Indentation Test Method Research Articles

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.

A novel impact indentation technique with dynamic calibration method for measurement of dynamic mechanical properties

High strain rates and continuous real-time data acquisition are difficult to balance in existing impact indentation techniques. Meanwhile, the inaccuracy of the testing P-h curves limits the development of quantitative applications for dynamic testing of mechanical properties at micro region. This article develops a momentum exchange impact indentation testing method, which extends the testing range of strain rate to above 105 s−1, and at the same time avoids secondary impact. Impact indentation tests are conducted on single-crystal aluminum specimens with impact velocity from 76.9 to 176 mm/s. Based on calibrated data, the comparison of calculation methods for dynamic hardness is carried out. The dynamic elastic modulus is obtained by means of the Oliver-Pharr method, which increases from 71.9 to 89.4 GPa with increasing impact velocity. A multi-dimensional data analysis method is proposed based on the obtained experimental data to quantitatively study the damping and stiffness characteristics of materials. This testing method is particularly useful for quantitatively obtaining the micro region dynamic mechanical properties of solid materials at high strain rates.

Spherical Indentation and Implementation of S3/P for yield stress determination of brittle materials

A mathematically transparent and robust experimental method has been developed to estimate the yield stress of brittle materials through the analysis of depth-sensing spherical indentation. Employing Hertzian contact mechanics, an elastically invariant ratio based on the simple equation S3/P=6REr2, (where S and P are contact stiffness and indentation load, respectively) has been derived that enables more accurate and confident determination of the transition from elastic to inelastic deformation; a transition that the yield stress dictates and represents. Using two diamond spheres with radii of 3.2 and 8.6 μm, the indentation test method and analyses are applied to two vitreous silicates: Corning's HPFS 7980® fused silica and Vitro's Starphire® soda-lime silicate. The estimated yield strengths are 8.15 GPa ± 2.5 % for the fused silica and 6.1 GPa ± 3.3 % for the soda-lime silicate, and both were independent of indenter radius. Verification of this new experimental method is demonstrated with an as-drawn titanium by showing equivalence of measured yield stress by its spherical indentation and that from uniaxial compression testing. This method will enable easier and more confident estimation of yield stress in brittle materials - a property that historically has been elusive to measure for these materials using common laboratory mechanical test methods.

Rapid evaluation of trade-offs between strength and impact toughness of wheel steels by instrumented spherical indentation test

In this paper, an improved size-independent instrumented spherical indentation test (ISIT) method was proposed to determine tensile strength and fracture toughness on wheel rims of two different types of wheel steels. Additionally, Charpy impact specimens were taken from three specific positions on the wheel rims and subjected to standard Charpy impact testing. The resulting Charpy impact energy (CVN) were matched with the fracture toughness measured by ISIT (KIc,IT) at the same positions. There was a clear linear correlation between CVN and the square of KIc,IT, which was consistent with the established relationship between both properties as determined by conventional Charpy impact and compact tension tests. Therefore, we expanded the ISIT method to study the impact of cooling rates on the variation of yield strength and Charpy impact energy across the wheel rim. To accomplish this, we designated additional testing points on the wheel rim using the ISIT method. The investigation found trade-offs between strength and impact toughness of wheel steels under different cooling rates. The above findings demonstrated the effectiveness of using the ISIT method, which facilitated high-resolution fracture toughness measurement, to establish accurate correlation between CVN and fracture toughness of wheel steels. Moreover, this ISIT method can be employed to regulate heat treatment of material properties to meet specific application requirements.

Use of a modified critical fracture strain model for fracture toughness estimation of high strength rail steels

This paper explores the feasibility of estimating fracture toughness (KIC,pred) for nine high-strength rail steels using data from smooth tensile and instrumented ball indentation test methods via a modified critical fracture strain model. The modification focuses on determining the equivalent plastic fracture strain and equivalent plastic strain from tensile and indentation tests, respectively, as well as the characteristic distance needed for estimation of fracture initiation. It shows that stress triaxiality plays a vital role by decreasing the ductility required to initiate fracture, based on the kinetic damage evolution law for a multiaxial stress state. A void growth index model was established from average grain sizes, and then used as the characteristic distance for fracture initiation. At the end, the KIC,pred defined based on equivalent plastic strain from tensile tests showed a strong correlation with KIC determined from ASTM standard method. KIC,pred from indentation also offers the opportunity for ascertaining the possibility of estimating the fracture toughness of high strength rail steels, non-destructively by focusing on the equivalent plastic strain and pressure at the tip of the indenter.

Semi-analytical creep model to obtain Norton's law of materials under flat indentation and its applications

In traditional indentation test methods for obtaining Norton's law of creep materials, an empirical correlation formula represents the relationship between the indentation strain rate and the uniaxial reference strain rate or indentation displacement rate. This study proposes an equivalent method for representative volume elements (RVE) of creep materials from a complex stress state to a simple stress state. Considering Norton's law as a constitutive relationship based on the equivalent method of stress state, a semi-analytical model describing the creep displacement vs. time relationship of flat cylindrical indentation (flat indentation) and a method for determining the parameters of the model were established under constant load conditions in this investigation. The finite element analysis (FEA), creep test results of zinc alloy ZA27, and results in the current literature were used to verify the semi-analytical creep model. The results showed that Norton's law and the displacement rate predicted by different indentation creep models are relatively close, and the partial results predicted by the new model are slightly better than those obtained by methods reported in the literature.

Indentation Testing Method for Determining Mechanical Properties and Tensile Flow Curve of High-Strength Rail Steels

Indentation Testing Method for Determining Mechanical Properties and Tensile Flow Curve of High-Strength Rail Steels

A novel flat indentation test method for obtaining stress–strain relationships of metallic materials based on energy density equivalence

For power-law hardening metallic materials under flat cylindrical indentation loading conditions, a theoretical model was derived to describe the relationships among the stress and strain of the equivalent material representative volume element, load, displacement, and diameter of the indenter based on energy density equivalence. Subsequently, a novel flat indentation test method was developed such that the stress vs. strain data points of a material with a known elastic modulus could be directly calculated by utilizing the collected load vs. displacement data points. Numerical verifications were performed on 64 elastoplastic materials with various combinations of elastic moduli, yield strengths, and strain hardening exponents. In addition, flat indentation tests were carried out on 12 metallic materials. The results showed that the stress–strain curves obtained by the proposed method were consistent with those pre-input in finite element analysis and those obtained from uniaxial tensile tests. Furthermore, the proof strength and tensile strength of the experimental materials were obtained according to the predicted Hollomon law parameters, and the relative errors between the predicted and standard test results were mostly within 3%.

Comparison and Analysis of Diffusion Models: Growth Kinetics of Diiron Boride Layers on ASTM A283 Steel

Hard-coated surfacing of a few micrometers is widely applied to increase the efficiency of tools, e.g., for cutting, forming, and casting applications. Therefore, the base thermodiffusion surface treatment is a practical solution to these issues by hardening surface layers with interstitial elements such as carbon, nitrogen, and boron. In particular, within this study, the growth kinetics of an iron boride layer on ASTM 283 steel were investigated with two diffusion models of the powder-pack boriding technique in the temperature range of 1123-1273 K with different treatment periods. The first model, called the steady-state diffusion model, used the modified version of the mass balance equations at the Fe2B/substrate growth interface, the parabolic growth law, and the solution of Fick's second law without time dependence. At the same time, the second diffusion model was based on Goodman's method, also called the integral heat balance method. Afterward, the diffusion coefficient of boron in the Fe2B phase was calculated by fitting the experimental data to the models. Nevertheless, the estimated value for the activation energy of ASTM A238 steel in both diffusion models was coincident (168.2 kJ∙mol-1). A mathematical analysis was implemented by means of a power series (Taylor series) to explain this similarity. The SEM examinations showed a solid tendency to saw-tooth morphology at the growth interface with the formation of the Fe2B layer, whose presence was verified by XRD analysis. The tribological characterizations, including the tests of Rockwell-C indentation, pin-on-disc, and Vickers hardness test method, were used to analyze the antiwear features of the Fe2B layers. Finally, this value of energy was compared to the literature for its experimental validation.

Control of Welding Residual Stress in Large Storage Tank by Finite Element Method

T-joint welding is a key manufacturing process of large storage tanks. However, complex residual stresses are generated and have a great effect on the structural integrity of storage tanks. The high residual stress caused by welding and the discontinuous structure may result in tank cracking and failure. In this work, the residual stress distributions on the inner surface, outer surface, and thickness direction of the T-joint were investigated by using the finite element method and indentation test method. The effect of local PWHT with different heating temperatures, heating rates, and heating widths on the residual stress distribution was also discussed. Results show that the residual stress of the T-shaped joint is high due to the serious structure discontinuity, multi-layer welding, and high strength. Among all the stresses, the circumferential residual stress is the highest and most concentrated in the outer weld connected with the annular plate. The residual stress gradually decreases with the increase in the heat treatment temperature. When the heating rate is less than 106 °C/h, the residual stress gradually decreases with the decrease in the heating rate. The large thermal deformation caused by heat treatment can be simultaneously avoided by heating the inside and outside of the T-joint. The residual stress decreases with the decrease in the width of the heating zone. The residual stress can be regulated by using a smaller width in the heating zone. An optimized heat treatment scheme with a heating temperature of 700 °C, heating rate of 56 °C/h, and heating width of 200 mm was proposed, which has a good ability to control residual stresses and improve the quality of the T-joint. It also has a good application in engineering.

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.

Indentation characterization of glass/epoxy and carbon/epoxy composite samples aged in artificial salt water at elevated temperature

Micro-level composite properties are a key determinant of the long-term performance and life span of marine-based composite structures. In this paper, the effect of the aging process in salt water at room temperature and elevated temperature on the elastic modulus and hardness of composite specimens have been investigated through indentation testing. To do this, carbon/epoxy (CE) and glass/epoxy (GE) samples were immersed in artificial sea water with 3.5% salinity at room temperature and 60 °C for 90 days. Matrix only and fibre/matrix (fibre constraint) cells have been examined by two different approaches, namely standard indentation testing and continuous stiffness measurement (CSM) methods to measure elastic modulus and hardness in micro level. It was indicated that degradation at 60 °C had a higher effect on elastic modulus than the room temperature aging process. According to the experimental results from the standard method indentation in matrix cells, the average modulus in the aged GE in 60 °C was 3.47 ± 0.1 GPa (22.3% loss). The average modulus in the reference CE samples was 4.7 ± 0.1 GPa, while those values for aged samples at room temperature and 60 °C showed 38.8% and 51.3% losses, respectively. The hardness for the reference GE specimen was 0.189 ± 0.004 GPa, and after the aging process, it dropped by 2.1% (room temperature) and 27.51% (60 °C). Based on the continuous stiffness measurement for matrix cells, the mean value of modulus for the dry GE and CE matrix material cells was calculated as 4 GPa and 3.7 GPa, respectively. During the aging process, the hardness of CE samples decreased from 0.048 GPa to 0.038 GPa at room temperature and 60 °C, respectively, while aging of GE samples at both temperatures after 90 days caused a 31% loss in the hardness compared to the reference specimen. It was evident from the CSM experiments in the fibre constraint cells that the indentation modulus of the dry epoxy matrix constituent increased by 7.5% and 14% by the neighbouring stiff glass and carbon fibre regions respectively. The indentation characterization in GE samples thorough the standard method in the fibre constraint cells showed a 12.58% reduction in modulus at room temperature, and 25.8% at 60 °C compared to the reference specimen.

Indentation Size Effect Model of Ti6Al4V Alloy by Combining the Macroscopic Power‐Law Constitutive Relation and Strain Gradient Theory

Indentation size effect (ISE) is a critical feature for investigating the local properties of materials using the indentation test method. Although there are numerous works on the indentation response, there is a lack of data in the literature on the association between nanoindentation and uniaxial compression. Herein this study, uniaxial compression tests combined with Digital Image Correlation Technique are conducted on Ti6Al4V alloy with a focus on investigating the elastic–plastic properties and obtaining the accurately constitutive relation. Then, an ISE model of Ti6Al4V is established based on this constitutive relation and strain gradient theory. Indentation hardness, predicted by this proposed model, agrees well with the measurement by nanoindentation experimental techniques. This model can be used to bridge the gap between the uniaxial stress–strain and the depth‐dependent hardness, and clarifies the effect of the strain hardening on indentation hardness. The significance of this model is that it provides a direct and reasonable theory foundation to investigate ISE by uniaxial compression, and promotes the potential application of nanoindentation.

Evaluation of mechanical properties of YSZ TBCs doped by different ratios of Eu3+ ions after isothermal oxidation

Thermal barrier coatings (TBCs) are essential to improve the thermal insulation performance of high-temperature components. Rare earth element (Eu3+) doped yttrium stabilized zirconia (YSZ) TBCs have been proved to be an ideal solution for non-destructive testing of internal damages. Based on this theory, two types of coatings deposited by air plasma spray (APS) on Hastelloy-X were investigated: (1) Eu3+ doped YSZ (dopant ratios 1 mol%, 2 mol%, 4 mol%, respectively), (2) traditional undoped 8YSZ. Isothermal oxidation treatment at 1100 °C, in increments of 10h until the failure of the coatings are conducted to evaluate the mechanical properties of different coatings. The microscopic morphology and phase of the coatings were analyzed by scanning electron microscope (SEM) and X-ray diffraction (XRD) patterns, respectively. The indentation testing methods were used to study the apparent interfacial fracture toughness and the hardness of the ceramic top coat. Results show that the Vickers hardness of the top coat increases with the decrease of porosity in the early stage and then decreases with the heat treatment time increasing in the long-term stage. Simultaneously, compared with the undoped 8YSZ coating, the fracture toughness increased with the dopant of Eu3+ ions increasing, from 1 mol% to 2 mol%, nevertheless, that of 4 mol% Eu3+ doped YSZ decreased compared with in the undoped 8 YSZ. For all types of specimens, the interfacial fracture toughness decreases with the increase of isothermal oxidation time. Results also indicate that the content of Eu3+ doping does not affect the microstructure and interfacial morphology of the YSZ coating as well as the growth law of thermally grown oxides (TGO). Furthermore, EDS detection found that the Eu3+ ions almost do not diffuse inside the TBCs system after isothermal oxidation treatment.

Effect of Spray Method and Sprayed Material on Creep Behavior of MCrAlY Coating

The blade of gas turbines used in combined cycle power plant are exposed to a high-temperature combustion gas. In order to protect it from such a harsh environment, a thermal barrier coating (TBC) is applied to the surface of the blade. TBC consists of a top coat (TC), which is a thermal barrier layer, and a bond coat (BC), which increases the adhesion strength between the TC and the substrate. Thermal stress is caused by the thermal expansion mismatch between the TC and substrate, which leads to delaminating in TC. In order to reduce such thermal stress in TC, creep deformability of BC is essential. In this study, we attempted to evaluate the creep deformation property of BC by creep indentation test method developed by our group. CoNiCrAlY and CoCrAlY are selected as BC materials and APS and HVOF are also as thermal spraying methods, and the creep indentation tests were conducted at various temperatures. It was found that material differences had little effect on creep deformation properties, and that creep properties were strongly affected by the thermal spraying method even if the material systems had the same chemical composition.

Determination of strength characteristics of high-strength sheet steels by hardness and instrumented indentation

The paper considers the method of instrumented indentation to evaluate the strength of high-strength steel sheets as one of the fastest and more accurate methods of nondestructive testing. Many different types of tests are used to determine the strength characteristics of metals. Tensile and hardness tests are the most common. Tensile tests are labor and energy-intensive, whereas hardness tests are less accurate compared to the instrumented indentation. The advantage of the instrumented indentation method as compared to the standard hardness measurement method lies in the following: the possibility to directly register the entire process of continuous local deformation of the material using the indenter, high speed and simplicity due to the process automation, as well as no visual measurement of the indentation imprint diameter. In addition, the correlation relationships for determining the strength characteristics of the indentation diagram parameters are valid for a wide class of materials. The authors use different methods, namely, uniaxial tension tests, Brinell hardness tests and instrumented indentation method, comparative analysis of the strength characteristics of 28GKhNMR and 20GR sheet steels with the thickness of 10 mm, and 30Kh2CN2MFA and 28GR steels with the thickness of 6 mm for special structures production to confirm the efficiency of the instrumented indentation test method. To assess the accuracy of the determination of strength characteristics by the method of instrumented indentation, the authors employed the procedure to determine the strength of high-strength steels via the Brinell hardness. As a result, deviations of certain strength characteristics Rp0.2 and Rm of the studied steels, as compared with the corresponding strength characteristics in uniaxial tension, do not exceed 10.4%. At the same time, deviations of strength characteristics obtained by the instrumented indentation method from the tensile strength characteristics do not exceed 5.2%.

Determination of mechanical properties from sharp dynamic indentation

In this study, a dynamic indentation test method based on the split Hopkinson pressure bar is proposed to obtain the dynamic parameters of Ludwik power law constitutive, namely, Young’s modulus E, strength coefficient K, and strain hardening index n by analyzing dynamic indentation load-indentation depth curve obtained from the theories relating to the Hopkinson pressure bar. The important parameters, namely, loading curvature C and transformation factor [Formula: see text], are invoked to examine the dynamic indentation response results in a wide range of target material parameters. Finite element calculation results are processed through simulation of dynamic indentation response with broad material parameters. Furthermore, the analytical method is used to fit simulation results to obtain the analytical equations for elastic–plastic parameters and curvature parameters for the subsequent analysis. The analytical equation of forward model to predict dynamic indentation response parameter–loading curvature C of a known material is proposed. Then, the elastic–plastic parameters of unknown materials (according to Ludwik power law) are obtained by substituting the dynamic indentation response parameters into an inverse analytical equation under the two types of half-cone angle indenters. The method is verified by other typical materials, which shows that the dynamic indentation test based on the split Hopkinson pressure bar can obtain sufficient conditions to obtain dynamic mechanical properties of target materials.

Evaluation of the elastic modulus of concrete based on indentation test and multi-scale homogenization method

This paper aims to quantitatively evaluate the elastic modulus of concrete through microscopic tests and a multi-scale mechanical homogenization method considering interface transition zone (ITZ). The mechanical properties tests were carried out for concrete samples with 0% or 10% silica fume . The elastic modulus and volume fraction of individual phases of hardened paste and elastic modulus and thickness of the ITZ around coarse aggregate were obtained by a series of microscopic tests and theoretical studies. The results showed that the incorporation of silica fume mainly increased the elastic modulus and volume proportion of the C–S–H gel, while results in the improvement on ITZ elastic modulus and reduction on its thickness. To further simulate macroscopic elastic modulus, the concrete was divided into four scales ranging from nano to macro and a model was established by homogenization scheme combining Mori-Tanaka (MT) and self-consistent (SC). The influence of bond-slip ITZ model or homogeneous ITZ model on the simulation results was discussed on the fourth scale. Moreover, the effects of the nanoscopic phases, microscopic phases and ITZ properties on the elastic modulus of concrete were analyzed to confirm the essential role of ITZ in the elastic deformation analysis. • The 2 μm displacement-controlled single row micro-indentation test was used to obtain the elastic modulus of ITZ. • The influence of bond-slip ITZ model or homogeneous ITZ model on elastic modulus simulation of concrete was compared. • The effect of silica fume on the elastic modulus of concrete was explained from nano to micro perspective.

Evaluation of concrete creep properties based on indentation test and multiscale homogenization method

This paper aims to quantitatively evaluate the creep properties of concrete through microscopic tests with a multiscale mechanical homogenization method considering interface transition zone (ITZ). The concrete samples with 0 or 10% silica fume were subjected to a 360-day macroscopic test. A series of indentation tests, microscopic tests and theoretical studies were carried out to obtain the creep properties of individual phases of hardened paste and contact creep modulus and thickness of the ITZ around coarse aggregate. Results indicated that the addition of silica fume significantly improved the quantity and quality of gel in the matrix. Meanwhile the performance of ITZ was enhanced while its thickness was decreased by 29%. The above effects contribute to the improved ability of concrete to resist creep. To quantitatively evaluate the creep properties, the concrete materials were divided into four different scales from nanoscale to macroscale. A homogenization method combining Mori-Tanaka (MT) scheme and self-consistent (SC) scheme was used to calculate the contact creep modulus of concrete. Besides, two ITZ simulation models of bond-slip and homogeneous solid were discussed on the fourth scale to verify the accuracy of the model and confirm the significances of ITZ properties and thickness in creep analysis.

Development of Surface Indentation Test Method for Evaluating TBC Property

Development of Surface Indentation Test Method for Evaluating TBC Property