Indentation Of Materials Research Articles

NUMERICAL MODELING OF DETERMINING THE ROCKWELL HARDNESS NUMBER OF A STEEL SAMPLE

In steel Hardness is a mechanical property that indicates the resistance of a material to local plastic deformation caused by mechanical indentation. In engineering, hardness is mainly used to determine the properties of various materials. In mechanical solids, the study of the hardness of materials is usually limited to the study of metals and their mechanical behavior. To understand the mechanism of hardness in metal structures, a basic understanding of materials science is necessary. Accurate hardness measurement is of great practical importance in the technical diagnosis of potentially hazardous industrial equipment (pipelines, pressure vessels, metal structures). This is primarily due to the fact that this characteristic has a strong correlation with strength and yield strength, which largely determine the possibility of further operation of the equipment. At the same time, one of the main advantages of hardness measurement is the speed of its determination and the non-destructive nature of its control. A finite element model was developed for the indentation process, and the contact radius and contact pressure were obtained. The Rockwell hardness measurement process was modelled in accordance with the test methodology of DSTU ISO 6508-1:2013. The indentation process was modelled using ANSYS software with different contact models and different loads. The relevance of solving the problem of modelling the process of determining the surface hardness number using the FEM software ANSYS is determined by the high degree of automation of the solution process. During the modelling, it is assumed that the material of the sample into which the indenter of any shape is pressed is homogeneous isotropic and elastoplastic according to the kinematic plasticity model. This model corresponds to the behavior of steels. In addition, the indenter material is isotropic and linearly elastic. In the developed numerical model, the indenter is taken in the form of a tungsten carbide ball, which corresponds to the scheme for determining the hardness number on the "B" scale. In conditions of limited access to laboratory equipment, numerical modelling of the process of determining the hardness number allows students to demonstrate all stages of the test at a qualitatively new level, and further, to compare with the results of full-scale tests. Keywords: structural materials, Rockwell method, finite element model, indenter, hardness.

A Comprehensive Review of Indentation of Gels and Soft Biological Materials

Abstract Indentation measurement has emerged as a widely adapted technique for elucidating the mechanical properties of soft hydrated materials. These materials, encompassing gels, cells, and biological tissues, possess pivotal mechanical characteristics crucial for a myriad of applications across engineering and biological realms. From engineering endeavors to biological processes linked to both normal physiological activity and pathological conditions, understanding the mechanical behavior of soft hydrated materials is paramount. The indentation method is particularly suitable for accessing the mechanical properties of these materials as it offers the ability to conduct assessments in liquid environment across diverse length and time scales with minimal sample preparation. Nonetheless, understanding the physical principles underpinning indentation testing and the corresponding contact mechanics theories, making judicious choices regarding indentation testing methods and associated experimental parameters, and accurately interpreting the experimental results are challenging tasks. In this review, we delve into the methodology and applications of indentation in assessing the mechanical properties of soft hydrated materials, spanning elastic, viscoelastic, poroelastic, coupled viscoporoelastic, and adhesion properties, as well as fracture toughness. Each category is accomplished by the theoretical models elucidating underlying physics, followed by ensuring discussions on experimental setup requirements. Furthermore, we consolidate recent advancements in indentation measurements for soft hydrated materials highlighting its multifaceted applications. Looking forward, we offer insights into the future trajectory of the indentation method on soft hydrated materials and the potential applications. This comprehensive review aims to furnish readers with a profound understanding of indentation techniques and a pragmatic roadmap of characterizing the mechanical properties of soft hydrated materials.

In-situ synthesis and oxidation behaviors of Ti-xAl coatings by high-frequency induction heated combustion

Ti-xAl coatings (x=25, 33.3, 50, 66.7, and 75 at%) were fabricated in situ using high-frequency induction heating synthesis (HFIHCS). The process parameters for preparing Ti-Al coatings via HFIHCS were orthogonally optimized employing the finite element method. The effect of the aluminum content on the microstructures and phase compositions of Ti-Al coatings fabricated by HFIHCS, as well as their oxidation behaviors at 900℃ for 100 h was investigated. The results showed that the distribution of interfacial temperature difference was influenced by induced current (62.11%), relative density of compact (9.86%), and indenter material (28.03%). The minimum interfacial temperature difference was achieved with an induced current of 300 A, a graphite indenter material, and a compact density of 82.9%. The Ti-xAl coatings exhibited a core (Ti)-shell (TixAly) ring structure. The rise in aluminum content in the Ti-xAl coatings led to a gradual reduction in the titanium-rich phase, accompanied by a progressive increase in the aluminum-rich phase and the interface thickness of zones Ⅰ and Ⅱ. The porosities of Ti-xAl coatings containing over 50 at% aluminum exhibited an order of magnitude higher than those of Ti-xAl coatings with 50% aluminum or lower. The mechanisms of reaction, pore-forming, and interfacial diffusion for Ti-xAl coatings were predominantly controlled by dissolution-precipitation, thermal expansion of intrinsic pores within the cold-pressed compact and voids formed after molten aluminum flow, and liquid-solid co-diffusion, respectively. The increase in aluminum content in the Ti-xAl coatings led to in a gradual decrease in its oxidative weight gain, a shift in the oxidation kinetics from a linear-parabolic to a parabolic law, and an enhancement in preservation of internal core-shell characteristics and the likelihood of forming a protective layer of thin Al2O3. The oxidation behaviors of Ti-xAl coatings with a core-shell structure were co-controlled by the aluminum content and the porosity affected by the aluminum content.

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.

Non-equibiaxial residual stress evaluation methodology using simulated indentation behavior and machine learning

Measuring the residual stress in the components in nuclear power plants is crucial to their safety evaluation. The instrumented indentation technique is a minimally invasive approach that can be conveniently used to determine the residual stress in structural materials in service. Because the indentation behavior of a structure with residual stresses is closely related to the elastic-plastic behavior of the indented material, an accurate understanding of the elastic-plastic behavior of the material is essential for evaluation of the residual stresses in the structures. However, due to the analytical problems associated with solving the elastic-plastic behavior, empirical equations with limited applicability have been used. In the present study, the impact of the non-equibiaxial residual stress state on indentation behavior was investigated using finite element analysis. In addition, a new nonequibiaxial residual-stress prediction methodology is proposed using a convolutional neural network, and the performance was validated. A more accurate residual-stress measurement will be possible by applying the proposed residual-stress prediction methodology in the future.

Asymmetric indentation: problem and solution

Vickers and Knoop testers are the most common tools used to measure the hardness of materials. However, a very small tilt in the sample surface even in the order of a fraction of a degree produces a noticeable asymmetry, which affects the accuracy of the measured hardness. In this investigation, a mathematical approach has been used to correct asymmetry in the Vickers and Knoop indentations in both metallic and ceramic materials. Measurements were taken for metals such as aluminium 6061(Al-6061), 304 stainless steel as well as various zirconia toughened ceramic materials including tetragonal zirconia doped with: 2.5 mol% Y2O3 (TZ2.5Y), 3 mol% Y2O3 (TZ3Y) and the composite containing 20 wt% alumina (TZ3Y20A), all prepared from commercial powders. A hardness tester equipped with Vickers and Knoop indenters was used for hardness and elastic modulus determination. Optical and scanning electron microscopes have been used to get the indentation micrographs. The method enabled accurate determination of both hardness and elastic modulus from corrected Vickers and Knoop indentations. The hardness and elastic modulus values obtained in this study are in good agreement with reported data for similar materials. The results obtained in this study have been successfully validated using the Zwick reference block. The developed method is readily applicable for the most widely used Vickers hardness machines for the correction of asymmetric indentations if existing, consequently leading to accurate determination of the hardness.

Towards a reliable nanohardness-dose correlation of ion-irradiated materials from nanoindentation tests: A case study in proton-irradiated vanadium

Nanoindentation has been commonly used for evaluating the hardening effects of ion-irradiated materials. Nonetheless, establishing a reliable correlation between the hardness and irradiation dose is never trivial, due to not only the intrinsic analytical challenges of this technique, such as size effects, pile-up effects, etc., but also the fact that the irradiation dose is usually uneven inside the stress volume under the indenter, especially near the depth of dose peak. In the present work, the hardening in pure V irradiated with 1 MeV proton at various fluences is investigated by using nanoindentation tests, combined with the characterization of both irradiation defects and dislocations of the indented material. Under the cross-sectional indentation, we demonstrate that the nanohardness-dose correlation can be unified from the samples irradiated to different fluences and at different depths on each sample, as long as the lateral spanning of indenter is carefully considered. Crystal-plasticity finite-element-modeling simulation results can well describe the measured hardening-dose correlation, as well as the observed features on the change in strained fields and pile-up effects after irradiations. Moreover, the measured hardness is further corrected for the dose-dependent pile-up based on the surface profiling, and the indentation size effects based on surface indentation tests for deeper indentation depth, to reach a reliable connection between the hardening effects and the irradiation dose. Furthermore, microstructural characterization of the indented materials shows the pinning of dislocation by irradiation defects and the sweeping of those defects during dislocation migration. Molecular dynamics results suggest that the drag of loops by edge dislocations might cause the annihilation or aggregation of small loops, which could be responsible for the lower density but the larger size of irradiation loops in the strained region.

Investigation of the Material Elasto-Plastic Response under Contact Indentation: The Effect of Indenter Material

When dealing with joints and bearings, high pressures localised at the contact interface lead to residual plastic strain. The present paper combines numerical simulations and experimental tests to investigate the role of the material constitutive law in the indentation process. Numerical indentation tests between similar materials showed a good agreement with the experiments when classical material laws recovered from tensile-compressive tests on bulk samples were accounted for. On the other hand, when simulating indentation between different materials in contact, the comparison between the numerical and experimental results highlighted the limits of using classical material laws. Bilinear material laws were then derived for different steel materials (ASP 2060 PM, 100Cr6, 440C, Marval X12, and Z15 CN17-03) in contact with a ceramic indenter, leading to the correct simulation of the residual indentation profiles (error less than 5%). The proposed approach to determine suitable material laws for indentation between dissimilar materials can be further applied when dealing with applications involving contacts undergoing local plastic deformation.

Characterizing dynamic load propagation in cohesionless granular packing using force chain

When dynamic load is applied on a granular assembly, the time-dependent dynamic load and initial static load (such as gravity stress) act together on individual particles. In order to better understand how dynamic load triggers the micro-structure's evolution and furtherly the ensemble behavior of a granular assembly, we propose a criterion to recognize the major propagation path of dynamic load in 2D granular materials, called the “dynamic force chain”. Two steps are involved in recognizing dynamic force chains: (1) pick out particles with dynamic load larger than the threshold stress, where the attenuation of dynamic stress with distance is considered; (2) among which quasi-linear arrangement of three or more particles are identified as a force chain. The spatial distribution of dynamic force chains in indentation of granular materials provides a direct measure of dynamic load diffusion. The statistical evolution of dynamic force chains shows strong correlation with the indentation behaviors.

Fluctuation of puncture force in medical needle puncture of soft solids

Puncture of soft solids involves the process of piercing through a soft solid material using a sharp object, which is of great interest in biomedical and industrial applications. In this work, we investigate the puncture of soft solids by a commercial medical needle using polyacrylamide (PAAm) hydrogel as the model material. We measure the relationship between the depth of puncture and force exerted on the needle as it penetrates and retracts from the PAAm hydrogel at different speeds, and interpret the results of the experiments. We find that the puncture force fluctuates with the increasing puncture depth during needle penetration, while the retraction force decreases almost linearly with the retraction depth. Both the puncture and retraction forces, as well as the amplitude and period of the puncture force fluctuation, are positively related to the loading speed. We estimate the size of the crack, which is difficult to directly recognize from experiments, induced by puncture using the critical puncture depth at which the needle first pierces the hydrogel. We find that the size increases with the puncture speed. Moreover, we obtain a work balance relationship between the energy done by the puncture force minus friction (Fp-Fr) and the sum of the energy required for crack propagation and the elastic energy stored in the hydrogel bulk. These findings from our research contribute to a comprehensive understanding of deep indentation and puncture in soft materials. These results carry important implications for the design of biomedical and industrial devices, where the puncturing of soft solids is a critical procedure.

Calculation of the depth of rope-tightening soft material and analysis of its relationship with the tightening force

To analyze the relationship between the tension force of a rope and the bundled material's indentation, a model of tightening by rope for soft material was designed for testing. By calculating the indentation depth of soft materials from rope stretching displacement, the variation law of the indentation depth of tightening soft materials with different mechanical properties of ropes was analyzed. As the stretching progresses, the more the rope winding turns, and the shallower the indentation depth. The friction coefficient between the soft material and the rope does not significantly affect the theoretical indentation depth. The theoretical indentation depth of high-strength ropes shows a linear variation pattern. The theoretical indentation depth of high-extension ropes is negative. With the theoretical indentation depth of the ordinary rope increasing first and then decreasing, its indentation depth curve shows a parabolic shape. Aromatic polyester rope, cotton chainette thread, and polypropylene rope were used to tighten ethylene-vinyl acetate (EVA) foam and test the indentation depth. The results show that the deformation of the rope is much lower than that of the EVA foam, and the depth of the strangulation is closely related to the tensile displacement and tightening tension. The measured value of the indentation depth is lower than the calculated value, and the greater the stiffness of the rope, the smaller the difference between the measured and calculated indentation depth. The indentation depth method was used to calculate the tightening effect of ropes with high rigidity and has excellent results.

Probing soft fibrous materials by indentation.

Indentation is often used to measure the stiffness of soft materials whose main structural component is a network of filaments, such as the cellular cytoskeleton, connective tissue, gels, and the extracellular matrix. For elastic materials, the typical procedure requires fitting the experimental force-displacement curve with the Hertz model, which predicts that f=kδ1.5 and k is proportional to the reduced modulus of the indented material, E/(1-ν2). Here we show using explicit models of fiber networks that the Hertz model applies to indentation in network materials provided the indenter radius is larger than approximately 12lc, where lc is the mean segment length of the network. Using smaller indenters leads to a relation between force and indentation displacement of the form f=kδq, where q is observed to increase with decreasing indenter radius. Using the Hertz model to interpret results of indentations in network materials using small indenters leads to an inferred modulus smaller than the real modulus of the material. The origin of this departure from the classical Hertz model is investigated. A compacted, stiff network region develops under the indenter, effectively increasing the indenter size and modifying its shape. This modification is marginal when large indenters are used. However, when the indenter radius is small, the effect of the compacted layer is pronounced as it changes the indenter profile from spherical towards conical. This entails an increase of exponent q above the value of 1.5 corresponding to spherical indenters. STATEMENT OF SIGNIFICANCE: The article presents a study of indentation in network biomaterials and demonstrates a size effect which precludes the use of the Hertz model to infer the elastic constants of the material. The size effect occurs once the indenter radius is smaller than approximately 12 times the mean segment length of the network. This result provides guidelines for the selection of indentation conditions that guarantee the applicability of the Hertz model. At the same time, the finding may be used to infer the mean segment length of the network based on indentations with indenters of various sizes. Hence, the method can be used to evaluate this structural parameter which is not easily accessible in experiments.

Nanoindentation test of a DLC coated high-speed steel substrate using a two-dimensional axisymmetric finite element method

Diamond-Like Carbon is a thin coating that has high hardness, chemical inertia and low coefficient of friction characteristics that can improve the performance of cutting tools and mechanical components. To identify the characteristics of this film it is important to carry out mechanical tests, such as nanoindentation, which can provide important information in understanding and improving coating techniques and, when combined with the finite element method, leads to more detailed results of material behavior during testing. Considering this, the present work aimed to study and apply a nanoindentation test simulation of a Diamond-Like Carbon coated high-speed steel specimen. The results of the indenter penetration versus load were compared with experimental data seeking correlation of the model. A great proximity was observed between the experimental results and the results obtained in the simulation. When comparing the final indentation force, a proximity of 93.9 % and 95.5 % was found for the model with only one indentation and with partial indentations, respectively, thus validating the created model. The impact of modifying the indenter tip radius for the partial indentation method was also evaluated. The tip radius variation did not have a significant impact on the results of final indentation force and material hardness. The material hardness was also obtained in the simulation, which was equal to the experimental: 9.25 GPa.

A novel model for obtaining both equi-biaxial and uniaxial residual stress of metallic materials by instrumented sharp indentation

As a new method, the indentation technique has become popular for measuring residual stress and mechanical properties at surfaces due to its simplicity of use, in-situ applicability, and nano-to-macro range of measurements. In this study, a novel model for obtaining the surface residual stress of metallic materials is proposed by instrumented sharp indentation. The metallic material containing surface residual stress is equivalent to another non-stressed material with a different yield stress in Hollomon law from the perspective of indentation response. Thus, a unified equivalent material indentation (UEMI) model is established for measuring both equi-biaxial and uniaxial residual stresses within metallic structural materials. Additionally, only five parameters need to be calibrated via finite element analysis (FEA) in this model. Moreover, the novel model is successfully verified using lots of simulated materials from FEA and seven metallic materials experimental data found in the references. The results show that the predicted residual stress agrees well with the pre-applied residual stress which meeting the needs of engineering.

Indenting glasses with indenters of varying stiffness and sharpness

In this study, the effects of both indenter sharpness and stiffness on the indentation response of oxide glasses have been investigated. Using five different indenters, the indentation response in terms of glass deformation mechanism, cracking behavior, and hardness has been examined for three glasses (sodium silicate, sodium borate, and sodium borosilicate). For right square-based pyramidal diamond indenters with varying tip angle, increased indenter sharpness reduces the magnitude of the indentation size effect. Additionally, increased indenter sharpness lowers the crack initiation resistance, which is linked to a reduction of densification. For indenters with the same geometry but made of different materials, the effect of the indenter material is insignificant when the indenter is substantially stiffer than the specimen. When the stiffness of the indenter is only slightly higher or similar to that of the sample, substantial deformation of the indenter occurs, reducing the effective indenter sharpness and hence affecting the indentation response.

Semi-analytical model and mechanical test method of flat indentation for ductile materials

Mechanical properties of small-size or in-service structural materials are challenging to obtain using traditional test methods. In this study, a theoretical indentation model, based on the energy-density equivalence, is proposed to describe the relationship between the strain energy and the indentation displacement under flat cylindrical indenter loading and a modified Brinell hardness prediction model. A series of tests for uniaxial tension, Brinell hardness, and flat indentation was performed for ten ductile materials. The results indicate that the stress–strain curves and strengths obtained by the flat indentation test method based on the indentation model are close to the tensile results. We also show that the predicted Brinell hardness agrees closely with that obtained by conventional hardness tests.

Deriving exponential and power law slow crack growth parameters from dynamic fatigue of indented or as-polished window material coupons

Knowledge of slow crack growth rate in a window material is required to determine the design life of a window in which cracks grow under the influence of applied service stress. Parameters that characterize crack growth rate can be measured by dynamic fatigue in which coupons are taken to failure at several constant stress rates. The slower the stress rate, the more time is available for cracks to grow during the strength measurement, and the lower the stress at which the coupon fails. That is, coupons tested at a slower stress rate are weaker than coupons tested at a faster stress rate. The rate of slow crack growth is commonly fit to either a power law or an exponential law. The exponential law provides the more conservative estimate of design life and is prescribed for use by the U.S. National Aeronautics and Space Administration to design windows for manned vehicles. Well-established analytical equations are used to derive the power law crack growth parameters from dynamic fatigue measurements of as-polished (unindented) coupons. There are no exact analytical equations to derive power law parameters from indented coupons or to derive exponential law parameters from unindented or indented coupons. Approximate procedures have been used to derive crack growth parameters when there are no exact equations. We now describe a numerical method that gives the power and exponential laws for both unindented and indented coupons by least-squares fitting of dynamic fatigue measurements. A MATLAB code is provided to carry out the calculations.

A study of effect factors on thermal drift rates during cryogenic indentation via Taguchi design and finite element method

Although nanoindentation at cryogenic temperatures has been widely used to evaluate mechanical deformation behaviors and damage mechanism, thermal drift has a significant effect on accuracy and reliability of measurements. In order to acquire high-quality data of indentation, this paper proposes a novel evaluation method on the significance of effect factors and their interactions for thermal drift rates during cryogenic indentation using a Taguchi robust design combined with finite-element analysis. The results of signal-to-noise (S/N) and analysis of variance (ANOVA) are indicated that the effects of the five control factors on the measurement of thermal drift are ranked as: specimen material > indenter tip assembly’s material > loading rate > testing temperature > peak of load. It demonstrates that temperature-dependent material properties for the contact pair are the most important factors in determining the thermal drift rate. Therefore, an upgraded indenter tip assembly with the Invar 36 shaft and the diamond tip is proposed for the cryogenic indentation of different materials. To further reduce thermal drift, an atmosphere pre-cooling method for tip assembly and specimen during cryogenic indentation is recommended owing to its minimum thermal drift and high homogeneity of temperature.

ε–greedy automated indentation of cementitious materials for phase mechanical properties determination

Microindentation and nanoindentation tests are very useful to assess the micromechanical properties of materials. However, statistical indentation tests require large matrices of indents for heterogeneous materials, which can be time-consuming. Given that specific properties of only one phase of interest can be looked for, a novel procedure is proposed to locate indents automatically. The procedure uses an ε–greedy strategy to determine the next indents to perform. The strategy is informed by the nature of predicted indents using unsupervised clustering of the indentation curves and Gaussian Process Classification. The influence of several parameters has been assessed, and the best combination performance has been quantified in the case of the microindentation of a cementitious mortar sample (500 mN) and the nanoindentation of a cement paste (1 mN). The proportion of indents in the phase of interest increased by around 20% in both cases, paving the way for faster indentation experiments.

Indentation of piezoelectric micro- and nanostructures

This study is focused on obtaining a comprehensive understanding of the influence of geometry — size and shape — on the indentation response of a large set of piezoelectric small-volume structures such as nanoislands, nanowires and thin films. Using three-dimensional finite element modeling, the complex interplay between the properties of the indented materials and the indentation response of piezoelectric micro- and nanostructures is analyzed. It is demonstrated that: (i) In general, the indentation response of thin film structures tends to be much stiffer than that of the piezoelectric nanoisland and nanowires, resulting in more charges being generated during the indentation of the thin-film structures. (ii) The indentation of the piezoelectric nanowire structures with a spherical indenter whose radius is substantially larger than the width of the nanowires, introduces a combination of deformation modes — structural bulging and indentation-induced compression. The combined effect of two deformation modes produces a maximum in the charges generated during the indentation process on a nanowire structure with a particular aspect ratio (i.e., wire width/wire height), which is greater than that produced in nanoisland and thin films structures with the same characteristic size.