# Failure Propagation Controlling for Frangible Composite Canister Design
## 3 Tail Design
\begin{table}
\begin{tabular}{c c} \hline \hline Density & 0.98 g/cm\({}^{3}\) \\ \hline Young’s Modulus & 8 GPa \\ \hline Poisson ratio & 0.3 \\ \hline Yield stress & 60 MPa \\ \hline Tangent modulus & 2.34 GPa \\ \hline Plastic strain at failure & 3\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material characteristics of Epoxy-862. Figure 8: Planar tailgate configuration: (**a**) 4 petals centred, (**b**) 4 petals asymetric, (**c**) 5 petals asymmetric. The values of unidirectional E-8962 are reported in the Table 3.  
In all investigated configurations the effective stress distribution of a square plate in composite material with diagonal curvings during impact was replicated, as shown in Figure 11. The effective stress is based on the equivalent stress concept derived from energy principles and is expressed in terms of a single three-variable criterion including the contribution of stress in the fiber direction. The areas with only resin start in the point of contact and continue until the corner. The contact is closer to the upper edge, so due to the constraint condition the stress propagation path has a fast track in this direction. As a result, it needed to reduce the dimensions of the upper petal because of an incomplete fragmentation, and this represented an obstacle for the missile ejection because the debris were too large. To face this issue the bottom petal, which is the bigger, is divided in two smaller triangular petals introducing a carving  
Figure 10: Normal stress-strain curve of Epoxy resin E\(-\)862. Figure 9: Shear stress-strain curve of Epoxy resin E\(-\)862.  
along the height of the triangle. This represents another fast track for stress propagation because the carving is directly on traction from the contact start. In addition, the new smaller bottom petals have lower flexural stiffness because the interlocking area is half while the arm is the same. The stresses are very high in both symmetric and asymmetric impact, but the introduction of a carvings area can mitigate the peak of stress by having a progressive failure, as reported in Figure 12.  
Figure 11: Planar tailgates: Stress Distribution. Figure 12: Planar Tailgates: stress distribution. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Property** & **Symbol** & **LS-DYNA Parameter** & **Value** \\ \hline density & \(\rho\) & RO & 1.5 g/cm\({}^{3}\) \\ \hline Modulus in 1-direction & \(E_{1}\) & EA & 134 GPa \\ \hline Modulus in 2-direction & \(E_{2}\) & EB & 7 GPa \\ \hline Shear modulus & \(G_{12}\) & GAB & 4.2 GPa \\ \hline Major Poisson’s ratio & \(\
u_{12}\) & - & 0.2 \\ \hline Minor Poisson’s ratio & \(\
u_{21}\) & PRAB & 0.1 \\ \hline Strength in 1-direction, tension & \(F_{1}^{tu}\) & XT & 1270 \\ \hline Strength in 2-direction, tension & \(F_{2}^{tu}\) & YT & 42 MPa \\ \hline Strength in 1-direction, compression & \(F_{1}^{cu}\) & XC & 1130 MPa \\ \hline Strength in 2-direction, compression & \(F_{2}^{cu}\) & YC & 141 MPa \\ \hline Shear strength & \(F_{12}^{su}\) & SC & 63 MPa \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Material properties of Carbon fiber E-862 unidirectional tape. The numerical simulations underlined how the asymmetric configuration with five petals achieves a good breaking path, but the stresses are too high, and the petals detach at the same time, hindering launch, as shown in Figure 13.  
An introduction of an angled impact allows for the exploiting of the constant acceleration profile and to reach a higher rotational speed of petals around the sides during the impact and therefore a greater kinetic energy. Curved structures can absorb large amounts of energy due to their shape and ability to deform and allow large displacements before breakage.