Deformation and failure of thin spherical shells under dynamic impact loading: Experiment and analytical model

Thin curved shells are widely used in engineering. A shallow spherical shell is an effective representation of a curved shell affected by local impact loading. Therefore, the dynamic response of spherical shells under impact loading should be investigated to provide a design reference for curved shells applicable to engineering fields. In this study, the dynamic response and perforation of an aluminum spherical shell impacted by a cylindrical projectile were investigated theoretically. An isometric transformation was adopted to describe the major bending deformation of the spherical shell around the impact point. In addition, an edge region between the major bending part and an undeformed part was observed experimentally and described using a deformation mode. Hamilton's principle was adopted to derive the governing equations of the dynamic response of the impacted spherical shell. Furthermore, a viscoplastic strengthened model was introduced to describe the membrane force and bending moment of the perforation, whereas a rigid–plastic model was used to calculate the force and moment of the other parts of the spherical shell. The governing equations combined with the strengthened model were solved using the Runge–Kutta method. A comparison between the theoretical predictions and experimental results indicated a good agreement between them. Finally, the effects of the parameters set in the governing equations of the theoretical prediction were analyzed. We observed that the theoretical model predicted dimple radius more accurately than dimple depth. The dimple depth is linearly proportional to the impact velocity. In addition, the assumed sizes of the shear region of perforation only affect the ballistic limit and deformation generated by a velocity higher than the ballistic limit. The deformation and perforation of the impacted shell are almost independent of the initial width of the edge region of deformation. Additionally, we observed that the ballistic limit of the shell is linearly proportional to the shell thickness.