Frangible bullets
I believe the first frangible-bullet ammo on the consumer market was the Remington "Rocket" .22 short. I think this was originally intended for the carnival shooting gallery market (this was the 1950's), then offered to the public. I believe the bullets were iron powder with a polymer binder, they were higher velocity than normal shorts and often gave off sparks when hitting a steel target. Problem was that when shot in .22 Long Rifle chambers, they could erode a ring in the chamber at the mouth of the short case in a relatively low number of rounds, and they were taken off the market.
If the current frangibles are copper-plated enough to make a difference, then there shouldn't be a problem; if the core is exposed upon firing, then I'd guess that erosion would be a problem.
Note that during the last days of WW2, the Germans resorted to sintered-iron bullets in the 9mm cartridge, simply because there was not enough copper or lead to devote to this secondary cartridge. Probably would wear out the bore of your MP-40 quickly, but it was better than no ammunition at all!
