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ASTM A694, is for high pressure service, or A420 for low temperatures, but you don't mention design temperatures.
If you want 52 yield, then Grade F52 should be specified.
I think you probably want A694. It is the standard specification that covers carbon and alloy steel forgings for pipe flanges, fittings, valves, and parts for high-pressure transmission service. Several grades of material based on the minimum yield strength requirements are covered under that spec. Specify the grade as F52 when you need the 52,000 psi yield strength, F60 for 60,000 psi, etc.
Note that for WPHY-52 the TENSILE STRENGTH REQIREMENT = 66ksi
ASTM A694 is listed in MSS SP-75 Specification for High Test, Wrought, Butt Welded, Fittings
The MSS SP-75 Grade you want is designated using "WPHY" prefix and the grade, 52
As ASTM A694 is referenced within MSS SP-75, as are others, and all other things are the responsibility of the mfgr, so I would specify this fitting simply as,
16" CAP, WALL THICKNESS = XXXX, BUTT WELD FITTING, MSS SP-75 GR WPHY-52, ASTM A694
Specify supplementary Notch Toughness requirements as applicable to your situation.
MSS SP-75 does not list A516
A516 is for Pressure Vessel Plate for Moderate Service
There is no intrinsic notch toughness requirement for this material.
Notch toughness requirement must be specified as a supplementary requirement in the P.O.
Here's the killer!
A516 Gr 70 has a tensile strength of 70ksi,
but has a yield strength of 38ksi