Plastic instabilities that could potentially develop in spherical shells under a variety of symmetric loading conditions are examined. First, a literature survey of both static and dynamic instabilities associated with spherical shells is presented, with emphasis on plastic tensile instability. Then, building upon work done elsewhere for cylindrical shells, a plastic instability condition for spherical shells subjected to displacement controlled and impulsive loading is developed and compared with earlier results reported in the literature. It is found that the instability point for displacement controlled loading and impulsive loading of a spherical shell is the same as for a uniaxial tension specimen and for an impulsively loaded plane-strain ring/cylinder. In addition, a simple, one-dimensional strain-softening model is developed that investigates the relationship between instabilities associated with displacement-controlled loading and impulsive loading. Conclusions of this work are that there are two fundamental types of instabilities associated with failure of spherical shells: local and global. Moreover, the local instability, associated with failure under displacement control and impulsive loading, is found to require an imperfection to develop, whereas the global instability does not require an imperfection. The need for experiments to verify these results is discussed.
Transient Solutions for One-Dimensional Problems With Strain Softening
