# Role of Piezoelectric Elements in Finding the Mechanical Properties of Solid Industrial Materials
## Using Piezoelectricity to Calculate Solid-Material Properties
### Fracture Toughness  
In recent years, interest in fracture toughness in the ultrasonic field has increased considerably. Fracture toughness is defined as the ability of the material to resist the progression of a crack. Material failure occurs when \(K_{1}=K_{1\text{C}}\) where: \(K_{1}~{}=~{}\gamma\sigma\sqrt{\pi c}\), \(K_{1}\) = mode 1 stress intensity factor, \(Y\) = constant, depending on geometry/loading, \(\sigma\) = average stress (i.e., away from the crack), \(c\) = crack size, and \(K_{1\text{C}}\) = is a material property named fracture toughness. One of the methods of measuring the increasing toughness of materials is by using a periodic residual stress model, which was explained in detail in [12]. A piezospectroscopic technique [13], a method that was described in detail in another report [14], was used to calculate the residual stress in an alumina matrix (ZrO\({}_{2}\)-Zr) from the measured frequency shifts according to a relation of linear proportionality through the average piezospectroscopic coefficients given by [PERSON] and [PERSON] [15]. Recently, most measurements of residual stresses in several alloys have been implemented by piezospectroscopic measurements based on the shift peak as a function of stress [16]. Table 1 highlights some of the roles of PEs in finding the fracture toughness property for some solid metals. \begin{table}
\begin{tabular}{l l l} \hline
**Description of PE** & **Role of PE** & **Description of the Advantage of PE** \\ \hline \multirow{6}{*}{(100 kHz to 2000 kHz)} & & An indenter tip was employed to obtain a convenient nanometer-resolution imaging of test surface for measuring the slim membrane toughness of the tetrahedral amorphous carbon of diamond [17]. \\  & & \\  & & More details on the piezo-scanner is available in the literature [18; 19]. \\ \hline \multirow{6}{*}{5 MHz} & & PE can eliminate any inertia effects associated with the higher velocity (5000 mm/s) test rates. Results show the magnitudes of \(K_{1\text{C}}\) within the range (\(2.5\pm 0.1\) MPa\(\sqrt{m}\)_to_\(1.7\pm 0.01\) MPa\(\sqrt{m}\)) at an applied load rate of 1 m/s [20]. More details on using PE as a load cell has been previously reported [21; 22; 23]. \\ \cline{1-1} \cline{3-3}  & & \\ \cline{1-1} \cline{3-3}  & & \\ \cline{1-1} \cline{3-3}  & & \\ \end{tabular}
\end{table} 
Table 1: Several piezoelectric element (PE) applications for measuring the fracture of toughness of metals. Figure 1: Behaviour of creep time at each creep case with changes in ultrasonic attenuation coefficient. Many common methods have used attenuation in ultrasonic waves as an indicator of fracture toughness [34; 35; 36]. For example, in the investigation of the influence of nitrogen on the fracture toughness (\(K_{\mathrm{1C}}\)) of stainless steel coatings, a 150 kHz PE was used as filter for signals (filter for interference noise during the test) for frequencies above 300 kHz and below 100 kHz [37]. In addition, the changing of the voltage values of the PE signal, within these bandwidth during the increasing of  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline
**Description of PE** & **Role of PE** & **Description of the Advantage of PE** \\ \hline \multirow{6}{*}{Lead zirconate titanate Pb[ZrxTi1-x]O\({}_{3}\) (PZT) 0.79 in \(\times\) 3.7 in (width\(\times\) length) and thickness 0.00115 in to 0.0063 in} & & PE was used as a sensor for load frequencies from 1 Hz to 10 Hz in epoxy and to study the effect of embedded materials on fracture toughness. \\  & & & Piezoelectric microfiber composite (MFC) (embedded piezoelectric sensors) was covered with a thin polymer film on its two sides. Then, the sandwich was inserted as an embedded material in glass/epoxy composite material (12-in\({}^{2}\) \\  & & & unidirectional panels), as shown in Figure 2 to function as a sensor [24; 25; 26]. More details on embedded sensors have been reported [27; 28].