# Identification of Deformation Stage and Crack Initiation in TC11 Alloys Using Acoustic Emission
## 4 Analysis of Experimental Results
### AE Signal Energy Ratio in Deformation Damage  
Based on the AE signal analysis in four stages, each component obtained by the VMD was first reconstructed into two signals positioned, respectively, in 50-200 kHz and 200-500 kHz. Then, the energy ratio R between two signals was calculated with Equations (3) and (4), as shown in Figure 10.  
Figure 8: Time- and frequency-domain components of the typical AE signals after the VMD in the necking stage. Figure 9: Time- and frequency-domain components of the typical AE signals after the VMD in the fracture stage. From Figure 10, we can find an obvious dividing line of R = \(-0.5\) for the four stages, which is represented by a black dashed solid line. In the elastic-yield stage (Figure 10a) of TC11 titanium alloy, the majority of the AE signal energy ratio was greater than \(-0.5\). This was due to the simultaneous elastic and plastic deformation of the material at this stage. Shifting and dislocation activities were extremely active, resulting in a great number of AE signals with large proportion of \(H_{\text{us}}\). Some signals showed R values of greater than \(0.5\). After the deformation, the specimen began to come to the strengthening stage (Figure 10b). The number of signals with R value greater than \(-0.5\) decreased sharply, and nearly no signals with R value greater than \(0.5\) were generated. At the same time, a large number of signals with R values less than \(-0.5\) were generated. Due to the crystal slip and dislocation freedom reduction, a large area of dislocation plugging occurred. This reduced the energy of the collected AE signal \(H_{\text{us}}\) from the deformation of the specimen, and the signals \(H_{\text{us}}\) from the friction and hydraulic systems began to dominate. At the necking stage of the specimen deformation (Figure 10c), the R value of most signals was less than \(-0.5\), and the plastic deformation of the material at this stage lost its balance. The plastic deformation, except the necking zone stops and the dislocation congestion produced by the necking area, increased significantly, which resulted in the AE signals generated by  
Figure 10: AE signal energy ratio of titanium alloy in four stages of deformation damage: (**a**) Elastic yield stage; (**b**) Strengthening stage; (**c**) Necking stage; (**d**) Fracture stage. the deformation of the piece being greatly reduced in both quantity and amplitude. During the fracture stage (Figure 10d), the R value began to show similar characteristics to that in the elastic-yield stage. This was because under the three-dimensional tensile force inside the necking region, the front edge of the dense dislocation group produced a large tensile stress and aggregated to the weak part to start small cracks. The gradual propagating of the macro cracks led to the complete fracture of the TC11. The occurrence of cracks caused the \(H_{us}\) to dominate, resulting in a much lager R value. In order to clearly show the distribution characteristics of the AE signal energy ratio R at the four stages of specimen deformation, a normal distribution curve was plotted and shown in Figure 11. It can be seen that the R value was mainly distributed in the (\(-\)0.5, 0.5) during the elastic-yield stage. There were two peaks in the strengthening stage. Most of the signal R values were distributed between (\(-\)1.5, \(-\)0.5), and some were in (\(-\)0.5, 0.5). The R value of the necking stage was mainly distributed over (\(-\)1.5, \(-\)0.5). The R values at the fracture stage were in (\(-\)0.5, 0.5). Table 5 shows the mean and standard deviation of the AE signal energy ratio of the four specimens in the tensile test. In traditional approaches, the energy of the AE signal is one of the significant characteristic parameters. In order to show the advantage of the AE signal energy ratio R, the change of the AE signal energy with time was plot in Figure 11. The AE energy gradually decreased with the progress of deforming, but the change did not apparently show the stage-related features.