# Role of Piezoelectric Elements in Finding the Mechanical Properties of Solid Industrial Materials
## Using Piezoelectricity to Calculate Solid-Material Properties
### Modulus of Elasticity  
In mechanical applications, the modulus of elasticity (\(E\)) of material is a measure of its stiffness. \(E\) is considered as an important material property. The famous rule for this factor is \(E=\sigma/\epsilon\), where \(\sigma\) is stress and \(e\)is strain. The tensile test is regarded as a classic method. To measure \(E\) for non-traditional specimens, non-traditional methods are needed. PE was used as an electric force measurement system (sensor, nominal range 0 N to 50 N). This PE was put just below the central bending point of the specimens (length = 70 mm, width = 4.021 mm to 4.2 mm, and thickness = 0.1 mm to 0.25 mm) to measure \(E\) for magnetron-sputtered thin films of different materials (C, W, W(C), Cr, TIN) with different thicknesses [81]. Two pairs of PEs were used with each pair three pieces of PE, type (air-transducers KG100-0.25, KG100-0.5, and KG100-1 with center frequencies of 250 kHz, 500 kHz, and 1 MHz)in the system shown Figure 8[82]. This approach was used to detect \(E\) based on the relationship \(c~{}=~{}(E/\rho)^{0.5}\) for 13 types of test paper made of different materials with thicknesses ranging from 60 \(\upmu\)m to 700 \(\upmu\)m. The term \(f(\sin\theta)^{2}\) was considered as a function of velocity (\(c\)). Then, they detected the term \((f(\sin\theta)^{2})\) from the method, as explained in the air-coupling technique discussed in Section 2.5. This method was explained in detail previously [83]. The most popular method in acoustic tests for the material properties test is the method of calculation of the time of flight of the wave (TOF). Several studies have been dependent on the TOF method, which depends on conversion formulas of elastic module for homogeneous materials as shown in Equation (5):  
\[E_{\text{TOF}}~{}=~{}2\rho C_{s}^{2}(1~{}+~{}v) \tag{5}\]  
where \(E_{\text{TOF}}\) is in MPa, \(\rho\) is in kg/m\({}^{3}\), \(C_{s}\) is the acoustic shear wave velocity in m/s, \(\
u\) is the Poisson's ratio \(\left(v~{}=~{}\frac{C_{L}^{2}-2C_{s}^{2}}{2(C_{L}^{2}-C_{s}^{2})}\right)\) and \(C_{L}\) is the longitudinal wave velocity. Many published studies used acoustic tests and regarded the two factors \(E_{\text{TOF}}\) and \(E\) is the same factor (no difference between them), and mentioned them as the modulus of elasticity (\(E\)); for example, [PERSON] et al. [84] estimated \(E_{\text{TOF}}\) for. Bismuth strontium calcium copper oxide (BSCCO) tapes and regarded \(E_{\text{TOF}}\) is the same with \(E\), [PERSON] and [PERSON] [85] evaluated the \(E_{\text{TOF}}\) for composite metal foams by experimental and numerical techniques without mention of this difference, in the same contract [PERSON] et al. [86] estimated \(E_{\text{TOF}}\) and regarded it \(E\) for plastics and wood plastic composites using a Taber stiffness tester.Genga et al. [87] studied the effect of Mo\({}_{2}\)C additions on the properties of spark plasma sintering (SPS) manufactured WC-TiC-Ni cemented carbides without mention to this difference too. To study the relationship of \(E\) with hydrostatic pressure (HP) and moisture content (\(\mu\)), the same relationship (Equation (5)) was used to calculate \(E\) for a bulk of cereal grains [88]. The initial state of the cylindrical sample was a length of 150 mm and a diameter of 70 mm in (for five levels of moisture 10%, 12.5%, 15%, 17.5%, and 20%). To achieve this relationship, a magnitude of \(\
u\) was taken from a Polish standard. Then, a PE was used as an emitter and receiver of acoustic shear waves (\(C_{s}\)) (1 KHz) as shown in Figure 9. The values of \(C_{s}\) were measured for each increasing of magnitude of HP. These values of \(\
u\) and \(C_{s}\) were employed to complete the Equation (5) requirements in order to calculate the value of \(E\). The positive relationship between \(E\) and Hp was found, but the relationship between \(E\) and \(\mu\) was negative.