Plastic Instabilities in Spherical Vessels for Static and Dynamic Loading

Significant changes were made in design limits for pressurized vessels in the 2007 version of the ASME code (Sec. VIII, Div. 3) and 2008 and 2009 Addenda, and these are now a part of the 2010 code. There is now a local damage-mechanics based strain-exhaustion limit, including the well-known global plastic collapse limit. Moreover, Code Case 2564 (Sec. VIII, Div. 3) has recently been approved to address impulsively loaded vessels. It is the purpose of this paper to investigate the plastic collapse limit as it applies to dynamically loaded spherical vessels. Plastic instabilities that could potentially develop in spherical shells under symmetric loading conditions are examined for a variety of plastic constitutive relations. First, literature survey of both static and dynamic instabilities associated with spherical shells is presented. Then, a general plastic instability condition for spherical shells subjected to displacement-controlled and short-duration dynamic pressure loading is given. This instability condition is evaluated for six plastic and viscoplastic constitutive relations. The role of strain rate sensitivity on the instability point is investigated. Conclusions of this work are that there are two fundamental types of instabilities associated with failure of spherical shells. In the case of impulsively loaded vessels, where the pulse duration is short compared with the fundamental period of the structure, one instability type is found not to occur in the absence of static internal pressure. Moreover, it is found that the specific role of strain rate sensitivity on the instability strain depends on the form of the constitutive relation assumed.