# Equivalent Analysis of Thermo-Dynamic Blow-Off Impulse under X-ray Irradiation
## 7 Responses of Cylindrical Shell Loaded LIHE to Simulate X-ray Effects  
Intense soft (cold) X-ray blow-off impulses induced by atmospheric nuclear explosions will lead to structural responses and consequently may even damage or destroy flying re-entry structures. Therefore, dynamic structural responses of typical structures are significantly necessary to be investigated for weapon design and validation. Without actual nuclear explosion or X-ray radiation environments, some test simulation techniques are used to generate equivalent impulsive loads, this study focuses on Light Initiated High Explosive (LIHE) method and numerically investigates the fidelity of test simulation.  
A typical impulse induced by X-ray blow-off can be given as Figure 13. On the surface of the axisymmetric structure, the impulse is cosine-distributed around the circumference, and uniformly distributed along the outer generating lines. The basic concept of LIHE technique and experimental photograph is illustrated as Figure 14. The load, i.e., the cosine-distributed specific impulse, is meshed into finite elements using generating lines (Spray process causes). In addition, the impulse in each element is simulated by the LIHE.  
The aluminum alloy cylinder shell was selected as the experimental object. The inner diameter of the cylinder shell was 150 mm, the wall thickness was 3 mm and the length was 180 mm. During the experiment, one end of the cylinder shell was lifted and presented an approximate free state, as shown in Figure 15. The photosensitive explosive is distributed within the range of \(\pm\)90\({}^{\circ}\). The pulsed flashlight source is used to initiate the metal wire to generate strong light and synchronously initiate the photosensitive explosive. The peak value of specific impulse designed in the experiment is 150 Pa-s, which is evenly distributed along the bus direction of the cylinder shell, and the circumferential direction is cosine distribution to complete the lateral load loading of the cylinder shell.  
Figure 12: Relation between blow-off impulse and angle of incidence of hard X-ray irradiation.  
Figure 13: X-ray blow-off impulse model on the surface of a cylindrical shell.  
The model was built in Dyna/CAE. A \(\Phi\) 150 mm \(\times\) 180 mm and 3 mm-thick cylindrical shell is considered. The material, assumed as Alloy, is characterized by linear elastic constitutive relationship. The density, Young's modulus and Poisson's ratio are 2.7 \(\times\) 10\({}^{3}\) kg/m\({}^{3}\), 72 GPa and 0.35, respectively. The 1/2 model is meshed into 360 (circumferential direction) \(\times\) 21 (axial direction) \(\times\) 4 (thickness direction) = 30,240 C3D8R elements, as shown in Figure 15.  
Figure 16 gives the statistics of the peak stress errors and shows the shapes of stress histories hardly vary in the mass, but the peaks change a little, the maximum error of stress peak keeps less than 8%. So, the influence of non-simultaneous initiation on simulation fidelity is rather significant. Thus, in practical tests, the detonating LIME should be insured in a cosine thickness as possible as we can.