## 5 Results and Discussion
### Deformation Measurement of the Liner
#### 5.2.3 FEA Strain Analysis  
In addition to the dataset of strain on the dome part of the liner, strain along the cylindrical part of the liner and its fluctuations caused by thickness variations were investigated. After the testing, the liner was cut along the generating-line and the thickness of walls was measured 5 times every 20 mm with a calliper. The measured thickness of walls fluctuated from 4.50 mm to 6.03 mm. The closer to the dome the measurement was taken, the greater the thickness was; however, there was a measurable, average difference in the thickness on one half of the liner. The side of the CC1 and LC1 sensor had an average thickness of 0.2 mm higher than the thickness of side with the CC3 and LC3 sensors. The measured thicknesses of the liner's walls in the locations of sensors were as follows:  
* Circumferential direction: CC1--5.02 mm, CC2--4.87 mm, CC3--4.68 mm,
* Longitudinal direction: LC1--5.08 mm, LC2--4.86 mm, LC3--4.82 mm.  
Figure 13: Strain in circumferential (\(\varepsilon_{xx}\)) and longitudinal (\(\varepsilon_{yy}\)) directions along the generating line using the DIC and FEM methods. Location of negative \(\varepsilon_{xx}\) area marked with arrows. Displacement of the liner shows collapse around this location.  
In Figure 14, strain along the cylinder part of the liner with FBG sensor location indications (\(\varepsilon_{xx}\) and \(\varepsilon_{yy}\)) and strain along the generating line of the cylinder, along with marked locations of sensors, are shown. Results of FBG strain measurements were combined with data from FEM and are given in Table 3. The strain in the location of the FBG sensors was comparable with the results of the FEA based on real thickness measurements of the cylinder. This means that differences of strain are explainable by wall thickness variation, and thus by the manufacturing method.  
Authors investigated the influence of defects on the strain field in the area close to the dome: numerical simulation and point-wise strain measurements were used. Bragg sensors were glued about 7 mm from the liner's edge, the distance between the glue points was about 20 mm. The same area was analyzed by FEM using a tetrahedral mesh. Figure 15 shows the circumferential strain and the location of the strain sensor. The strain obtained from the numerical method was calculated based on the node displacement, of which locations correspond to the glue point and were compared with the strain measured by FBG (in Table 3). Figure 15a shows the circumferential strain for the dome without any defects; Figure 15b shows the circumferential strain for the dome with the defects modeled as an elliptical void. The location of the defect is shown in the wireframe model in Figure 15b,c.  
Figure 14: Strain along the cylinder part of the liner with FBG sensor location indication.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Sensor** & **FBG** [\(\mu\epsilon\)] & **FEM** [\(\mu\epsilon\)] \\ \hline CC1 & 5370 & 5400 \\ \hline CC2 & 5450 & 5600 \\ \hline CC3 & 6900 & 6000 \\ \hline LC1 & 480 & 580 \\ \hline LC2 & 240 & 500 \\ \hline LC3 & 730 & 790 \\ \hline CD1 (bubble) & 300 & 351 \\ \hline CD2 (no bubble) & 270 & 232 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Strain measured with FBG sensors compared with FEM results.