# Identification of Deformation Stage and Crack Initiation in TC11 Alloys Using Acoustic Emission
## 1 Introduction
[PERSON] et al. studied the AE phenomenon of aluminum alloys during ductile fracture and pointed out that there was a strong correlation between the growing amount of cracks and the cumulative count of the AE signals [21]. Nowadays, the waveform analysis method is usually applied to the processing of the AE signals. [PERSON] et al. evaluated the intensities of the AE sources at different deformation stages using a normalized spectral density curve [22]. [PERSON] and [PERSON] applied the time-frequency analysis method to process the AE signals from composite materials in order to estimate the damage process and degree of material degradation [23; 24]. In order to remove the noises of nonstationary signals, Kalman Filter (KF), Wavelet Transform (WT), Empirical Mode Decomposition (EMD), and other technologies have been presented in signal processing. The KF algorithm is a recursive estimation algorithm based on the minimum mean square error. It can process the time-varying system, nonstationary signal, and multidimensional signal, but it can cause errors when dealing with fast-changing signals [25]. The WT can decompose the signals into different frequency components through multiscale analysis and has good time-frequency localization characteristics, but it has problems with the selection of the wavelet basis function [26]. The EMD is a classical method of signal decomposition with good adaptability and it can reflect the local frequency characteristics of the signal very well [27]. It should be noted, however, that the method lacks strict mathematical proof in theory, and there are some problems, such as end-point effect, modal aliasing, etc. The Variable Mode Decomposition (VMD) has the ability of determining the frequency center and bandwidth of the decomposed component by iteratively searching the optimal solution of the variational model. Therefore, it can adaptively decompose the nonstationary signals with strong noise resistance and no modal aliasing [28; 29]. In this work, a tensile test over TC11 titanium alloy was performed to obtain the AE signals produced at different stages of damaging. Then, one of the AE signals was decomposed and denoised using the VMD, in which the signal was divided into two different frequency bands corresponding to the signal generated by metal deformation and by friction and hydraulic system. To analyze these AE signals during the damage of TC11, the logarithm of the energy ratio between the two frequency parts of the signal was calculated as a AE characteristic parameter (AE signal energy ratio). It was shown that the signal energy ratio was different from each other at different stages of the specimen deformation, indicating that the signal energy ratio performs better than the peak amplitude and the peak energy in terms of distinguishing the deforming. In order to identify crack initiation, a method combining Partial Energy Ratio (PER) and Weighted Peak Frequency (WPF) of AE signal characteristic parameters was employed. The results showed that the method could provide real-time monitoring over the aero-engine blade cracks.