# Role of Piezoelectric Elements in Finding the Mechanical Properties of Solid Industrial Materials
## Using Piezoelectricity to Calculate Solid-Material Properties
### Hardness  
Hardness is defined as the resistance to plastic deformation, such as scratching, cutting, or abrasion. Several classic methods to determine the hardness of a material include the Rockwell hardness test, Brinell hardness, Vickers, Knoop hardness, and Shore. A number of researchers suggested different methods to use PE in finding the hardness of materials. PE was used as a 1 Hz actuator in a nano/micro-hardness tester to apply load on a specimen to check the hardness [38]. Similarly, PE was regarded as load actuator in the hardness measurements for JNI, JN2, SUS304, SUS 316L, Ti alloy, and copper at cryogenic temperatures less than 4.2 K, where the piezo-actuator is expected to maintain the given load constant when the applied load fluctuates [39]. Another application in this field is PE as a piezoscanner [40]. As a sensor of load, PE with a frequency of 5 MHz, was connected with an amplifier and displayed on a memory oscilloscope. PE was used to calculate the dynamic and static hardness of different materials [41]. In the same context, five piezo-elements in series were used as a force sensor, where the maximum displacement of dynamic part in that device was 15 \(\upmu\)m [42; 43]. The authors in [44; 45; 46; 47; 48; 49] used the PE in the ultrasonic contact impedance (UCI) method to measure the frequency shift. However, MIC10 and MIC20 can be also used for standardization according to ASTM A 1038 and DIN 50159 to evaluate the hardness of the material, as indicated in Figure 3 [46]. When a 70 kHz PE excite s the metal rod, the end of this rod will penetrate the specimen as provided by Vickers Diamond. This penetration will cause a frequency shift and allow the indentation area to be electronically detected by measuring the shift of an ultrasonic frequency using a piezoelectric receiver. The frequency shift is proportional to the size of the Vickers test indentation. Then, hardness can be evaluated using Equation (2):  
\[\Delta\mathrm{f}=f\;\mathrm{(Eeff,\;A)};\;\mathrm{HV}=\mathrm{F}/\mathrm{A} \tag{2}\]  
where \(\Delta\mathrm{f}\) is the frequency shift, A is the area of indentation, Eeff is the effective Young's modulus, HV is the Vickers hardness value, and F is the test load. Figure 3: The ultrasonic contact impedance (UCI) method (MIC 10, MIC 20). To characterize and identify a traffic-hardened layer in a rail surface and to identify a minimum detectable hardness gradient requirement in this rail, three different frequency angle-wedge PEs (ultrasonic transducers) were used to develop the handled prototype (Lunch Box PC) [50; 51]. This box has the ability to produce Sezawa waves that have been used in inspections for rail specimens, as shown in Figure 4a,b. These PE pieces, with frequencies ranging from 1 MHz to 5 MHz, were included after a grinding cycle to the rail specimen (to use in pulse echo technique). Then, this process was repeated for several depths at 1.9 mm to 5.65 mm of grinding to check the amplitude of the Sezawa wave after each grinding cycle. Afterward, they compared these results (maximum amplitudes of the Sezawa wave) from the different depths of the grinding cycles with a standard rail hardness profile and used the amplitude of these waves as an indication of hardness. The design of Gutt [52] is regarded as one of the modern apparatuses in the field of using an acoustic technique for testing the properties of materials, because they used PE as a device for sensing the elastic reaction force from a specimen after force removal. This PE was located after a press part, as shown in Figure 5a, and the output voltage from this PE suits the dynamic force Fd, as shown in Figure 5b. The shadowed area represents the elastic and plastic deformation energy. This energy is relative to the kinetic energy of impact calculated from a connected superior photo barrier coupled to an electronic counter and other facilities, and it is proportional to dynamic hardness. The references [53; 54; 55]provide more details about how to create equivalent voltage from mechanical load by using PE.