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