## 6 NDT Applications
### The Acoustic Emission Propagation in Guided Wave
The strain linked to the maximum loading capacity in each bar is called critical strain (\(\varepsilon_{p}\)) and it is represented in the Figure 1c. This value is a random variable that depends on \(Gf\). The minimum value of \(\varepsilon_{p}\), is linked to the global strain, will be the global strain where the specimen loses its linear behavior. The bar failure occurs only by tensile solicitation. In compression, the bars have a linear elastic behavior, thus, in compression the failure will be by indirect tension. More details about this version of the lattice model can be found in [53; 54; 55; 56]. In addition to that, applications in the simulation of acoustic emission could be found in [57; 58; 59]. Description of the Model Implemented: The same prismatic waveguide used in the article was simulated using an LDEM + FEM model implemented in the ABAQUS system environment. Details of this implementation could be found in [60]. In this model, a specific toughness must be defined with the value of Gf = 90 KN/m; this value was adopted using as reference [61]. The value of \(p=1\times 10^{-3}\), the third parameter that must be defined in the LDEM constitutive model was defined taking into account that in the global results for tensile strain test, the model begins to lose its linear behavior. A pre-fissure was induced by weakening the bars indicated in red in Figure 19. In the same figure, the arrows indicate the forces applied in the three cases analyzed to induce the fissure propagation in each characteristic fracture mode, that is, Mode I, II, and III depicted in Figure 20a. Moreover, in Figure 19, the positions of 300 nodes are indicated with a red line showing where the higher displacements are measured. Then, the same procedure presented in Section 3 is applied so as to present the results of the AE event in the frequency vs. wavenumber domain. ResultsIn Figure 20b-d, the displacement in the z-direction for the solicited pre-fissure in Modes I and II and the displacement in the y-direction for the Mode III are presented in the frequency vs. wave-number domain. Notice that, in Mode I and II, the acoustic emission that emanates from the pre-fissure is polarized, concentrating their energies in the axial wave mode. In the AE event linked to Mode III, the wave energy in the torsional and flexural wave modes are concentrated. It should be also noticed that the excited frequency spectrum was more widely distributed in Mode I than in the other two modes analyzed. In [62], a similar study was performed with a pre-fissure in the x-y plane. The possibility to know the polarization of the acoustic event in a characteristic structure could be used to design a specific sensor aimed to capture displacement in the range of frequency and specific mode wave expected. In the present application, the potentiality of the simulation scheme to represent an acoustic emission test in the context of a metallic waveguide is shown. In Figure 21, the results obtained in other publications using LDEM and other studies conducted by some of the authors are presented with the aim of illustrating the potential of the methodology proposed related the simulation of the acoustic emission events. Figure 19: The pre-fissured prismatic metallic waveguide modeled with LDEM + FEM. The boundary conditions are also depicted. Figure 20: Results in the Frequency vs. wave-number domain. (**a**) in Mode I, (**b**) in Mode II, (**c**) in Mode III. (**d**) The spatial distribution of the three modes of fissure crack propagation, AE emitted from the pre-fissure solicited. In Figure 21a, the elastic and dissipated energy balance when an AE event happens is shown. The fall of the elastic energy and increase of the dissipated energy appear clearly, in the same plot, the successive increments of the dissipated energy that have an indirect relation with the acoustic emission event are depicted. In Figure 21b, the kinetic energy and its successive increments in the interval in which the AE happens is presented.