## 3 Numerical Simulation of AE Signals
### Simulation of Debonding  
The FE model was extended to account for fiber/matrix debonding. It can be noted that debonding at the fiber/matrix interface was not observed experimentally in the tested \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \begin{tabular}{c} **Elastic** \\ **Modulus (GPa)** \\ \end{tabular} & **Poisson’s Ratio** & \begin{tabular}{c} **Density** \\ **(kg/m3)** \\ \end{tabular} & \begin{tabular}{c} **Rayleigh Parameter** \\ \(\alpha_{\text{R}}\) (s\({}^{-1}\)) \\ \end{tabular} & \begin{tabular}{c} **Rayleigh Parameter** \\ \(\beta_{\text{R}}\) (s) \\ \end{tabular} \\ \hline Fiber & Carbon & 187 & 0.22 & 1800 & - & - \\ \hline Matrix type \(\alpha\) & \begin{tabular}{c} \(\alpha_{1}\) \\ DGEBD-3 DCM \\ \end{tabular} & 1.41 & 0.38 & 1034 & 50,000 & \(10^{-8}\) \\ \hline Matrix type \(\alpha\) & \begin{tabular}{c} \(\alpha_{2}\) \\ Hexply 913 [33] \\ \end{tabular} & 3.39 & 0.35 & 1230 & 50,000 & \(10^{-8}\) \\ \hline Matrix type \(\alpha\) & \begin{tabular}{c} \(\alpha_{3}\) \\ PMMA [50] \\ \end{tabular} & 6.2 & 0.32 & 1160 & 1000 & \(10^{-10}\) \\ \hline Matrix type \(\beta\) & \begin{tabular}{c} \(\beta_{1}\) \\ Carbone [53] \\ \end{tabular} & 35 & 0.22 & 2200 & 10,000 & \(3\times 10^{-9}\) \\ \hline Matrix type \(\beta\) & \begin{tabular}{c} \(\beta_{2}\) \\ SiC [54] \\ \end{tabular} & 350 & 0.2 & 3150 & 10,000 & \(4\times 10^{-10}\) \\ \hline Matrix type \(\gamma\) & \
\begin{tabular}{c} \(\text{CFRP}\) \\ [33] \\ \end{tabular} &
\begin{tabular}{c} \(\text{D}_{11}=147.1\); \(\text{D}_{12}=4.11\) \\ D\({}_{13}=4.11\); \(\text{D}_{22}=10.59\) \\ D\({}_{23}=3.09\); \(\text{D}_{33}=10.59\) \\ D\({}_{44}=3.75\); \(\text{D}_{55}=5.97\) \\ D\({}_{66}=5.97\) \\ \end{tabular} & 1550 & 10,000 & \(6\times 10^{-10}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Set of material properties used for FE simulation with three kinds of surrounding medium, matrix type \(\alpha\): polymer medium, matrix type \(\beta\): ceramic medium, matrix type \(\gamma\): anisotropic composite medium. Figure 3: Variation of the damping ratio as a function of frequency according to Rayleigh model for matrix \(\alpha_{1}\) (DGEBD-3 DCM). specimens. However, this damage mechanism is usually observed in composite materials and could have been observed with the same constituents but with another fiber surface treatment, for instance. Indeed, the debonding characteristics depend on the quality of the fiber/matrix interface. Since the proposed FE model was quantitatively validated against experimental results in the case of fiber break, we extended it to simulate debonding and assess the influence of the damage mechanism on the AE signal. Several cases of debonding between the epoxy matrix and the fiber were studied. Contrary to fiber break, for which the crack surface was perpendicular to the loading direction, debonding along the fiber surface occurred in a direction that was parallel to the imposed loading direction. Debonding was assumed to occur over the whole fiber/matrix interface along a given length in the fiber direction, centered with respect to the fiber break location. It should be pointed out that debonding was assumed to occur at the same applied load as the one applied for the fiber break, which is usually experimentally observed and confirmed by numerical simulations in composites. These simulations [55] showed that debonding could not occur before cracking because there is not enough stress at the interface and that debonding starts immediately after cracking, thus at the same loading level. Figure 4 shows different kinetics of debonding. For Model A, several crack lengths were investigated between 20 and 200 \(\upmu\)m. First, it was assumed that crack growth was quasi-instantaneous (Figure 4a). In this case, we had a single jump of the debonding. Numerically, the quasi-instantaneous debonding corresponded to a separation of nodes for a duration equal to one calculation time step (0.1 \(\upmu\)s). The corresponding debonding velocity thus varied between 200 and 2000 m/s.