Do the mechanicals change on bars when ground down to different diameters, if yes, shouldn't they be retested after being ground?
I assume you are referring to the tensile properties of bars machined to different diameters. As long as your bars have a uniform microstructure in the radial direction (NO surface decarburization/carburization/intergranualar oxidation, similar deformation flow lines, etc.), equi-sized tensile specimens taken from different regions of the cross section must exhibit identical tensile properties. Due to the effect of preceding processing steps (casting, forming, heat treatment, etc.), a uniform microstructure in the radial direction is in practice not easy to obtain with relatively thick bars.
Please note that the tensile specimens taken from the very same uniform material may exhibit different total elongations; the smaller the gauge length, the larger the post-uniform elongation and therefore the total elongation. Other important tensile properties such as yield strength, ultimate tensile strength, and uniform elongation are basically not affected by the size of tensile specimens. The reason for the inequality of post-uniform elongations with different gauge lengths is that for the calculation of the post-uniform elongation, the localized deformation in the necked zone of the gauge section is divided by the entire gauge length. This leads to overestimated total elongation with sub-sized tensile specimens.