# Fatigue Assessment of Explosive Bolts Considering Vibration of Fixtures
## 4 Mechanical Behavior Analysis of Explosive Bolts Based on FEM  
In order to obtain the stress responses of explosive bolts during vibrations on roads, we model the assembly of vehicle frame, warhead, missile body, explosive bolts, and nuts together. The FEM model is shown in Figure 5. The local meshes around the weaken groove are refined to get the mesh convergence. Properties and convergent meshes of the whole geometry missile model are listed in Table 2. Contacts and constraints of the missile vehicle are assigned as listed in Table 3.  
Figure 4: (**a**) Longitudinal, (**b**) vertical, and (**c**) pitch angle accelerations of point A on the missile vehicle when driving on Class A, C, and E roads.  
The pretension force of explosive bolts are assigned as \(F_{pre}=0.4\,\sigma_{b}A_{s}\), where \(A_{s}\) is the area of the dangerous cross-section, i.e., the root section of the weaken groove. Thus, the pretension force is \(F_{pre}=180\) kN. In this paper, for the complexity of the system we simplify the model and the loads. Suppose that the wheels will experience the same road surface model if they are at the same longitudinal position at the same time. Neglecting the loads of lateral (along \(Z\) axis), yaw angle (about \(Y\) axis) and roll angle (about \(X\) axis), the loads are applied by the longitudinal, vertical, and pitch angle accelerations (about \(Z\) axis), \(a_{x}\), \(a_{y}\), and \(a_{\alpha}\), of the missile vehicle obtained in Section 3, as noted in Figure 6.  
Because the Class E road is the most serious condition, we take this to present our results. Figure 7 gives the typical Tresca stress distribution at the weaken groove of bolt C when driving at the Class E road. In our calculation results, the Tresca stress is obviously larger than the Mises stress. Thus,  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Parts**} & \multicolumn{3}{c}{**Material Properties**} & \multirow{2}{*}{**Element Type**} & \multirow{2}{*}{**Number of Elements**} \\  & **Density** & **Elastic** & **Poisson’s** & **Ultimate Tensile** & **Element Type** & **Elements** \\  & **(g/m\({}^{3}\))** & **Modulus (GPa)** & **Ratio** & **Strength \(n_{\gamma}\) (MPa)** & & \\ \hline Vehicle frame & 7800 & 210 & 0.3 & 410 & C3 DR & 22,755 \\ Warhead & 7800 & 210 & 0.3 & 410 & C3 DR & 8092 \\ Missile body & 7800 & 210 & 0.3 & 410 & C3 DR & 80,013 \\ Explosive Bolt & 7790 & 211 & 0.3 & 1570 & C3 DR, C3 DR & 91,128 \\ Nut & 7790 & 211 & 0.3 & 1570 & C3 DR & 5802 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Properties and meshes of the half missile model.  
Figure 5: Meshes of the half missile model.  
Figure 6: Loads of the missile vehicle.  
it will be safer to take the Tresca stress as referring to the maximum shear stress strength theory into account to assess the fatigue of the explosive bolts. The maximum Tresca stress is 1222.32 MPa at the root of the groove, namely the dangerous point, which is lower than the conditional yield strength \(\sigma_{0.2}=1480\) MPa. Thus, the explosive bolt is fully in an elastic deformation state. Figure 8 presents the variation of the Mises and Tresca stress of the dangerous point on the explosive bolt C with time. It shows that the stress varies in small amplitude and that the maximum amplitude is about 14 MPa under the design pretension force. This is because of the existence of enough pretension force and the friction produced between contact surfaces.