# Identification of Deformation Stage and Crack Initiation in TC11 Alloys Using Acoustic Emission
## 4 Analysis of Experimental Results
### AE Crack Initiation Identification Method  
From Figure 5 to Figure 9, we observed that the AE signal in the fracture stage had obvious sudden signal characteristics, with two peak frequencies located between 150-200 kHz and 200-250 kHz. In Figure 9, the signals in these frequency ranges originated from the beginning of the AE activity, eliminating the possibility of these high-frequency signals being related to wave reflection. For the remaining three stages of deformation, there were stable signal components within 50-150 kHz. These signals were mainly generated from the friction between the specimen and the fixture and the hydraulic system of the testing machine.  
Based on the analysis results of the time- and frequency-domain of the AE signals, two Partial Energies (PE), PE1 and PE2, were employed, corresponding to the signal energy with frequency positioned in the range of 50-150 kHz and 150-500 kHz, respectively. The VMD was used to decompose the signal in 10 layers. The \(i\)th component obtained by the decomposition was recorded as \(u_{i}\), and the Peak Frequency (PF) corresponding to each component was recorded as \(pf_{i}\). For each AE signal, the values of PE1 and PE2 were:  
\[\begin{array}{l}\text{PE1}=\sum\limits_{i=1}^{n_{1}}E(u_{i})\quad\,\,\,pf_{ i}\in[50,150]\text{kHz}\\ \text{PE2}=\sum\limits_{i=1}^{n_{2}}E(u_{i})\quad\,\,\,pf_{i}\in[150,500]\text{ kHz}\end{array} \tag{5}\]  
where \(E(u_{i})\) is the energy ratio between the \(u_{i}\) component and the total energy of the signal.  
From Figure 5, by comparing the signal in the elastic-yield stage to the signal peaks in the fracture stage, we found that there was no significant difference of signal peaks between 150-300 kHz at the fracture stage. In order to distinguish the AE signals between these two stages, a AE characteristic parameter, Weighted Peak Frequency (WPF), is presented, which is expressed by:  
\[\text{WPF}=\left\{\begin{array}{ll}\frac{\sum\limits_{i=1}^{n_{1}}E(u_{i})pf _{i}}{\text{PE1}}&\text{PE1}>\text{PE2}\\ \frac{\sum\limits_{i=1}^{n_{2}}E(u_{i})pf_{i}}{\text{PE2}}&\text{PE1}\leq\text {PE2}\end{array}\right., \tag{6}\]  
We found that the calculated Weighted Peak Frequency can distinguish the AE signals dominated by PE1 and PE2, respectively. Additionally, for all the AE signals dominated by PE2, the different energy distribution characteristics can be displayed in the frequency of greater than 150 kHz. Thus, the AE signal generated after the crack initiation can be identified from the elastic yield stage.  
In every stage of deformation damage, 200 AE signals were selected (uniformly distributed in the time history) for each stage of TC11 titanium alloy deformation. The PE2 values of the decomposed 800 AE signals for the four stages were plotted in a two-dimensional scatter diagram as shown in Figure 12, with the WPF being the abscissa. We can see that the AE signal after the crack was clearly distinguished, and it was mainly concentrated in the range of PE2 \(>\) 0.7 and WPF \(<\) 235 kHz. For the signals of PE2 \(<\) 0.5 and WPF \(<\) 150 kHz, these ranges were mainly related to the AE signals generated by the friction and hydraulic systems with low signal-to-noise ratio. The AE signal in the elastic-yield stage was mainly distributed in the range of PE2 \(>\) 0.7 and WPF \(>\) 235 kHz. Therefore, the combination of PE2 and WPF can effectively identify the crack initiation during the tensile process of the specimen. In the fracture stage, 8 out of the 200 signals fell outside the crack initiation area, but these points did not lead to a misjudgment of the result. We also found that there were 22 out of the 600 signals in the remaining three stages which fell in the crack initiation area. These 22 points gave us a small percent error. Therefore, the correct rate of judgment on the crack is 96.33%, which was calculated with the presented two parameters. We should also notice that using this method caused the crack initiation time showed to be earlier than the macroscopic crack time recorded by the micro camera.