## 2 Material and Equipment  
### Material  
The material employed in the present study was TR 360E250S pre-preg CFRE laminates, manufactured by Mitsubishi Chemical Corporation (Tokyo, Japan). The pre-preg consists of PYROFIL TR 50S15L continuous PAN-based carbon fibers and PYROFIL #360 130 \({}^{\circ}\)C curing modified epoxy resin. The material was cured in compression molding for 7 min at a temperature of 140 \({}^{\circ}\)C and a pressure of 8 MPa, with no additional post-curing. The flat specimens were cut with dimensions according to ASTM D3039 [30], with a total length of 250 mm, width of 25 mm, and thickness of 1.83 mm. All of the specimens were tabbed for a length of 50 mm on both sides, to avoid unwanted failure caused by the gripping system. The material used for the tabs was the same CFRE material with a \([45^{\circ}/-45^{\circ}]_{\text{2s}}\) lay-up, and an epoxy, Araldite 420A+B, was used to bond the end tabs to the specimens. The mechanical properties of the material were obtained by standard tests on \([0^{\circ}]_{4}\), \([90^{\circ}]_{8}\), and \([+45^{\circ}/-45^{\circ}]_{\text{2s}}\) specimens, with dimensions according to ASTM D3039 [30], and are listed in Table 1 (with \(\sigma_{1,ult}\), \(\sigma_{2,ult}\), and \(\sigma_{6,ult}\) representing the ultimate longitudinal, transverse, and shear strengths, respectively; \(E_{1}\), \(E_{2}\), and \(G_{12}\) the longitudinal, transverse, and shear elastic moduli, respectively; and \(\upsilon_{12}\) the Poisson's ratio, all calculated in the material coordinates system). Three repetitions of each lay-up regarding the standard tests were performed in order to obtain the material properties. The choice of the lay-up of the tested laminates was made in such a way that specific bi-axiality ratios were developed in their off-axis layers. The bi-axiality ratios are used in multiaxiality studies, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Engineering Property** & **Units** & **Value** \\ \hline \(\sigma_{1,ult}\) & (MPa) & 2272.43 \(\pm\) 88.73 \\ \(\sigma_{2,ult}\) & (MPa) & 52.50 \(\pm\) 2.00 \\ \(\sigma_{6,ult}\) & (MPa) & 52.27 \(\pm\) 1.06 \\ \(E_{1}\) & (GPa) & 125.83 \(\pm\) 3.93 \\ \(E_{2}\) & (GPa) & 9.40 \(\pm\) 0.25 \\ \(G_{12}\) & (GPa) & 4.06 \(\pm\) 0.13 \\ \(\upsilon_{12}\) & - & 0.335 \(\pm\) 0.014 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimentally measured material properties. \(\sigma_{1,ult}\)—longitudinal strength; \(\sigma_{2,ult}\)—transverse strength; \(\sigma_{6,ult}\)—shear strength; \(E_{1}\)—longitudinal modulus; \(E_{2}\)—transverse modulus; \(G_{12}\)—shear modulus; \(\upsilon_{12}\)—Poisson’s ratio. with the aim of expressing the relation between the normal and the shear stress components. Specifically, the bi-axiality ratios are defined as follows:  
\[\lambda_{1}\ =\ \frac{\sigma_{2}}{\sigma_{1}},\ \lambda_{2}\ =\ \frac{\sigma_{6}}{ \sigma_{1}},\ \lambda_{12}\ =\ \frac{\sigma_{6}}{\sigma_{2}}, \tag{1}\]  
where \(\sigma_{1}\) and \(\sigma_{2}\) are the longitudinal and transverse normal stress components, and \(\sigma_{6}\) is the in-plane shear stress in the material coordinates system. In this case, two angle-ply and unbalanced laminates, namely \([0^{\circ}/30^{\circ}]_{\text{2s}}\) and \([0^{\circ}/60^{\circ}]_{\text{2s}}\), were experimentally investigated under quasi-static tensile loading conditions. By using the classical laminate theory, the \(\lambda_{12}\) ratio in the off-axis layers of a \([0^{\circ}/\theta]_{\text{2s}}\) laminate for different values of the angle \(\theta\) is plotted in Figure 1, showing that in the \([0^{\circ}/30^{\circ}]_{\text{2s}}\) laminates, \(\lambda_{12}\) is equal to 2.02, whereas in the \([0^{\circ}/60^{\circ}]_{\text{2s}}\) laminates, it equals 0.64. These values are a first indication that in the \([0^{\circ}/30^{\circ}]_{\text{2s}}\) laminates, the in-plane shear stresses are the dominant ones, whereas in the \([0^{\circ}/60^{\circ}]_{\text{2s}}\) laminates, the transverse stresses dominate the damage process.