Actually, the military use of "ball" has little to do with armor piercing as a rule and more to do with the Hague Accords (not the Geneva Convention).
As per the First Hague Conference, 1899:
The Undersigned, Plenipotentiaries of the Powers represented at the International Peace Conference at The Hague, duly authorized to that effect by their Governments,
Inspired by the sentiments which found expression in the Declaration of St. Petersburg of the 29th November (11th December), 1868,
Declare as follows:
"The Contracting Parties agree to abstain from the use of bullets which expand or flatten easily in the human body, such as bullets with a hard envelope which does not entirely cover the core, or is pierced with incisions."
The present Declaration is only binding for the Contracting Powers in the case of a war between two or more of them.
It shall cease to be binding from the time when, in a war between the Contracting Parties, one of the belligerents is joined by a non-Contracting Power.
The US is not actually a signatory of this accord, but tends to respect it as an informal matter of military policy.
Further, one accord to which the US is a signatory is the Hague Convention IV of 1907 - Article 23(e), which states (in part):
…it is especially forbidden -
To employ arms, projectiles, or material (sic) calculated to cause unnecessary suffering...
I put 'sic' because 'material' should actually be either 'materials' for consistent parallel plurality with the sentence, or 'materiel' for further correctness in military jargon of the time.
And, as covered very nicely on this page:
http://www.thegunzone.com/hague.html
The use of frangible ammunition has been authorized when engaging "non-state-affiliated" forces, such as insurgents in Afghanistan. The Sierra MatchKing projectile, which many may recognize as a jacketed hollow-point (albeit a very, very small hollow point), has also been authorized for use since its design is due to an accuracy requirement rather than intentional frangibility. However, with the earlier ruling that even purpose-built frangible ammunition may be used against "non-state-affiliated" combatants, this point is somewhat moot. However, it does hold water when, in the future, such occasion arose to engage an enemy's standing military forces or affiliated reserves.
At any rate, the long and the short of it is that - and ask any of our resident bullet-swagers who are on the forum, which doesn't describe me at present time but is something I have planned for the future - when creating jackets and complete projectiles, the open-bottomed FMJ is king when it comes to overall tooling simplicity.
-M
