Dear Ferdowsi,
The choice of material depends on many factors such as the design temperature, what it will be holding, does the material need to be normalized etc. Typically, the process engineer determines the material and size of the vessel, then the designer determines the thickness of the vessel based on all of the design conditions.
ASME Section II Part D contains a list of approved materials of construction for ASME pressure vessels. You can review Tables 2A and 2B for more information. These tables specifically are for Division 2 vessels.
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Scott MayeuxCADWorx & Analysis Solutions
Intergraph Process, Power, & Marine