Doubler plate is the same as reinforcing plate. Insert plate is an integral type of reinforcement of an opening, typically with cross section minimum of total required reinforcement for that opening. It is normally butt welded into the opening, refer to definition of integral reinforced openings in ASME VIII-1.
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Terms RF pad and doubler plate are commonly used with same meaning. RF pad is however to provide reinforcement to any opening or a load bearing component where existing shell/ head thisckness is not sufficient.
Double plate on the other hand is just a barrier/ pad plate which is of the same material/ grage/ weldable quality as of shell plate. This is provided to avoid direct welding of any non pressure part/ accessory which might not be of same same welding quality as of pressure component.