# Measurement of Elastic Properties of Brittle Materials by Ultrasonic and Indentation Methods
## 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; 5; 6; 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 Lame coefficients; (b) microstructuree.g., grain size, texture, density etc; (c) flaw (porosity, creep damage, fatigue damage etc. ), and other mechanical properties such as tensile strength, shear strength, hardness as discussed by [PERSON] [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 [PERSON] et al.