## 4 Conclusions  
The research mainly comes from the military field on the deformation, damage, and failure modes of cylindrical shell structures under explosive loading. It is a complex process that expansion of shell under explosive load which involves material failure under a strong impact load and structural failure under high strain rate loading. This problem is of great significance in structural protection and weapon design. Therefore, the problem has always been the focus of research, namely the expansion and fracture of cylindrical shells under an explosive load. There are various factors related to the failure process and fracture mode of the metal cylindrical shell under the detonation load. A thorough understanding of the physical mechanism of the expansion fracture of metallic cylindrical shells under explosion loading can provide a basis for military and industrial design and manufacturing.  
Based on the plasticity theory, the paper discusses the evolution characteristics of stress state during the expansion process of cylindrical shells under different explosion pressures, and provides an analysis of the explosion pressure effect on the tensile fracture and shear fracture. Experiments were carried out to investigate the effects of load pulse width and explosive pressures on the fracture characteristics of the shell. Through the macroscopic and microscopic analysis of the recovered fragments, the effects of different load characteristics on the expansion deformation, failure process, and fracture mode of the 20\(\upmu\) shell structure were discussed. The results show the following:  
1. The results from the plasticity theory show that when the detonation pressure is small, the closer the zero hydrostatic interface to the inner wall, the larger the tensile fracture zone. As the explosion pressure increases, the hydrostatic stress zone increases, indicating that the thermoplastic instability of the material is more likely to occur near the inner surface, resulting in a shear weak zone and adiabatic shear failure starting near the inner wall.  
Figure 14: Shear characters and metallography of fragment surface. (**a**) Fragment of section; (**b**) Metallographic 1; (**c**) Metallographic 2.  
Figure 13: Metallography of 20\(\upmu\) shell before the experiment.  
2. The adiabatic shear band was only found in front of the crack starting from the inner wall, rather than in the inner wall area. With the increase of the load peak value, cross or parallel adiabatic shear bands appear in the inner wall of the shell, and their spacing decreases with the increase of the load peak value. When the load peak is further increased, the shell locally presents a single-spin failure mode, and there are a large number of adiabatic shear bands parallel to the fault plane along the direction of the shell wall thickness.  
Conceptualization, D.W.; methodology, X.Q. and W.C.; validation, D.W.; formal analysis, D.W. and W.C.; investigation, D.W.; data curation, D.W.; writing--original draft preparation, D.W.; writing--review and editing, D.W., X.Q. and S.W.; supervision, S.W.; funding acquisition, S.W. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the key project of Intergovernmentmental International Scientific and Technological Innovation Cooperation in China under Grant No.2016 YFE0128900, and the National Natural Science Foundation of China under Grant No.11775166.  
Not applicable.  
All data included in this study are available upon request by contact with the corresponding author.  
The authors declare no conflict of interest.