Likely wrong. Typically hardness is only measured on the surface. To measure hardness in the core, a destructive cutup must be done, and that likely requires a specific drawing note or contract requirement.

For heat-treated parts it is common to see a note like "hardness at 1/2r in the range of ...".
This implies that they must destroy a part (and charge you for it).
On the other hand a difference of a 2 points HRC isn't much.
Have you pulled tensiles or done impacts?
Are the properties what you wanted?
Do you have notes about limits of decarb?
This sounds very loose on you end.

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P.E. Metallurgy, consulting work welcomed

I agree with the interpretation of your vendor of checking surface hardness.

It sounds like your print didn't adequately describe the part you need, so you received something slightly different than your expectations.

IME hardness is specified bc you're concerned about controlling the surface condition against wear or damage so internal hardness is irrelevant. Why are you concerned about internal hardness?

Finished part print calls out a core hardness of 50-60hrc. At our facility parts undergo an additional induction hardening process to increase the surface hardness further.

What do you order from the vendor?

A finished part (with associated core hardness spec), or a forging (with ill-defined hardness)?

A forging with a vague hardness callout.

So, if I understand correctly, the forging vendor is not responsible to meet the 50-60 HRC core hardness requirement which exists only on the finished part print.

They are to meet a 50-60 HRC Hardness but that is admittedly vague.

Take a look at ASTM A668, Standard Specifications for Steel Forgings.
In my copy they have instructions on added material for testing, FIG. 1

what pars are these? how big? what material? will you have it further heat treated after machining?

my interpretation of what has happened:

- part was forged
- part was (through) hardened
- part was annealed/tempered to specs at surface

the annealing must have been too short to soften the core properly. (is there another explanation?)

also:

- hrc is a crude measurement. the last calibration puck i saw had +/- 2 hrc on it (if i recall correctly).

- depending on the application, alloy and it thermo-mechanical history the part might ideed be useless. at hrc 60+ most materials get pretty fragile. that thing might even crack on you spontaniously.

- most commonly for wear protecton the part is in the hrc 40ies and surface hardened.

- for larger parts its impossible to achive identical properties in core and at surface because of solidification/grain structure mechanisms. the core is weaker. (thats why high end parts are machined from "solid" rather than forged.)

- be very cautious to extrapolate hardness to other mechanical properties (like uts or wear attributes).

- has the testing been done professionaly (surface prepped to specs) or did somebody just cut it appart and stick it in the machine?