Measurement of Elastic Properties of Brittle Materials by Ultrasonic and Indentation Methods

applied sciences

Article Measurement of Elastic Properties of Brittle Materials by Ultrasonic and Indentation Methods

Shih-Jeh Wu, Pei-Chieh Chin * and Hawking Liu Department of Mechanical and Automation Engineering, I-Shou University, Kaohsiung 84001, Taiwan; [email protected] (S.-J.W.); [email protected] (H.L.) * Correspondence: [email protected]

Received: 16 March 2019; Accepted: 14 May 2019; Published: 20 May 2019

Abstract: The measurements of acoustic properties of three brittle materials i.e., ITO (alkaline earth boro-aluminosilicate) glass, bulk metallic glass (BMG) and nickel-based superalloy (CM247LC) are conducted in this work to obtain various properties. The elastic moduli of materials are derived from the results by simple acoustic speed-elasticity relationship and compared with the data obtained with nanoindentation. The difference between the Young’s modulus of ITO glass by ultrasonic and nanoindentation is 0.83%, a perfect match within range error. As for BMG, the difference (Young’s modulus) is 23.59%, and 5.11% for the CM247LC superalloys. The pulse-echo method proves to be reliable for homogeneous amorphous glass, however, the elastic moduli of metallic glass and CM247LC superalloy by ultrasonic are quite different from those by nanoindentation. The difference is large enough to cover the maximal error associated with the nanoindentation method. The relationship of acoustic speed and elastic constants must be reviewed in dealing with compound materials.

Keywords: ultrasonic pulse-echo method; nano-indentation; intermetallic; nickel-based superalloy

1. Introduction A material is considered to be brittle if it exhibits low strain at the point of fracture when subjected to tensile stress. That is to say, unlike ductile materials, it has very little plastic capability and hence no specific yield point. Brittle materials include a wide range of material classes ranging from polymers to metals, through to glass, ceramics, and composites. The measurement of the elastic properties of brittle materials (Young’s modulus and Poisson ratio) is still always difficult due to the low strain if the stress-strain relationship of elongation is employed in the experiments. Alternative partially destructive or non-destructive methods have been developed to challenge the task. However, the validity or right occasion really depends on the target material. In this paper, we tried different popular methods on different special materials and demonstrated some considerable discrepancy of data between them under measurement. Elastic modulus is an intrinsic material property and a key parameter in engineering design and materials development. The measurement of elastic moduli is a fundamental work to understand the mechanical behavior of materials. ASTM [1] has a wide range of test methods available for measuring modulus, but there is currently some uncertainty within parts of the user community about the reliability of modulus data, to the extent that many use values from Springer Handbook [2] in their calculations and designs. There are a few standardized methods such as destructive tensile or compression test, flexural bending, resonance [3], and ultrasonic testing [4–7] for general applications on regular materials. The associated uncertainty and right occasion of usage depends on the configuration such as shape and size, and material of the test subject. The ultrasonic method is a nondestructive and convenient modality. Normally, the ultrasonic NDT (nondestructive test) of material characterization is used for the determination of (a) elastic constants e.g., shear, bulk, Young’s and Lamé coefficients; (b) microstructure

Appl. Sci. 2019, 9, 2067; doi:10.3390/app9102067 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 2067 2 of 11 e.g., grain size, texture, density etic; (c) flaw (porosity, creep damage, fatigue damage etc.), and other mechanical properties such as tensile strength, shear strength, hardness as discussed by Auld [8]. It includes afore-mentioned pulse-echo [4], resonance [3] and mode transformation approaches [9]. Of the three approaches, pulse-echo is the most popular technique due to its convenience and ease to use. It is also superior to the tensile test when applied on brittle materials that fracture under small strain. A normal compression test is used for stress-strain measurement instead. The quantities, ultrasonic velocity and attenuation are the important parameters which are required for the ultrasonic nondestructive technique of material characterization. The acoustic speed is generally related to the elastic constants and density of material. Henceforth, it offers the information about the mechanical, anisotropic, and elastic properties of the transmitting medium. The elastic moduli are derived from the acoustic speed in pulse-echo method. It is desirable to validate of the relationship between the acoustic speeds and elastic moduli of the test subjects as the ultrasonic method is applied. The other parameter is the acoustic attenuation which is defined as the loss of energy of the acoustic waves travelling through different media. The general causes may be classified as scattering by heterogeneities (not applicable in the current study) and absorption by physical acoustics [8]. For the absorption part, as the ultrasonic wave propagates through the medium, some energy is attenuated through different complex mechanisms such as thermal loss, scattering, absorption, electron-phonon interaction, phonon-phonon interaction, and magnon-phonon interaction etc., called the acoustic attenuation. The coefficient of ultrasonic attenuation is also associated with several intrinsic physical properties as discovered in Pandey et al. [5], e.g., Grüneisen parameter, thermal conductivity, thermal relaxation time, thermal energy density, specific heat, granular size, Debye average velocity, and concentration etc. It is also a certain trace imprinted on material that may be used for characterization. Instrumented indentation [10] is a technique investigated for determining both the elastic and plastic properties of the materials. The nanoindentation method [11] gained popularity with the development of advanced instruments that can record micro load and displacement with high precision. If the indentation is taken at a nanoscale level it can provide accurate measurements of the continuous variation of indentation load down to micro Newton, as a function of the indentation depth down to nanometer. Dao et al. [12] used standardized experimental procedure and analytic models (depending on the indenter shape identified by Cheng et al. [13]) the load-displacement data can be used to determine elastic moduli, hardness and other mechanical properties including residual stresses. Metallic glasses can be described as metals or metal alloys without crystalline structure. Metallic glasses exhibit unique characteristics, i.e., the absence of translational periodicity and compositional homogeneity. They are usually prepared by rapid solidification during liquid phase. According to Chen [14], the crystallization can be avoided when the cooling rate is high enough, so that the atoms can be frozen in their liquid configuration as the solidification occurs. Unlike conventional metallic materials, metallic glasses do not exist in long-range atomic order, from which endowed some unique and interesting properties, e.g., high strength, elastic limit, toughness, good corrosion resistance, wear resistance and soft magnetic properties [15]. In industry, bulk metallic glasses (BMG) have been used as material for golf club heads, mobile phone casing, scalpels, tennis rackets, high-frequency power coils, and high torque geared motor parts [16–19]. It is very interesting to investigate how the special inherent structure impacts the acoustic properties of BMG. However, very few studies associated with the acoustic properties were made and most of the mechanical properties were performed by other modalities, most frequently by the tensile tests. The turbine disk and blades of many small gas turbines, especially small aircrafts, turbo-fan missiles and vehicular engines, are usually cast into a single piece, generally known as integral wheels. There is a considerable variance of loading conditions from blade to disk, i.e., lower temperature and high stress at the hub versus high temperature and low stress at the tip. The materials used to construct the integral wheel must fit in the requirement of both blade and disk. These materials, therefore, must have a very high tensile strength at operating temperature of the hub to protect the parts from bursting, and high creep strength under the blade operating condition. CM247LC is a class of cast Appl. Sci. 2019, 9, 2067 3 of 11 nickel-based superalloys with low carbon content, which was investigated by Rajendran et al. [20]. Moore [21] discovered that it is a modified superalloy based on the chemical composition of Mar-M247, specifically designed for producing directionally solidified (DS) turbine blades. The reason for the designated application is that the CM247LC superalloy is exceptionally castable to form an equiaxed grain structure if the casting parameters are well controlled. Therefore, high strength and superior creep resistance can be achieved. The control of the grain size (finer grain is preferred) is crucial for maintaining the required standard of both physical and mechanical properties [22,23]. In spite of the unique granular structure of the above stated materials, rather little research has touched upon the relationship between the acoustic properties and elastic moduli. In this paper the elastic moduli of three brittle materials, namely, ITO (alkaline earth boro-aluminosilicate) glass, BMG, and CM247LC superalloy, are measured by the pulse-echo method and compared to the data obtained from the nanoindentation method. The relationship between the granular structure and acoustic wave propagation and the validation of commonly used formula deriving the elastic moduli will be discussed. Acoustic attenuation is a measure of the energy loss of sound propagation in media. Most media have viscosity or a certain relaxed nature, i.e., non-ideal media. When sound propagates in such media, there is always thermal consumption of energy caused by viscosity. This is true for most of the materials; however, some are more lossy than others. Acoustic attenuation in a lossy medium plays an important role in many scientific studies and engineering fields, such as medical ultrasonography, vibration and noise reduction. The classical analysis of dissipative acoustic wave propagation involves frequency-independent and frequency-squared dependent attenuation, such as damped wave equation. General power law frequency-dependent acoustic attenuation has also received much attention in recent years. In general, the acoustic attenuation property depends on many factors, e.g., the intrinsic physical properties (thermal conduction ... ), micro (crystalline) and macro (layered, or matrixed) structures [24,25].

2. Experiments and Methods Two 40 40 1.1 mm ITO glass (sample No. 1 and 2), one 10 10 2 mm Zr-Cu-Ni-Al × × × × ((Zr53Cu30Ni9Al8)Si0.5) BMG (sample No. 3) [26] and one Ø 12 3.5 mm CM247LC superalloy × sample [21] (sample No. 4) were prepared for the measurement. The CM247LC superalloy sample was cut from raw material ingot and polished down by 1.0 m aluminum-oxide powders to avoid any surface oxidation. The density measurement was performed under ASTM D792 (Standard Test Methods for Density and Speciﬁc Gravity of Plastics by Displacement) with relative controlled under 0.05%. The ultrasonic measurements are performed under ASTM standard D2845-08 [27]. The setup is as shown in Figure1 with Panametrics 5073PR pulse-receiver, GaGe 100 MHz sampling rate 12-bit A /D converter, Olympus M208-RM 0.125-inch 20 MHz longitudinal, and V157-RM 0.125-inch 5 MHz shear 7 transducer. The errors of the A/D conversion are less than 10− s in time and 0.2 mV in amplitude. The density is measured by the Archimedes principle from samples of proper sample size as listed in Table1. The Young’s modulus E, shear modulus G and Poisson ratio υ are calculated as follows [6,7]:

V2ρ(1 + υ)(1 2υ) E = L − (1) 1 υ − 2 G = VT ρ (2) 2 1 2(VT/VL) υ = − (3) 2 2 2(VT/VL) − Appl. Sci. 2019, 9, 2067 4 of 11

where VT is the transverse acoustic speed, VL is the longitudinal acoustic speed which equals two times thicknessAppl. Sci. 2019 divided, 9, x FOR by PEER round REVIEW trip transit time, ρ is the density. Attenuation coeﬃcient α, is calculated4 of as 11 follows [5,7,8,28]: 𝐴 𝐴 2020log log(A 0/⁄A1) α 𝛼= (4)(4) Appl. Sci. 2019, 9, x FOR PEER REVIEW 22𝑡t 4 of 11 where A and A are the peak amplitude of the ﬁrst and second echo signal respectively. where A00 and A11 are the peak amplitude of the first and second echo signal respectively. 20log 𝐴⁄𝐴 (4) 𝛼 2𝑡

where A0 and A1 are the peak amplitude of the first and second echo signal respectively.

Figure 1. Experimental setup for ultrasonic measurement. Figure 1. Experimental setup for ultrasonic measurement.

Table 1. Size and density of each sample used in the measurements. Table 1.Figure Size and1. Experimental density of eachsetup sample for ultrasonic used inmeasurement. the measurements. Sample Size and Density Sample Table 1. Size and density of eachSample sample usedSize inand the Density measurements. Sample Material Length Width Thickness Air Water Density NumberMaterial Thickness Density Number Length (mm)(mm) Width (mm)(mm) Sample(mm) SizeAir and Weight DensityWeight (g) (g) WaterWeight Weight (g) (g) (g/mm3) Sample 3 Material Thickness(mm) Density(g/mm ) No.Number 1 ITO-glassLength (mm) 39.37 Width (mm) 39.37 1.11Air Weight (g) 4.11 Water Weight 2.42 (g) 2.42 No. 1 ITO‐glass 39.37 39.37 (mm)1.11 4.11 2.42 (g/mm3)2.42 No. 2 ITO-glass 39.28 39.31 1.11 4.09 2.41 2.43 No. 2No. 1ITO ITO‐glass‐glass 39.2839.37 39.3139.37 1.111.11 4.114.09 2.422.41 2.42 2.43 No. 3 BMG 9.55 9.95 2.11 1.47 1.27 7.28 No. 3No. 2 BMGITO‐ glass 9.5539.28 9.9539.31 1.112.11 4.091.47 2.411.27 2.43 7.28 No. 4 CM247LC 12.20 12.20 3.49 3.54 3.13 8.56 No. 4No. 3CM247LC BMG 12.209.55 12.209.95 2.113.49 1.473.54 1.273.13 7.28 8.56 No. 4 CM247LC 12.20 12.20 3.49 3.54 3.13 8.56 TheThe nanoindentationnanoindentation measurementmeasurement isis performedperformed byby MTSMTS NanoNano IndenterIndenter XPXP systemsystem capablecapable ofof The nanoindentation measurement is performed by MTS Nano Indenter XP system capable of ContinualContinual Sti Stiffnessffness Measurement Measurement (CSM) (CSM) with with software software TestWorks TestWorks as shown as inshown Figure in2. Figure The hardness 2. The Continual Stiffness Measurement (CSM) with software TestWorks as shown in Figure 2. The Hhardnessis defined H is as defined the maximum as the maximum loading Pmax loadingdivided Pmax by divided the normal by the contact normal projection contact projection area A(hc) areai.e., hardness H is defined as the maximum loading Pmax divided by the normal contact projection area HA(h= cP) maxi.e.,/ A(hH =c P),max where/A(hc)h, cwhereis the h depthc is the (displacement) depth (displacement) of contact of contact [10]. The [10]. relationship The relationship between between initial A(hc) i.e., H = Pmax/A(hc), where hc is the depth (displacement) of contact [10]. The relationship between unloading stiffness S and reduced Young’s modulus Er can ber obtained by initialinitial unloading unloading stiffness stiffness S Sand and reduced reduced Young’s modulus modulus E rE can can be be obtained obtained by by r 𝐴A𝐴ℎ(ℎh𝑐c𝑐) S = 2 E (5) 𝑆 22 𝐸𝐸𝑟r 𝑟 (5) (5) 𝑆 𝜋π𝜋

FigureFigure 2. 2.MTS MTS NanoNano Indenter XP XP system. system.

Metallurgical microscopicFigure photos 2. MTSare alsoNano taken Indenter from XP the system. BMG and CM247LC superalloy samples to explain how the acoustic property is affected by the peculiar microstructure. Metallurgical microscopic photos are also taken from the BMG and CM247LC superalloy samples to explain how the acoustic property is affected by the peculiar microstructure. Appl. Sci. 2019, 9, 2067 5 of 11

Metallurgical microscopic photos are also taken from the BMG and CM247LC superalloy samples to explain how the acoustic property is aﬀected by the peculiar microstructure.

Appl. Sci. 2019, 9, x FOR PEER REVIEW 5 of 11 3. ResultsAppl. Sci. and 2019, Discussions9, x FOR PEER REVIEW 5 of 11 3.The Results ultrasonic and Discussions measurement provides both the longitudinal and shear elastic constants, thus 3. Results and Discussions is discussedThe firstultrasonic for clarity. measurement On the provides other hand, both thethe nanoindentationlongitudinal and shear measurement elastic constants, can only thus deliver is longitudinaldiscussedThe ultrasonic data first andfor clarity.measurement is discussed On the subsequentlyprovides other hand, both thethe for nanoindentationlongitudinal comparison. and The measurement shear samples elastic of constants,can the only three deliverthus di ffiserent materialsdiscussedlongitudinal underwent first data for and bothclarity. is methods.discussed On the othersubsequently Three hand, ultrasonic the for nanoindentation comparison. measurements The measurement samples are performed of the can three foronly eachdifferent deliver sample longitudinal data and is discussed subsequently for comparison. The samples of the three different and thematerials average underwent values areboth taken. methods. In each Three measurement, ultrasonic measurements three data are points performed were taken,for each and sample the and average materials underwent both methods. Three ultrasonic measurements are performed for each sample and valuesthe were average recorded. values Shownare taken. in In Figures each 3measurement,–6 are the of three results data from points the ultrasonicwere taken, measurement and the average where thevalues average were recorded.values are Shown taken. inIn Figures each measurement, 3–6 are the of threeresults data from points the ultrasonic were taken, measurement and the average where the horizontal-axisvalues were recorded. is time Shown (ns) in while Figures the 3–6 vertical-axis are the of results is the from amplitude the ultrasonic of signals measurement (mV). The where values of thethe echo horizontal amplitude‐axis is and time arrival (ns) while time the and vertical are read‐axis fromis the aamplitude cursor provided of signals by(mV). the The data values acquisition of the horizontalecho amplitude‐axis is andtime arrival (ns) while time the and vertical are read‐axis from is the a amplitudecursor provided of signals by the(mV). data The acquisition values of software. Once the cursor is moved to the selected point, a pair (time, amplitude) is shown on the thesoftware. echo amplitudeOnce the cursorand arrival is moved time to and the are selected read frompoint, a acursor pair (time, provided amplitude) by the datais shown acquisition on the screensoftware. and recorded. Once the Forcursor example, is moved round-trip to the selected travel point, time a ( ∆pairt = (time,t1 t 2amplitude)) in Figure is3a shown is 380 on ns the for the screen and recorded. For example, round‐trip travel time (Δt = t1 − t−2) in Figure 3a is 380 ns for the longitudinalscreenlongitudinal and waves. recorded. waves. Similarly, Similarly, For example, the the round-trip roundround‐‐triptrip traveltravel time time is(Δ is tcalculated calculated= t1 − t2) in as Figure as631 631 ns 3a nsfor is for the380 the transversens for transverse the waveslongitudinalwaves in Figure in Figure 3waves.b. 3b. The TheSimilarly, attenuation attenuation the ofround of acoustic acoustic‐trip travel waves waves time is weak is calculated so so that that the as the echo631 echo ns signals for signals the can transverse can be easily be easily recognizedwavesrecognized in for Figure glassfor glass 3b. samples. Thesamples. attenuation However, However, of theacoustic the attenuation attenuation waves is of of weak acoustic acoustic so that waves waves the isecho strong is strong signals for forthe can theCM247LC be CM247LCeasily superalloyrecognizedsuperalloy sample samplefor glass and and samples. the the echo echo However, signals signals are are the more more attenuation didifficultfficult of to toacoustic identify, identify, waves especially especially is strong in the in for the case the case ofCM247LC traverse of traverse superalloy sample and the echo signals are more difficult to identify, especially in the case of traverse waves.waves. Proper Proper adjustment adjustment of of impulse impulse energy energy was was made made to make to make sure sure no ambiguity no ambiguity in picking in picking up the up waves. Proper adjustment of impulse energy was made to make sure no ambiguity in picking up the the arrivalarrival timings.timings. Examples Examples of of the the selection selection of the of thedata data points points for calculation for calculation e.g., t1 e.g.,, t2, At01,, andt2, A A01, are and A1 arrivaldepicted timings. in the ExamplesFigures. The of the average selection elastic of the moduli, data points longitudinal for calculation attenuation e.g., tand1, t2, PoissonA0, and Aratios1 are are depicteddepicted in thethe Figures.Figures. The The average average elastic elastic moduli, moduli, longitudinal longitudinal attenuation attenuation and and Poisson Poisson ratios ratios obtainedobtained by the by ultrasonicthe ultrasonic measurement measurement are are tabulated tabulated in in Table Table2. 2. The The variation variation of of data data is is very very low,low, and obtainedand the measurement by the ultrasonic precision measurement is quite good are tabulated as the mean in Tablevalues 2. of The measurement variation of are data listed. is very low, the measurementand the measurement precision precision is quite is goodquite good as the as mean the mean values values of measurement of measurement are are listed. listed.

(a) (b) (a) (b) Figure 3. The ultrasonic pulse‐echo signal of the ITO‐glass sample #1: (a) Longitudinal; (b) Transverse FigureFigureWave. 3. 3.The The ultrasonic pulse pulse-echo‐echo signal signal of the of ITO the‐glass ITO-glass sample #1: sample (a) Longitudinal; #1: (a) Longitudinal;(b) Transverse (b) TransverseWave. Wave.

(a) (b) (a) (b) FigureFigure 4. 4.The The ultrasonic pulse pulse-echo‐echo signal signal of the of ITO the‐glass ITO-glass sample #2: sample (a) Longitudinal; #2: (a) Longitudinal;(b) Transverse (b) Figure 4. The ultrasonic pulse‐echo signal of the ITO‐glass sample #2: (a) Longitudinal; (b) Transverse TransverseWave. Wave. Wave. Appl. Sci. 2019, 9, x FOR PEER REVIEW 6 of 11 Appl. Sci.Appl.2019 Sci. ,20199, 2067, 9, x FOR PEER REVIEW 6 of 116 of 11

(a) (b) (a) (b) Figure 5. The ultrasonic pulse‐echo signal of the BMG sample: (a) Longitudinal; (b) Transverse Wave. FigureFigure 5. The 5. The ultrasonic ultrasonic pulse-echo pulse‐echo signal signal of the BMG BMG sample: sample: (a) ( Longitudinal;a) Longitudinal; (b) Transverse (b) Transverse Wave. Wave.

(a) (b) (a) (b) FigureFigure 6. The 6. The ultrasonic ultrasonic pulse-echo pulse‐echo signal of of the the CM247LC CM247LC superalloy superalloy sample: sample: (a) Longitudinal; (a) Longitudinal; (b) Figure 6. The ultrasonic pulse‐echo signal of the CM247LC superalloy sample: (a) Longitudinal; Transverse(b) Transverse Wave. Wave. (b) Transverse Wave. TableTable 2. Ultrasonic 2. Ultrasonic measurement measurement results results andand derived elastic elastic coefficients. coefficients. Longitudinal Longitudinal and andshear shear attenuationattenuationTable 2. were Ultrasonic were measured measured measurement at at 20 20MHz MHz results andand 5MHz 5and MHz derived respectively. respectively. elastic coefficients. Longitudinal and shear attenuation were measured at 20MHz and 5MHz respectively. Young’s AttenuationAttenuation Coefficient Coeffi cientα PoissonPoisson Young’s LongitudinalLongitudinal Transverse Transverse ModuluYoung’s SampleSample Number Number Attenuation(dB/mm)α (dB Coefficient/mm) α PoissonRatioRatio Modulus Longitudinal Transverse Modulus Sample Number t (ns) V (m/s) t (ns) V (m/s) Longitudinal(dB/mm) Transverse Ratioν GPa t (ns) VL (m/s) t (ns) VT (m/s)T Longitudinal Transverse ν GPas No.No. 1 (ITO-glass) 1 (ITO‐glass) 380t380 (ns) V5836.8 5836.8L (m/s) t632 (ns) 632 V3509.4T (m/s) 3509.4 Longitudinal0.35 0.35 Transverse1.1 1.1 ν 0.22 0.22 72.67GPa 72.67 No.No. 2No. (ITO-glass) 2 1 (ITO (ITO‐glass)‐glass) 377377380 5867.3 5867.35836.8 634632 634 3488.93509.4 3488.9 0.170.35 0.17 0.911.1 0.91 0.230.22 0.23 72.5272.67 72.52 No.No.No. 3 (BMG)2 3(ITO (BMG)‐glass) 881881377 4790.0 4790.05867.3 1970634 1970 2142.13488.9 2142.1 0.580.17 0.58 2.790.91 2.79 0.380.23 0.38 91.9072.52 91.90 No.No. 4 (CM247LC)No. 4 (CM247LC) 3 (BMG) 11741174881 5940.3 5940.34790.0 20561970 2056 3392.02142.1 3392.0 5.510.58 5.51 5.642.79 5.64 0.260.38 0.26 248.6791.90 248.67 No. 4 (CM247LC) 1174 5940.3 2056 3392.0 5.51 5.64 0.26 248.67 The Young’s modulus of different common types of glass ranges from 51 (high‐lead glass) to 88 The Young’s modulus of different common types of glass ranges from 51 (high-lead glass) to 88 GPa GPa (aluminosilicateThe Young’s modulus glass) ofand different 69 GPa common for the most types commonly of glass ranges used fromsoda ‐51lime (high glass.‐lead The glass) average to 88 (aluminosilicate glass) and 69 GPa for the most commonly used soda-lime glass. The average Young’s Young’sGPa (aluminosilicate moduli measured glass) from and the 69 glassGPa forsamples the most are respectivelycommonly used 72.52 soda (max‐lime error glass. @1.94) The and average 72.67 moduli(maxYoung’s measured error moduli @0.602) from measured GPa, the which glass from samples is the consistent glass are samples respectivelywith the are previous respectively 72.52 published (max 72.52 error (max data. @1.94) error The and [email protected]) 72.67 and ratio (max 72.67 of error @0.602)different(max GPa, error types which @0.602) of glass is GPa, consistent ranges which from is with consistent 0.2 the to previous0.25 with according the published previous to [29] published data.while a The consistent data. Poisson The valuePoisson ratio of ofratio0.22 di ffisoferent typesobtaineddifferent of glass intypes ranges the results.of glass from The ranges 0.2 ultrasonic to 0.25from according 0.2 pulse to 0.25‐echo toaccording method [29] while performed to [29] a consistent while very a consistentsatisfactory value of value 0.22 in measuring is of obtained 0.22 is in the results.theobtained elastic The inconstants the ultrasonic results. of homogeneous The pulse-echo ultrasonic and method pulse amorphous‐echo performed method glass performed material. very satisfactory very satisfactory in measuring in measuring the elastic constantsthe elasticThe of measured homogeneous constants average of homogeneous and Young’s amorphous modulus and amorphous glass and material. Poisson glass ratio material. of BMG samples are 91.90 (max error The measured average Young’s modulus and Poisson ratio of BMG samples are 91.90 (max error @0.9)The measuredGPa and 0.38. average There Young’sis no published modulus data and related Poisson to BMG ratio material of BMG with samples the same are Zr 91.90‐Cu‐ (maxNi‐Al error @0.9) GPa and 0.38. There is no published data related to BMG material with the same Zr‐Cu‐Ni‐Al @0.9)constitution. GPa and 0.38. The elastic There properties is no published of Cu‐Zr data‐Ti BMG related was toinvestigated BMG material by the withelectromagnetic the same Zr-Cu-Ni-Alacoustic constitution. The elastic properties of Cu‐Zr‐Ti BMG was investigated by the electromagnetic acoustic constitution.resonance The (EMAR) elastic technique properties [29]. of The Cu-Zr-Ti Young’s BMG modulus was and investigated Poisson ratio by shown the electromagnetic are about 125 GPa acoustic andresonance 0.36, which (EMAR) are technique reasonably [29]. close The to Young’s the values modulus in current and Poisson study. ratioFurthermore, shown are the about amorphous 125 GPa resonance (EMAR) technique [29]. The Young’s modulus and Poisson ratio shown are about 125 GPa structureand 0.36, of which the BMG are inreasonably this study close is slightly to the different values fromin current the poly study.‐crystalline Furthermore, structure the BMG amorphous in [29]. and 0.36,structure which of the are BMG reasonably in this study close is slightly to the different values in from current the poly study.‐crystalline Furthermore, structure BMG the amorphous in [29]. structure of the BMG in this study is slightly different from the poly-crystalline structure BMG in [29]. The measured average Young’s modulus and Poisson ratio of CM247LC superalloy sample are 248.67 (max error @0.6) GPa and 0.26. According to the data published in [20] the Young’s modulus and Poisson ratio of CM247LC-EA superalloy at ambient temperature are 196.7 GPa and Appl. Sci. 2019, 9, x FOR PEER REVIEW 7 of 11 Appl. Sci. 2019, 9, 2067 7 of 11 The measured average Young’s modulus and Poisson ratio of CM247LC superalloy sample are 248.67 (max error @0.6) GPa and 0.26. According to the data published in [20] the Young’s modulus and 0.15.Poisson The ratio discrepancy of CM247LC of‐ theEA superalloy data is substantially at ambient temperature at about 25%. are 196.7 Although GPa and it may0.15. The be due discrepancy to the diofff erencethe data of is material substantially and sample at about preparations, 25%. Although the it validity may be due of the to ultrasonicthe difference data of has material to be examinedand sample bypreparations, other modality. the validity of the ultrasonic data has to be examined by other modality. TheThe ultrasonic ultrasonic longitudinallongitudinal attenuation coefficients coefficients of of the the two two glass glass samples samples are are 0.35 0.35 and and 0.17 0.17dB/mm dB/mm at 20 at MHz. 20 MHz. The transversal The transversal attenuation attenuation coefficients coe ffiofcients the two of glass the twosamples glass are samples 1.1 and are0.91 1.1dB/mm and 0.91 at dB5 /MHz.mm at As 5 MHz. the glass As the is glass fully is fullyamorphous amorphous and andhomogeneous, homogeneous, the the low low attenuation attenuation is isreasonable reasonable and and predictable. predictable. The The ultrasonic longitudinallongitudinal andand transversaltransversal attenuation attenuation coe coefficientsfficients of of BMGBMG sample sample are are 0.58 0.58 (20 MHz) (20 MHz) and 2.79 and dB /2.79mm (5dB/mm MHz). (5 The MHz). longitudinal The longitudinal and transversal and attenuation transversal coeattenuationfficients of coefficients the CM247LC of superalloythe CM247LC sample superalloy are 5.51 sample dB/mm are (20 MHz)5.51 dB/mm and 5.64 (20 dB MHz)/mm (5 and MHz), 5.64 respectively.dB/mm (5 MHz), As the respectively. material constitution As the material and structure constitution get more and complicated structure get the more acoustic complicated attenuation the isacoustic raised accordingly. attenuation Notably,is raised the accordingly. attenuation coeNotably,fficients the of CM247LCattenuation superalloy coefficients is muchof CM247LC higher thansuperalloy normal metalsis much [28 higher,30,31 ]than e.g., steel,normal homogeneous metals [28,30,31] alloy, e.g.,... which steel, normallyhomogeneous lies within alloy, 1 … dB which/mm. Thenormally measured lies transverse within 1 dB/mm. attenuation The coe measuredfficients followtransverse the same attenuation trend. This coefficients is a unique follow property the same not usuallytrend. This found is ina unique commonly property used not metal usually and ceramic found in materials. commonly Current used metal findings and of ceramic high ultrasonic materials. attenuationCurrent findings are similar of high to what ultrasonic Wu et attenuation al. [32] have are reported, similar atto 1.0what dB Wu/mm et (15MHz) al. [32] have from reported, the family at of 1.0 NidB/mm3Si intermetallic (15MHz) from materials the family previously. of Ni3Si intermetallic materials previously. ThreeThree nanoindentation nanoindentation measurements measurements are are performed performed for for each each sample sample and and the averagethe average values values are 2 taken.are taken. The originalThe original (loading-unloading) (loading‐unloading) and deduced and deduced loading loading (P) versus (P) versus square square of displacement of displacement (h ) (loading-unloading)(h2) (loading‐unloading) diagrams diagrams of metallic of metallic glass glass (sample (sample #3) sample #3) sample in the in nanoindentation the nanoindentation test are test shownare shown in Figure in 7 Figureas an example. 7 as an The example. elastic coe Theffi cientelastic and coefficient hardness measured and hardness by nanoindentation measured by arenanoindentation calculated with are assumed calculated Poisson with ratio assumed and tabulated Poisson ratio in Table and3 tabulated. in Table 3.

(a) (b)

FigureFigure 7. 7.The The (a ()a original) original loading-unloading loading‐unloading loading loading vs. vs. displacement displacement and and (b ()bP) -Ph‐2hrelation2 relation curve curve by by thethe nano-indentation nano‐indentation measurement measurement from from BMG BMG sample. sample.

Table 3. Elastic coeﬃcient and hardness measured by nanoindentation. Table 3. Elastic coefficient and hardness measured by nanoindentation.

ElasticElastic Coefficient Coeﬃ andcient Hardness and Hardness SampleSample Number Number Young’sYoung’s Modulus Modulus (GPa) (GPa) Hardness Hardness (Unload) (Unload) (GPa) (GPa) Test‐1 71.76 7.33 Test-1Test‐2 70.39 71.76 7.04 7.33 No. 1 (ITO‐glass) Test-2 70.39 7.04 No. 1 (ITO-glass) Test‐3 69.55 6.81 Test-3mean 70.57 69.55 7.06 6.81 mean 70.57 7.06 Test‐1 72.79 7.87 Test-1Test‐2 72.15 72.79 7.75 7.87 No. 2 (ITO‐glass) Test-2Test‐3 72.81 72.15 7.85 7.75 No. 2 (ITO-glass) Test-3mean 72.58 72.81 7.82 7.85 meanTest‐1 119.63 72.58 7.87 7.82 No. 3 (BMG) Test‐2 120.28 7.92 Test‐3 119.19 7.71 Appl. Sci. 2019, 9, 2067 8 of 11

Table 3. Cont.

Elastic Coeﬃcient and Hardness Sample Number Young’s Modulus (GPa) Hardness (Unload) (GPa) Test-1 119.63 7.87 Test-2 120.28 7.92 No. 3 (BMG) Test-3 119.19 7.71 mean 119.70 7.83 Test-1 234.75 7.55 Test-2 235.54 7.86 No. 4 (CM247LC) Test-3 236.75 7.48 mean 235.68 7.63

The average Young’s modulus of the four samples from both ultrasonic and nanoindentation are also listed in Table4 for ease of comparison. The average Young’s moduli measured from the glass samples are 72.58 and 70.57 (max error @1.1) GPa, which is in accordance with the ultrasonic measurement. The average Young’s modulus measured from the BMG is 119.70 (max error @0.1) GPa. Compared to 91.90 GPa from ultrasonic measurement the difference is 23.59%. The Young’s modulus measuredAppl. Sci. from 2019, the9, x FOR CM247LC PEER REVIEW superalloy is 235.68 (max error @0.1) GPa. Compared to 248.678 GPa of 11 from ultrasonic measurement the difference is 5.11%. The disparity of the results by the two methods for mean 119.70 7.83 these two materials is quite substantial.Test‐1 However,234.75 the nanoindentation results7.55 are closer to previously published data. This indicates thatTest the‐2 approach235.54 by which the elastic7.86 coe fficient calculated from No. 4 (CM247LC) acoustic speed has to be cautiouslyTest examined.‐3 236.75 7.48 mean 235.68 7.63 Table 4. Comparison of elastic coefficient measured by ultrasonics and nanoindentation. The average Young’s modulus of the four samples from both ultrasonic and nanoindentation are also listed in Table 4 for ease of comparison. TheYoung’s average Modulus Young’s (GPa) moduli measured from the Sample # glass samples are 72.58 and 70.57 (max error @1.1) GPa, which is in accordance with the ultrasonic Ultrasonics Nano-Indentation measurement. The average Young’s modulus measured from the BMG is 119.70 (max error @0.1) GPa. Compared1 (ITO-glass) to 91.90 GPa from ultrasonic 72.507measurement the difference 70.568is 23.59%. The Young’s modulus measured2 (ITO-glass) from the CM247LC superalloy 71.980 is 235.68 (max error @0.1) 72.582 GPa. Compared to 3 (BMG) 91.463 119.698 248.67 GPa from ultrasonic measurement the difference is 5.11%. The disparity of the results by the 4 (CM247LC) 248.377 235.679 two methods for these two materials is quite substantial. However, the nanoindentation results are closer to previously published data. This indicates that the approach by which the elastic coefficient calculatedDifferent fromfrom acoustic that of conventional speed has to be metals cautiously the atoms examined. of metallic glasses are “frozen” in a random, disorderedDifferent structure, from rather that thanof conventional arranging themselvesmetals the intoatoms repeating of metallic patterns glasses of are grains, “frozen” just likein a glass. The metallurgicalrandom, disordered microscopic structure, photo rather ofthan BMG arranging sample themselves (500 ) is into shown repeating in Figure patterns8. of In grains, general, just it is × homogeneouslike glass. The and metallurgical no well-defined microscopic grain boundary photo of BMG can sample be found, (500×) although is shown there in Figure are sparse 8. In general, precipitate it it homogeneous and no well‐defined grain boundary can be found, although there are sparse crystalline phases as indicated in the area enclosed by the red bracket. It may be regarded without precipitate crystalline phases as indicated in the area enclosed by the red bracket. It may be regarded question as poly-crystalline or even amorphous depending on the manufacturing process. without question as poly‐crystalline or even amorphous depending on the manufacturing process.

FigureFigure 8. Metallurgical8. Metallurgical microscopic microscopic photo of of BMG BMG sample sample (500×). (500 ). × The metallurgical microscopic photo of CM247LC sample (500×) is shown in Figure 9. The dendrite structure can be seen with no pores. It is not refined or directionally solidified so that there is no unified grain growth although columnar grains i.e., polycrystalline [23] may exist in different directions with strong matrix gain boundary with carbide and γ–γ’ eutectic phase as indicated in the area enclosed by the red bracket. One common trait for both materials is the disordered structure and broken grain boundary.

Figure 9. Metallurgical microscopic photo of CM247LC superalloy sample (500×). Appl. Sci. 2019, 9, x FOR PEER REVIEW 8 of 11

mean 119.70 7.83 Test‐1 234.75 7.55 Test‐2 235.54 7.86 No. 4 (CM247LC) Test‐3 236.75 7.48 mean 235.68 7.63

Appl. Sci. 2019, 9, 2067 9 of 11

Figure 8. Metallurgical microscopic photo of BMG sample (500×). The metallurgical microscopic photo of CM247LC sample (500 ) is shown in Figure9. The dendrite × structureThe can bemetallurgical seen with nomicroscopic pores. It isphoto not refined of CM247LC or directionally sample (500×) solidified is shown so that in thereFigure is 9. no The unified graindendrite growth structure although can columnar be seen with grains no i.e.,pores. polycrystalline It is not refined [23 or] directionally may exist in solidified different so directions that there with strongis no matrix unified gain grain boundary growth although with carbide columnar and γgrains–γ’ eutectic i.e., polycrystalline phase as indicated [23] may inexist the in area different enclosed directions with strong matrix gain boundary with carbide and γ–γ’ eutectic phase as indicated in the by the red bracket. One common trait for both materials is the disordered structure and broken area enclosed by the red bracket. One common trait for both materials is the disordered structure and grain boundary. broken grain boundary.

FigureFigure 9. Metallurgical 9. Metallurgical microscopic microscopic photo photo of CM247LC superalloy superalloy sample sample (500×). (500 ). × Majumdar et al. [33] compared ultrasonics with the nanoindentation method on titanium alloy material and concluded that elastic modulus can be measured more accurately by the ultrasonic method. The reason cited by them is that the accuracy of elastic modulus measurement using nanoindentation technique depends on more issues while ultrasonic method is directly related to the elastic property and density of the material. Both methods have some potential sources of errors. Factors that can lead to misleading results of nanoindentation include frame compliance, area function, tip sharpness, piling-up, unloading analysis, and specimen Poisson’s ratio [10,11]. However, determination of the elastic modulli matrix is rather complicated for non-homogeneous and anisotropic materials by ultrasonic method. For the homogeneous material such as amorphous glass, we can use simple elastic constant-acoustic velocity relationship to get consistent results with nanoindentaion if care is taken during measurements as in samples 1 and 2. However, the metallic glass and CM247LC materials are partially anisotropic (or poly-crystalline) materials as aforementioned in the Introduction section. The elastic constant matrices are material dependent and difficult to determine. Acoustic mode transformation (longitudinal-transversal and vice versa) is prominent and even more complicated than pure metallic materials with regular domain structure [9]. Direct comparisons between both methods are difficult. This may be the main cause for the discrepancy between the data from the two methods. Up until now, there was a lack of similar intermetallic data to be found for comparison. The velocity dispersion of these materials may contribute to some degree, but not enough to bring up 5 even 20% difference. Another factor related to the acoustic velocity-elastic constant relationship is acoustic dispersion which is discussed in polymer, porous, layered, materials, and sea water with sediment. Acoustic dispersion is the phenomenon of a sound wave decomposed into different frequency components as it passes through a medium. The phase velocity of the sound wave can be viewed as a function of frequency. Hence, frequency components are measured by the rate of change in phase velocities as the radiated waves progress. In general, velocity dispersion can hardly be observed unless enough broadband measurement is taken to cover frequency components at both ends of spectrum, usually in the range of 100 MHz. For the frequency applied at 5 and MHz transducer, effect of velocity dispersion is supposed to be insignificant. The attenuation of ultrasonic wave in solids may be attributed to a number of physical mechanisms within the propagating media. Although the exact nature of the cause of the attenuation may not always be fully understood, however, the possible causes of attenuation in the solid materials under study may be: loss due to thermoelastic relaxation, electron phonon interaction, phonon phonon interaction, magnon-phonon interaction, lattice imperfections, grain boundary losses, and Bardoni relaxation Appl. Sci. 2019, 9, 2067 10 of 11 and internal friction [5,34]. Lattice imperfections and grain boundary losses are the characteristics of the metallic glass and CM247LC materials in addition inherent thermoelastic relaxation, although there is a lack research on the rest of the causes to be referred to. Of the few previous studies on the similar structure superalloy, Wu et al. [32] reported that the Ni3Si superalloy compound in L12 ordered face-centered cubic (fcc) structure has high acoustic attenuation. They are similar in serious dislocation and discontinued granular boundary due to in situ beta phase precipitation which is a good supporting validation for the current finding.

4. Conclusions The ultrasonic method provides a convenient and nondestructive modality to measure mechanical properties of brittle materials. However, the acoustic property may vary with target material, especially the compound materials. The following can be concluded based on the results from the current study. For amorphous glasses, the ultrasonic pulse-echo method is very accurate in measurement of elastic constants. The resulting data matches well with nanoindentation. This is due to the fact that the glass material is isotropic and slightly dispersive. The calculation for elastic constant is uncomplicated. CM247LC superalloy (and other intermetallic alike) is a material of high acoustic attenuation. The reason may be due to strong grain boundary losses and lattice imperfections caused by the inherent strong matrix gain boundary with carbide and γ–γ’ eutectic phase. This family of materials is strongly viscoelastic. For both BMG and CM247LC superalloys, the ultrasonic pulse-echo method deviates signiﬁcantly from nanoindentation. The diﬀerence is large enough to cover the maximal error associated with the nanoindentation method. The relationship of acoustic speed and elastic constants must be reviewed in dealing with compound materials.

Author Contributions: Data curation, H.L.; Formal analysis, P.-C.C. and H.L.; Investigation, S.-J.W. and P.-C.C.; Methodology, S.-J.W.; Software, S.-J.W., P.-C.C. and H.L.; Writing—original draft, S.-J.W.; Writing—review & editing, P.-C.C. Funding: This research received no external funding. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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