Bullets that are designed to fragment upon impact because this causes damage to living things. My question is whether frangibility is desired when the purpose is to cause the most structural damage, e.g when the target is an airplane or tank.
I suppose depleted uranium or tungsten carbide bullets match this description, because they are designed to go through armor before they start to disintegrate. But these types of bullets are still meant to eventually hit humans.
It's "useful" because all that, the breaking in half and possibly fragmenting, provides much more stopping power to an otherwise not very effective round. If that doesn't happen, the effect is more like getting stuck with a pencil, except that the bullet will turn 180 degrees and likely exit back first; the M16 is infamous for inconsistent stopping power.
Note that according to the Hague Convention, our military isn't allowed to design bullets to do this....
Fragmentation is very much not a desired feature for creating any type of structural damage; there you want all energy possible to be transmitted to the target. Even expansion is undesired, because the physical work done to deform the bullet is not available to penetrate the structure and then do further damage once past it.
This often gets into the realm of armor piercing (AP) ammo, which has steel or harder metals inside the bullet, sometimes comprising almost all of it, sometimes as a smaller penetrator, like the steel rod inside the .30-06 ammo that I've read became the standard for the US towards the end of WWII (although that was in part because steel was cheaper than lead), or the steel pellet that's in the 5.56 NATO SS109, M855 green tip for the US, design bullet (which is really machine gun ammo/designed to satisfy a silly requirement of piercing a metal helmet at a very long distance, it's not really good ammo for rifles for a whole bunch of reasons).
With the exception of 5.56 NATO AP, there should be no differences in wounding capability, larger caliber bullets don't depend on deformation for wounding. Our M995 black tip ammo ... well, look at this picture: http://www.ar15.com/archive/topic.html?b=3&f=16&t=56...
I assume the bullet is not as likely to break at the cannelure, that the aluminum boot in which it sits is no more likely to cause damage ... but that would have to be tested. Certainly gunners would try to avoid wasting ammo by using AP on humans....
Then we get to exotic stuff that includes an explosive payload, normally 20 mm ammo and above, generally intended for aircraft until we get into serious anti-armored vehicle ammo. You're really not supposed to use that on humans, but of course that's not so well observed in wars. And there's this exotic and inherently expensive .50 BMG round that's intended to provide the destructive power of a 20 mm shell: http://en.wikipedia.org/wiki/Raufoss_Mk_211 ; see the Legality section on expected effects on humans.
It has a role in e.g. GAU-8 (A-10's) PGU-14/B ammo, cast around a depleted uranium perpetrator, acting somewhat like a sabot in allowing the bullet to be lighter in weight and therefore faster, but outside of that sort of thing I don't see it having a role in ammunition.