## 2 Description of the Test Structures
### Elliptical Reference Damage Model  
For composite structures in the aviation industries, the relevant design-driving damage types can be narrowed down to accidental damages, as the others are highly unlikely to occur [28]. For the currently appointed visual inspection, allowable damage limits are generally described in terms of dent depth or projected damage area. Tolerable damage sizes are specifically defined for each airframe part. Damages equal to or larger than this threshold are assumed to reduce the residual strength and must therefore be reliably detected by scheduled or directed field inspections. In a standard aerospace application a residual strength analysis is not performed. This is because airlines do not have the material information and critical load cases of the structure to perform such analysis. In the current operational process, all deliminations are surrounded by an ellipse and the area of the ellipse is determined. This area is compared with values of the maintenance \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Stiffness (GPa)** & & & \\ \hline C\({}_{1111}=130\) & C\({}_{1122}=6.1\) & C\({}_{1133}=6.1\) & & \\ C\({}_{2222}=11.2\) & C\({}_{2233}=5.2\) & & \\ C\({}_{3333}=11.2\) & & & \\  & & & \(C_{2323}=4.2\) & \\ \hline
**Density (kg/m\({}^{3}\))** & & & \\ \hline \hline \(\rho=1571\) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Stiffness values and density for unidirectional Hexply \({}^{\text{@}}\) M21/34%/UD134/T700/300 material used for the plate, taken from [11]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Stiffness (GPa)** & & \\ \hline \(C_{1111}=174.145\) & C\({}_{1122}=4.076\) & C\({}_{1133}=4.076\) & \\ C\({}_{2222}=9.611\) & C\({}_{2233}=2.950\) & & \\  & & \(C_{3333}=9.611\) & & \\  & & & \(C_{1212}=3.330\) & \\  & & & \(C_{2323}=5.882\) & \\  & & & \(C_{1313}=5.882\) \\ \hline
**Density (kg/m\({}^{3}\))** & & & \\ \hline \hline \(\rho=1580\) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Stiffness values and density for unidirectional Hexply \({}^{\text{@}}\) M21/34%/UD194/IMA-12K as material used for the stringer. \begin{table} \begin{tabular}{c c c} \hline \hline
**Transducer ID** & **x-Coordinate (mm)** & **y-Coordinate (mm)** \\ \hline
1 & 50 & 470 \\
2 & 130 & 470 \\
3 & 210 & 470 \\
4 & 290 & 470 \\
5 & 370 & 470 \\
6 & 450 & 470 \\
7 & 50 & 30 \\
8 & 130 & 30 \\
9 & 210 & 30 \\
10 & 290 & 30 \\
11 & 370 & 30 \\
12 & 450 & 30 \\ \hline \hline \end{tabular}  \end{tablemanual provided by the aircraft manufacturer. If the area is defined as critical, the structure has to be repaired or replaced. Based on the currently implemented certification, damage assessment approaches requires repair action for projected damages beyond 600 mm\({}^{2}\)[29; 30]. An example of a projected damage is given in Figure 4. The example is taken from [31]. In this thesis, a model-based evaluation of different impact damages was performed. For this purpose, an automated mapping software (DaMapper) was developed. The software used standard ultrasonic measurement technique and determines the delaminations between layers. The measurement was performed at the German Aerospace Center with a Hillgus system equipped with an Olympus V309-2 transducer; 5 MHz sampling rate and 0.25-0.25 mm measurement grid resolution [31]. Figure 4 shows delaminations between 12 interfaces from a fourteen layer CFRP composite [45/0/135/90/135/0/45]s caused by a 20J impact. The surrounding ellipse illustrates the projected damage area. In this paper, we consider a reversible damage model and demonstrate its application for the reliability assessment of a GW-based SHM system. A metallic disc is used that is attached to the composite structures by a tacky tape as introduced in [20]. The reference damage are not tuned to real impacts. This would require a distribution function of the most frequently occurring impact damages.