There are several ASTM specs which cover castings, including A47, A48, A536, and A668.
ASTM A47
A47 covers malleable castings intended for general use up to temperatures around 750⁰ Fahrenheit. A47 castings come in one grade, available in metric and imperial.
Common forgings specified to A47: Shear Plates, Beveled Washers
ASTM A48
A48 covers gray iron castings intended for general use. A48 castings are supplied based on tensile strength. There are 9 classes in this grade with various tensile strengths and 4 class types with different required test bar diameters.
Common forgings specified to A48: Ogee Washers, Hillside Washers
ASTM A536
A536 covers castings made of ductile iron. A536 castings are available in 5 grades with various tensile, yield, and elongation requirements.
Common forgings specified to A536: Hillside Washers, Rosette Washers
ASTM A668
A668 covers heat treated and untreated carbon and alloy steel forgings for industrial use. A688 forgings are available in six classes for carbon steel, and seven classes for alloy steel.
Common forgings specified to A668: Clevises, Turnbuckles