materials.

Realization of Martens hardness method in macro range with high accuracy force and indentation depth

TÜBİTAK UME Hardness Laboratory has been working on instrumentation in the field of hardness metrology since 2005 and three generations of hardness standardizing machines were developed since then to be used as reference (calibration/standardizing) machines in Türkiye. In former designs conventional hardness methods such as Rockwell, Brinell and Vickers scales were the main scope of the projects. In the final Project that was supported and funded by TÜBİTAK UME to develop three hardness standard machines to be used as national standards for the conventional hardness scales mentioned, the Instrumented Indentation Test (IIT) was also aimed at and some parameters like Martens hardness, creep, indentation hardness, (elastic and plastic) indentation work, etc. were also implemented onto the machines developed. It was a good occasion that the measurands in Rockwell hardness and IIT were the same, force and indentation depth besides time and this made it easier to realize the IIT on the same machine with a more suitable design to achieve the highest accuracy in terms of the measurands mentioned. In this paper the new design of the Rockwell-Brinell-Vickers hardness standard machine developed also for Martens hardness in macro range (3 kgf – 150 kgf) and preliminary Martens hardness measurements are explained.

Meso-mechanics of packed C-S-H colloids by nanoindentation: A coarse-grained molecular dynamics study

Colloidal calcium silicate hydrate (C-S-H) gel significantly contributes to cement paste's strength and durability. In this study, the coarse-grained (CG) models for packed C-S-H colloidal particles with different packing densities were established and meso-mechanically assessed via nanoindentation. Load-depth curves showed indentation hardness values (0.55, 1.16, and 2.63 GPa) for the systems with packing densities (η) of 0.50, 0.55, and 0.60, respectively. Structurally, the nano-indenter had a broader impact on low-density C-S-H (η=0.5, impact radius = 118 and 150 nm respectively at indentation depths = 50 and 100 nm) than high-density C-S-H (η=0.6, impact radius = 106 and 140 nm at the same depths). Low-density colloids were easily compressed without deforming low-depth nearby regions, while high-density colloids were squeezed laterally, causing deformation in these regions. Packed C-S-H colloids displayed two-stage stress relaxation behavior: rapid initial relaxation due to nanoindentation-induced instability, followed by slower relaxation due to C-S-H's viscous nature. Furthermore, higher loading rates caused initial unstable deformation, but better stability after stress relaxation compared to lower loading cases. However, the effect of loading rate on the impact region was negligible. These meso-level insights enhance our comprehension of the C-S-H gel properties in cement paste as well as the nanoindentation mechanics.

Low temperature nitriding behavior in annealed 2205 duplex stainless steel

ABSTRACT Low-temperature gaseous nitriding response of annealed 2205 stainless steel was investigated through a series of nitriding treatments at different temperatures in the range 380–430°C for 25 h. Reflected light microscopy, X-ray diffraction and hardness indentation were utilized to investigate the dependence of the formation of nitrides and cracks on pre annealing temperatures and subsequent nitriding parameters. For most annealing and nitriding conditions applied, the surface adjacent region of the steels was transformed into expanded austenite, or a mixture of expanded austenite and expanded ferrite, supplemented by the presence of iron-based nitrides. Nitriding at a relatively low temperature at a gentle nitriding potential was found to be acceptable as it resulted in a sound nitrided case, where neither chromium nitrides nor cracks developed. Annealing at a relatively low temperature can improve the threshold of nitriding temperature up to 400°C without cracking, while annealing at a high temperature promotes the formation of nitrides.

Micromechanical characterization of zirconia and silicon nitride ceramics using indentation and scratch methods

Micromechanical characterization of brittle ceramics remains challenging due to the difficulty in sample preparation required by conventional tests. The micromechanical properties (e.g., elastic modulus EIT, indentation hardness HIT, and fracture toughness KIC) of ZrO2 and Si3N4 were investigated by indentation and scratch tests with different indenters (e.g., Vickers, Knoop, and Berkovich indenters) under various loads. The ratio of the true hardness by the Vickers indenter over that by the Knoop indenter is approximately a constant of 1.13 and independent of material. Elastic recovery of residual imprint by the Knoop indenter was also used to assess elastic modulus of ZrO2 and Si3N4, and modified equations were proposed. The length of Vickers indenter-induced cracking was found to be proportional to the applied load under large loads, and a modified formula for calculating fracture toughness was proposed for ZrO2 and Si3N4, which have relatively large fracture toughness of about 9 MPa⋅m1/2. The critical void volume fraction f* in the nanoindentation energy-based methods was found to linearly decrease with the exponent mf of the power-law equation used for curve fitting of the degradation of HIT or EIT with hmax. The determination of fracture toughness by scratch methodology was found to be affected by mechanical properties of material, indenter geometry, and data range.

Surface Composites Synthesized through the Incorporation of Atomic Layer Deposited AlOx into Nanoporous Fuzzy Tungsten.

The incorporation of energetic helium gaseous species into materials such as tungsten (W) imparts intrinsic surface fragility, yielding fuzzy tungsten. To enhance the robustness of the surface layers, aluminum oxide (AlOx) was deposited by atomic layer deposition into the fuzzy W. The conformally deposited ceramic yields a new class of surface composites. Structural characterization of the fuzzy W-AlOx composites through nanoindentation testing indicated enhanced indentation modulus (Eind) and hardness (Hind) and was modeled through various rules of mixtures approaches. The distribution of AlOx in fuzzy W was explored and a systematic study of the extent of incorporation of the AlOx into the fuzzy W was carried out. The synthesized composites may be utilized for improved structural characteristics, e.g., in reducing crack initiation and fracture.

Mechanical Response of Cu/Sn58Bi-xNi/Cu Micro Solder Joint with High Temperatures

Sn58Bi solder is considered a promising lead-free solder that meets the performance requirements, with the advantages of good wettability and low cost. However, the low melting point characteristic of Sn58Bi poses a serious threat to the high-temperature reliability of electronic products. In this study, Sn58Bi solder alloy based on nickel (Ni) functionalization was successfully synthesized, and the effect of a small amount of Ni on creep properties and hardness of Cu/Sn58Bi/Cu micro solder joints at different temperatures (25 °C, 50 °C, 75 °C, 100 °C) was investigated using a nanoindentation method. The results indicate that the nanoindentation depth of micro solder joints exhibits a non-monotonic trend with increasing Ni content at different temperatures, and the slope of the indentation stage curve decreases at 100 °C, showing that the micro solder joints undergo high levels of softening. According to the observation of indentation morphology, Ni doping can reduce the indentation area and accumulation around the indentation, especially at 75 °C and 100 °C. In addition, due to the severe creep phenomenon at 100 °C, the indentation hardness rapidly decreases. The indentation hardness values of micro solder joints of Cu/Sn58Bi/Cu, Cu/Sn58Bi-0.1Ni/Cu, and Cu/Sn58Bi-0.2Ni/Cu at 100 °C are 14.67 ± 2.00 MPa, 21.05 ± 2.00 MPa, and 20.13 ± 2.10 MPa, respectively. Nevertheless, under the same temperature test conditions, the addition of Ni elements can improve the high-temperature creep resistance and hardness of Cu/Sn58Bi/Cu micro solder joints.

Scratch hardness of diamond-like carbon (DLC) coatings deposited by closed-field unbalanced magnetron sputtering

Thin coatings are subject to scratch and wear damage in tribological applications. Scratch hardness numbers are used to evaluate scratch and abrasive wear resistance. Few studies have measured the scratch hardness of thin films, and a proper scratch hardness measurement method for thin coatings is still lacking. In this study, the scratch hardness of these DLC coatings was measured at both micro-scale and nano-scale, respectively. The micro-scratch test using a 200 µm tip is an inapplicable method because the substrate effect has dominated the scratch hardness measurement. On the other hand, a nano-scratch hardness test using a sharper tip is an effective method to measure the scratch hardness of thin coatings. Although the scratch hardness introduces a lateral force compared with the indentation hardness, it well correlates with the nano-indentation hardness. The ratio of the scratch hardness to the indentation hardness is close to 1 for DLC coatings due to the amorphous structure. It proves that the tangential force induced by scratching does not influence the hardness property. In addition, a simple approach is proposed to obtain the scratch hardness of DLC coatings qualitatively without width measurement.

Microstructure-Informed Prediction of Hardening in Ion-Irradiated Reactor Pressure Vessel Steels

Ion irradiation combined with nanoindentation is a promising tool for studying irradiation-induced hardening of nuclear materials, including reactor pressure vessel (RPV) steels. For RPV steels, the major sources of hardening are nm-sized irradiation-induced dislocation loops and solute atom clusters, both representing barriers for dislocation glide. The dispersed barrier hardening (DBH) model provides a link between the irradiation-induced nanofeatures and hardening. However, a number of details of the DBH model still require consideration. These include the role of the unirradiated microstructure, the proper treatment of the indentation size effect (ISE), and the appropriate superposition rule of individual hardening contributions. In the present study, two well-characterized RPV steels, each ion-irradiated up to two different levels of displacement damage, were investigated. Dislocation loops and solute atom clusters were characterized by transmission electron microscopy and atom probe tomography, respectively. Nanoindentation with a Berkovich indenter was used to measure indentation hardness as a function of the contact depth. In the present paper, the measured hardening profiles are compared with predictions based on different DBH models. Conclusions about the appropriate superposition rule and the consideration of the ISE (in terms of geometrically necessary dislocations) are drawn.