Hello Waqas;
If the WPS is qualified using a listed base metal specification and list that material on the PQR, all is good asuming the testing verifies the mechanical properties listed by the code are met.
If the WPS is qualified using an unlisted base metal specification and if there are no mechanical properties listed, the WPS cannot be said to meet code requirements. That's why AWS and ASME do not permit the use of AISI base metals with no published properties.
We are aware that the mechanical properties are dependent on the chemistry, manufacturing processes, and the final state of heat treatment. The last two factors are not considered by the AISI system of specifying base metals.
ASTM material specifications may include specific AISI alloys, but ASTM also specifies the state of heat treatment and manufacturing processes along with minimum mechanical properties. Thus, if you use an ASTM listed base metal specification that happens to have the same grade or alloy as the AISI material you "like", i.e., chemistry meeting AISI 1045, you are good to go. However, ordering AISI 1045 only gets you the chemistry, not the mechanical properties.
Once the WPS is qualified using the ASTM with the desired chemistry, it does not mean you are qualified for all AISI 1045, because, once again, the AISI material can be supplied in any one of several heat treatments and it could be forged, hot formed, cold formed, so the properties are not known.
Good luck - Al