As the maker! I can add the following to Elliot's information.
what happens between the hammer and the flat anvil, is the
softer metal gets squeezed between the 2 harder metals so moves in both directions ie the x and y planes. Its not stretched, its pushed! . Thats why Ive never had one crack .
A rolling mill on the other hand moves the metal in 99% of the time in just one direction. Ie it gets longer buy not wider, just the x dimension.. Same process.
In my forging process the metal is pushed not only in the center but all over the surface of the disc.
In theory, if one has a 15in disc 1/8in thick then raising/ sinking! it 7 in would thin it to 1/16th at the center, and progressively less till the edge would at 15 in still be 1/8in.
Hope you follow.
Whats important is the customer was delighted, which resulted in a friend of his comissioning one as well. He also said could I make him one in gold?. No problem I said, but he'd have to pay the metal cost up front I then just charge for my sore arm!.