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Ta-Te Chen, [Ikumu Watanabe](https://orcid.org/0000-0002-7693-1675), Tatsuya Funazuka

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[Characterization of the Strain-Rate-Dependent Plasticity of Alloys Using Instrumented Indentation Tests](https://mdr.nims.go.jp/datasets/9489e325-930d-48d9-bafc-71f11b0bb7dc)

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Characterization of the Strain-Rate-Dependent Plasticity of Alloys Using Instrumented Indentation TestscrystalsArticleCharacterization of the Strain-Rate-Dependent Plasticity ofAlloys Using Instrumented Indentation TestsTa-Te Chen 1,2 , Ikumu Watanabe 1,2,* and Tatsuya Funazuka 3�����������������Citation: Chen, T.-T.; Watanabe, I.;Funazuka, T. Characterization of theStrain-Rate-Dependent Plasticity ofAlloys Using InstrumentedIndentation Tests. Crystals 2021, 11,1316. https://doi.org/10.3390/cryst11111316Academic Editor: Umberto PriscoReceived: 30 July 2021Accepted: 26 October 2021Published: 28 October 2021Publisher’s Note: MDPI stays neutralwith regard to jurisdictional claims inpublished maps and institutional affil-iations.Copyright: © 2021 by the authors.Licensee MDPI, Basel, Switzerland.This article is an open access articledistributed under the terms andconditions of the Creative CommonsAttribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).1 Graduate School of Science and Technology, University of Tsukuba, Tsukuba 305-8577, Japan;s1930121@u.tsukuba.ac.jp2 Research Center for Structural Materials, National Institute for Materials Science, 1-2-1 Sengen,Tsukuba 305-0047, Japan3 Faculty of Engineering, University of Toyama, 3190 Gofuku, Toyama 930-8555, Japan;funazuka@eng.u-toyama.ac.jp* Correspondence: WATANABE.Ikumu@nims.go.jpAbstract: Instrumented indentation tests are an efficient approach for the characterization of stress–strain curves instead of tensile or compression tests and have recently been applied for the evaluationof mechanical properties at elevated temperatures. In high-temperature tests, the rate dependenceof the applied load appears to be dominant. In this study, the strain-rate-dependent plasticity ininstrumented indentation tests at high temperatures was characterized through the assimilationof experiments with a simulation model. Accordingly, a simple constitutive model of strain-rate-dependent plasticity was defined, and the material constants were determined to minimize thedifference between the experimental results and the corresponding simulations at a constant hightemperature. Finite element simulations using a few estimated mechanical properties were comparedwith the corresponding experiments in compression tests at the same temperature for the validationof the estimated material responses. The constitutive model and determined material constants canreproduce the strain-rate-dependent material behavior under various loading speeds in instrumentedindentation tests; however, the load level of computational simulations is lower than those of theexperiments in the compression tests. These results indicate that the local mechanical responsesevaluated in the instrumented indentation tests were not consistent with the bulk responses inthe compression tests at high temperature. Consequently, the bulk properties were not able to becharacterized using instrumented indentation tests at high temperature because of the scale effect.Keywords: strain-rate-dependent plasticity; instrumented indentation test; finite elements; mechani-cal testing1. IntroductionA database of fundamental material properties is essential for effective utilization ofexisting materials and exploration of new materials. For structural materials, tensile andcompression tests among various mechanical tests are the standard testing methods forthe characterization of mechanical properties based on the stress–strain curve because ofthe simple stress state. However, material tests require considerable effort and time forspecimen preparation and for conducting tests under various conditions.Accordingly, instrumented indentation tests are an efficient approach for the evalua-tion of mechanical properties, such as effective elastic stiffness and hardness. These testsrequire less effort for specimen preparation and provide multiple results from a singlespecimen. In addition, the test method is applicable for the characterization of nano- andmicroscopic mechanical behaviors through the control of the magnitude of the appliedload. Therefore, instrumented indentation tests have been widely employed in materialscience and engineering, e.g., the studies of scale-dependent plasticity [1–3], microscopicheterogeneity [4–6], and complex deformation mechanisms [7–9].Crystals 2021, 11, 1316. https://doi.org/10.3390/cryst11111316 https://www.mdpi.com/journal/crystalshttps://www.mdpi.com/journal/crystalshttps://www.mdpi.comhttps://orcid.org/0000-0002-0553-4736https://orcid.org/0000-0002-7693-1675https://orcid.org/0000-0001-8743-2874https://doi.org/10.3390/cryst11111316https://doi.org/10.3390/cryst11111316https://creativecommons.org/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://doi.org/10.3390/cryst11111316https://www.mdpi.com/journal/crystalshttps://www.mdpi.com/article/10.3390/cryst11111316?type=check_update&version=1Crystals 2021, 11, 1316 2 of 10Recently, instrumented indentation tests at elevated temperatures have attracted con-siderable attention for the characterization of the temperature dependency of mechanicalproperties, which has the potential for efficiently obtaining material databases for the re-search and development of heat-resistant materials. In this context, Chen et al. [10] appliednanoscopic instrumented indentation tests at elevated temperatures to the high-throughputscreening of alloy compositions in AlFeCrNiMn high-entropy alloy systems. In particular,high-temperature nanoindentation equipment has been developed in recent years. Suzukiand Ohmura [11] first reported high-temperature nanoindentation measurements up to600 ◦C on silicon samples. Ruzic et al. [12,13] extended the maximum temperature to800 ◦C under an inert atmosphere. Minnert et al. [14] developed an improved nanoindenta-tion system and characterized the creep behavior of a nickel single crystal at temperaturesup to 1100 ◦C.In instrumented indentation tests at high temperatures (high-temperature indentationtests), strain-rate-dependent plasticity becomes dominant in comparison with those atroom temperatures. Therefore, various studies have been conducted to characterize thecreep properties based on the results of high-temperature indentation tests. Chu et al. [15]first reported the determination of the creep properties of β-Sn single crystals using aninstrumented indentation test. Dean et al. [16] proposed an approach for characterizingthe primary and secondary creep behaviors using a spherical indenter. Takagi et al. [17,18],Takagi and Fujiwara [19], and Fujiwara et al. [20] determined the creep characteristics ofvarious alloys under several loading conditions of instrumented indentation tests usinga conical indenter. In the above studies, the creep behavior under an applied load in aninstrumented indentation test was examined to correlate the results with creep properties,requiring long tests with duration over 1 min. The duration of high-temperature inden-tation tests should be minimized to prevent the degradation of the specimen surface andthe indenter tip [12]. In creep measurements, the loading and unloading processes aregenerally ignored. However, they must be considered in an instrumented indentationtest with a short duration. The material response in these processes depends not onlyon strain-rate-dependent properties but also on other mechanical properties, includingelastic stiffness, strength, and work hardening. Therefore, it is difficult to simultaneouslycharacterize the mechanical properties.In instrumented indentation tests at room temperature, various approaches have beenproposed to estimate the stress–strain relationship corresponding to a tensile test from load–depth (P− h) curves. Because a unique stress–strain relationship cannot be estimated fromthe P− h curve of a single indentation test using a standard sharp indenter [21–23], dual-indenter and sphere indenter methods were proposed to determine a unique set of materialconstants in a simple constitutive model. For instance, in dual-indenter methods [24–26],two sharp indenters with different apex angles were employed. By contrast, sphereindenter methods [27–29] are based on the nonlinear relationship between the indentationdepth and cross-sectional area of the indentation. These approaches focus on the P− hcurves. Goto et al. [30,31] used topography around the indentation marks with P − hcurves in a single indentation test using a standard sharp indenter to determine the plasticproperties. In the above-mentioned estimation approaches, the computational simulationsof the instrumented indentation tests play an important role in reproducing the materialbehavior and determining the material constants of a constitutive model. The frameworkdeveloped in instrumented indentation tests at room temperature is based on the strain-rate-independent plasticity. Therefore, it can be extended to high-temperature indentationtests by employing a strain-rate-dependent plasticity.In this study, we developed an approach for estimation of strain-rate-dependentplasticity based on the results of the high-temperature indentation tests. Initially, thesimple constitutive model used in existing approaches [25,26,30,31] was extended to astrain-rate-dependent format. Next, high-temperature indentation tests were performedunder different loading rates for an aluminum alloy specimen. Subsequently, the materialconstants of the proposed constitutive model were determined to minimize the differenceCrystals 2021, 11, 1316 3 of 10between the experimental P− h curves and the curves obtained from their correspond-ing finite element simulations, as shown in Section 4. Lastly, the estimated mechanicalproperties were validated using a compression test at the same temperature.2. Finite Element ModelingA constitutive model in a strain-rate-dependent format and a finite element modelwere defined for the following computational simulations of high-temperature indenta-tion tests.2.1. Strain-Rate-Dependent Constitutive ModelAn isotropic elastoplastic constitutive model for alloys was employed, which wascharacterized by the Saint-Venant’s elasticity and metal plasticity based on the von Misesyield criterion. The elasticity was set as strain-independent, whereas the plastic constitutiveequation was defined in a strain-rate-dependent format. In this study, the equivalentstress–strain relationship is expressed as follows:{σ∗ = E∗ε∗ if σ∗ < σY(elasticity)σ∗ = K(ε∗)nΓ(ξ̇) if σ∗ = σY(elasto–visco–plasticity),(1)where σ∗, ε∗, E∗, σY, K, n, Γ, and ξ are the von Mises stress norm, equivalent strain,equivalent elastic modulus, yield stress, plastic coefficient, work-hardening exponent,strain-rate function, and equivalent plastic strain, respectively. The equivalent strain andelastic modulus are defined as follows:ε∗ =√23dev[ε] : dev[ε] =σ∗E∗+ ξ and E∗ =3E2(1 + ν), (2)where ε, E, and ν are the strain tensor, Young’s modulus, and Poisson’s ratio, respectively.In this study, the strain-rate function was defined asΓ(ξ̇) = (1− α) + α(ξ̇ξ̇0)mα ∈ [0, 1], (3)where α, ξ̇0, and m are the viscoplastic ratio, reference strain rate, and strain-rate exponent,respectively. Then, Equation (1) can be written asσ∗ =(σ∗E∗+ ξ)n{(1− α)K + αK(ξ̇ξ̇0)m}=(σ∗E∗+ ξ)n{Kp + Kvpξ̇m}, (4)where Kp = (1− α)K and Kvp = αKξ̇−m0 . Thus, this constitutive model contains four strain-rate-independent and two strain-rate-dependent material constants at a high temperature:E, ν, Kp, n, Kvp, and m. The strain-rate-independent initial yield strength is formulated asσY ={(E∗)−nKp} 11−n . At a high temperature, α can be assumed to be equal to one, i.e.,Kp ≡ 0. In the special case, a pure-elastic state does not exist.2.2. Finite Element Model of the Instrumented Indentation TestA three-dimensional finite element model of a specimen and Berkovich indenterwas constructed for the computational simulations of the instrumented indentation testsdescribed in Section 3.2, as shown in Figure 1. A mirror symmetrical boundary conditionwas applied to the X−Y plane along the center of the object, and the vertical displacementalong the bottom of the finite element model was constrained. The finite element modelcontains 15,358 nodes and 14,138 eight-node hexahedral elements with reduced integration,in which the contact area between the specimen and indenter was discretized more finelythan the other areas. The indenter was assumed to be a rigid body. The friction betweenCrystals 2021, 11, 1316 4 of 10the indenter and the sample was not considered in this study because the effect of frictionon the indentation results is insignificant in the case of Berkovich indenter [25]. The frictioneffect was confirmed to be minor in simulations of the instrumented indentation testsusing the strain-rate-dependent plasticity. A load was applied to the top of the indenter.Quasi-static boundary value problems were solved using the applied load control with animplicit scheme.XYZ1.6 mm0.8 mm0.8 mmFigure 1. Finite element model of the instrumented indentation test.2.3. Finite Element Model of the Compression TestAn axisymmetric finite element model was constructed for the computational simula-tions of the compression tests described in Section 3.2.1, as shown in Figure 2. The finiteelement model contained 990 nodes and 940 four-node quadrilateral and 4 three-node tri-angular axisymmetric elements, where triangular elements were employed for the cornersof the specimen to avoid excessive distortion of the elements. The vertical displacementalong the bottom of the finite element model was constrained. Coulomb friction modelwas employed, and its coefficient was calibrated as 0.16 to reproduce the experimentalbarreling deformation in the simulations.Simulations were performed using displacement control at the top of the model andsolved as quasi-static boundary value problems with an implicit scheme.4 mm12 mmaxis of symmetryyrFigure 2. Finite element model of the compression tests.Crystals 2021, 11, 1316 5 of 103. ExperimentsExperimental data were acquired to characterize and validate the strain-rate depen-dency of the plastic properties, where the instrumented indentation and compression testsat high temperature were performed at different test speeds.3.1. SpecimenA wrought aluminum alloy with a grain size of approximately 200 µm was used inthis study. The alloy composition is shown in Table 1. A melting temperature of a similaralloy (A7204) is 635 ◦C [32]. For instrumented indentation tests, mechanical polishing wasconducted on the sample surface, followed by electrical polishing to remove the residualplastic strains.Table 1. Alloy composition of the aluminum alloy [wt%].Zn Mg Zr Cu Fe Si Ti5.60 1.34 0.16 0.15 0.03 0.02 0.02A tensile test at room temperature (approximately 20 ◦C) was performed, and thematerial constants of the constitutive model were determined under the assumption of anindependent strain-rate (α ≈ 0, m ≈ 0).(E, ν, Kp, n, ) = (70 GPa, 0.3, 353.4 MPa, 0.08), (5)that also can be determined from the instrumented indentation tests [33]. The work-hardening exponent was approximately zero.3.2. Instrumented Indentation Tests at High TemperaturesInstrumented indentation tests were performed at 300 ◦C using a diamond Berkovichindenter with the TI 950 TriboIndenter and xSol High-Temperature Stage (Bruker, Billerica,MA, USA), preventing the degradation of the specimen surface and indenter tip in themeasurements in an inert argon atmosphere. The following experimental procedure forhigh-temperature indentation tests was established in our previous study [12].After passively preheating the indenter tip at 300 ◦C, the instrumented indentationtests were performed for a maximum applied load of 1.5 N. The applied load was appliedwith three different load rates, i.e., 0.1, 1.0, and 10 N/s, with the unloading rate set to0.1 N/s for each case after 10 s holding time at the maximum load. The indentation testswere performed five times for each condition to ensure reproducibility. The impressions ofhigh-temperature indentation tests in loading rates of 0.1 and 10 N/s are shown in Figure 3,which were observed with a scanning electron microscopy (JSM-7001F, JEOL Ltd., Tokyo,Japan). According to these figures, the indentation tests were performed without crack,and no significant difference between them was found in the impressions.100 mm 100 mm(a) 0.1 N/s (b) 10 N/sFigure 3. Impressions of high-temperature indentation tests in loading rates of 0.1 and 10 N/s.Crystals 2021, 11, 1316 6 of 103.2.1. Compression Tests at High TemperaturesFor the validation of the estimated material response, compression tests of the alu-minum alloy were performed at three different test speeds (1.20, 0.12, and 0.06 mm/s;0.10, 0.01, and 0.005/s in strain rate) in a chamber heated at 300 ◦C. Cylindrical samples(12 mm height, 8 mm diameter) corresponding to Figure 2 were compressed in the axialdirection under displacement control using a precision Autograph AG-X Series universaltester (Shimadzu, Kyoto, Japan). The sample surface was lubricated to minimize bulgingdeformation in these tests.4. Characterization of Strain Rate DependencyIn this section, material constants of the strain-rate-dependent plasticity were deter-mined to minimize the difference between experiments and its computational simulationsin high-temperature indentation tests. Moreover, the material response based on the consti-tutive model and the determined material constants was validated in compression tests atthe same temperature.4.1. Determination of Material ConstantsThe material constants were determined to minimize the difference in the P− h curvesbetween the experiments and the corresponding simulations for three loading speeds. Inthis study, the elastic constants E and ν at 300 ◦C were obtained from the literature [34] as59 GPa and 0.35, respectively. The work-hardening exponent n was assumed to be 0.08,which is considered identical to that of the tensile test at room temperature for simplicity.Thus, the optimization problem is defined as follows:minimize[∆(Kp, Kvp, m)],∆ := ∑Ncasei=1{1hexp,ehi(∣∣∣hexp,bhi − hsim,bhi∣∣∣+ ∣∣∣hexp,ehi − hsim,ehi∣∣∣)}, (6)where hexp,bhi , hexp,ehi , hsim,bhi , and hsim,ehi are the indentation depths at the beginningand end of the holding process in the experimental and simulation results of the i-thcase, respectively. Ncase is the number of the loading rate cases. In this study, Ncase = 3,as specified in Section 3.2. ∆ is the difference between the experimental and simulatedP− h curves.In the both cases of α ∈ (0, 1) and α = 1, the sets of material constants were deter-mined to solve the optimization problem (Equation (6)) using the Levenberg–Marquardtmethod [35] as follows:α ∈ (0, 1) : (Kp, Kvp, m) = (17.4 MPa, 115.5 MPa, 0.2367),α = 1 : (Kvp, m) = (120.0 MPa, 0.160),(7)where ∆ was 0.0731 for α ∈ (0, 1) and 0.0784 for α = 1. For α ∈ (0, 1), the strain-rate-independent initial yield strength is calculated as σY = 8.48 MPa. Although the strength isnon-negligible, the appropriate material constants can be found even in the case of α = 1(under the constraint of Kp ≡ 0).The P− h curves obtained in the experiments and simulations using the determinedmaterial constants are shown in Figure 4. Additionally, the relationship between the depthand time during the holding process at the maximum applied load is shown in Figure 5.The strain-rate-dependent deformation behavior in the instrumented indentation tests wasreproduced in computational simulations using the constitutive model in both cases.From the results of the finite element analyses in the case of α ∈ (0, 1), the distributionsof Mises stress and equivalent plastic strain at the beginning and end of the holding pro-cesses for the loading rates of 0.1 and 10 N/s are shown in Figures 6 and 7, respectively. Inthe beginning of the holding process at the maximum applied load, the stress concentrationaround the indenter tip was observed in the case of a high loading rate, whereas the stressCrystals 2021, 11, 1316 7 of 10distribution was uniform in the case of a slow loading rate due to the relaxation providedby the strain-rate-dependent deformation during the loading process. In addition, thedistributions of an equivalent plastic strain before and after the holding process exhibitthe evolution of the equivalent plastic strain during the holding process, which is moreprominent in the case of a high loading rate.00.20.40.60.811.21.41.60 5 10 15 20 25Load [N]Depth [μm]Exp. 10N/sSim. 10N/sExp. 1N/sSim. 1N/sExp. 0.1N/sSim. 0.1N/s00.20.40.60.811.21.41.60 5 10 15 20 25Load [N]Depth [μm]Exp. 10N/sSim. 10N/sExp. 1N/sSim. 1N/sExp. 0.1N/sSim. 0.1N/s(a) α ∈ (0, 1) (b) α = 1Figure 4. Load–depth curves obtained in the experiments and simulations using the determinedmaterial constants. The dashed lines indicate the simulation results.05101520250 2 4 6 8 10Depth [μm]Time [s]Exp. 10N/sSim. 10N/sExp. 1N/sSim. 1N/sExp. 0.1N/sSim. 0.1N/s05101520250 2 4 6 8 10Depth [μm]Time [s]Exp. 10N/sSim. 10N/sExp. 1N/sSim. 1N/sExp. 0.1N/sSim. 0.1N/s(a) α ∈ (0, 1) (b) α = 1Figure 5. Depth–time curves obtained in the experiments and simulations using the determinedmaterial constants. The dashed lines indicate the simulation results.0 130[MPa] Max:  60.7 MPa0 130[MPa] Max:  45.8 MPa(a1) Beginning of holding (a2) End of holding(a) 0.1 N/s0 130[MPa] Max: 127.5 MPa0 130[MPa] Max:  48.9 MPa(b1) Beginning of holding (b2) End of holding(b) 10 N/sFigure 6. von Mises stress distribution at the beginning and end of the holding processes in thecomputational simulations using the determined material constants for α ∈ (0, 1).Crystals 2021, 11, 1316 8 of 100 0.9Max: 0.7420 0.9Max: 0.819(a1) Beginning of holding (a2) End of holding(a) 0.1 N/s0 0.9Max: 0.6000 0.9Max: 0.827(b1) Beginning of holding (b2) End of holding(b) 10 N/sFigure 7. Equivalent plastic strain distribution at the beginning and end of the holding processes inthe computational simulations using the determined material constants for α ∈ (0, 1).4.2. Validation in Compression TestsUsing the constitutive model (Equation (4)) and determined material constants(Equation (7)), computational simulations of the compression tests at three test speeds(1.20, 0.12, and 0.06 mm/s) were performed. The load–stroke curves obtained from theexperiments and simulations at 300 ◦C are shown in Figure 8. The results indicate that theload levels of the simulations are less consistent than those of the experiments, althoughthe strain-rate-dependent material responses were characterized in the computationalsimulations. In other words, the constitutive model is applicable for reproducing thematerial behavior at high temperature; however, the material responses evaluated in theinstrumented indentation tests did not agree with those obtained in the compression tests.02468101214160 0.5 1 1.5 2 2.5 3 3.5 4Load [kN]Displacement [mm]Exp. 1.2mm/sExp. 0.12mm/sExp. 0.06mm/sSim. 1.2mm/sSim. 0.12mm/sSim. 0.06mm/s02468101214160 0.5 1 1.5 2 2.5 3 3.5 4Load [kN]Displacement [mm]Exp. 1.2mm/sExp. 0.12mm/sExp. 0.06mm/sSim. 1.2mm/sSim. 0.12mm/sSim. 0.06mm/s(a) α ∈ (0, 1) (b) α = 1Figure 8. Load–stroke curves in the experiments and simulations using the determined materialconstants. The dashed lines indicate the simulation results.The critical difference between the instrumented indentation test and bulk test is thescale of the deformation domain. In the instrumented indentation tests, the influence regionof the residual stress and plastic deformation is estimated as smaller than a hemispherewith a radius of 500 µm as shown in Figures 6 and 7; i.e., the evaluation domain containeda few crystal grains. Therefore, the instrumented indentation tests were not carried out fora polycrystal. This can be considered as an origin of the discrepancy. In fact, distinctivematerial behaviors at high temperature such as grain boundary sliding were reportedin aluminum alloys [36,37]. The microscopic heterogeneity does not have a significanteffect at room temperature [30,31,33]; however, the discrepancy arises particularly at hightemperature. The scale and temperature effects require further investigations.Crystals 2021, 11, 1316 9 of 105. ConclusionsA new estimation approach for strain-rate-dependent plasticity was developed basedon the instrumented indentation tests, where the material constants of the strain-rate-dependent constitutive model were determined from the results of experiments and thecorresponding computational simulations at different test speeds. This approach canestimate the strain-rate-dependency of the material response in high-temperature inden-tation tests; however, the estimated mechanical properties were not consistent with theresults of the compression tests. The estimation of bulk properties using high-temperatureindentation tests remains an unsolved problem.In this study, we focused on the material behavior of one alloy sample under theisothermal single condition. Through a systematic examination of various samples andthermal conditions, the microstructure and temperature dependencies can also be charac-terized using the proposed approach.Author Contributions: Conceptualization, data curation, formal analysis, methodology, software,investigation, writing—original draft preparation, and visualization, T.-T.C. and I.W.; resources andvalidation, T.-T.C., I.W. and T.F.; writing—review and editing, supervision, project administration, andfunding acquisition, I.W. All authors have read and agreed to the published version of the manuscript.Funding: This research was funded by JSPS KAKENHI [grant number 21H01220] and AmadaFoundation for Metal Work Technology [grant number AF-2018035-C2].Institutional Review Board Statement: Not applicable.Informed Consent Statement: Not applicable.Data Availability Statement: Not applicable.Acknowledgments: The authors wish to acknowledge Y. Yamamoto, E. Nakagawa, D. Araki, and H.Murakami of the National Institute for Materials Science for their technical support.Conflicts of Interest: The authors declare no conflict of interest.References1. Spary, I.; Bushby, A.; Jennett, N.M. On the indentation size effect in spherical indentation. Philos. Mag. 2006, 86, 5581–5593.[CrossRef]2. Rester, M.; Motz, C.; Pippan, R. Indentation across size scales–A survey of indentation-induced plastic zones in copper {1 1 1}single crystals. Scr. Mater. 2008, 59, 742–745. [CrossRef]3. Fincher, C.D.; Ojeda, D.; Zhang, Y.; Pharr, G.M.; Pharr, M. Mechanical properties of metallic lithium: from nano to bulk scales. ActaMater. 2020, 186, 215–222. [CrossRef]4. Ruzic, J.; Emura, S.; Ji, X.; Watanabe, I. Mo segregation and distribution in Ti–Mo alloy investigated using nanoindentation. Mater.Sci. Eng. A 2018, 718, 48–55. [CrossRef]5. Hintsala, E.D.; Hangen, U.; Stauffer, D.D. 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