below_freezing
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Cute. Racist to boot. Way to stir that "evil whitey" pot.
Why not address the test, or the system, instead?
Warhead would have to rely on kinetic energy, and/or chemical explosives. Of the two, the former is more important, as there simply isn't enough room for a devastating bomb blast. And the shell of the RV would necessarily have to be incredibly thick hardened steel to first penetrate, and then detonate, hence KE is the more probable tool.
The thing about KE penetrators at high mach - they tend to punch relatively clean holes. There is a lot of void space in a carrier. The penetrator could conceivably punch right through the whole ship, but a hole a foot or two across isn't going to sink it. It might cut critical systems if it gets lucky, or it might simply be an annoying hole for damage control parties to deal with.
If there is an explosive device within the missile to break it apart just before impact, the shrapnel will continue traveling at the same speed due to momentum conservation, but cover a larger area due to fragmentation. However, steel is extremely tough, deforms readily and needs to be thick to resist temperature gradients. This is why I believe the DF-21 will not utilize thick steel as the heat shield, but rather heat absorbing ceramic bricks on top of a thin steel/titanium shell. Ceramics are brittle due to microscopic cracks rapidly and spontaneously propagating due to their ionic structures, but they're extremely resistant to heat and friction. A small explosive device would be more than enough to completely shatter the heat shield and turn it into a numerous fragments. A DF-21 that explodes into hundreds of 100 cm^2 ceramic penetrators (which also tend to be self sharpening) would easily create a huge area of holes in the aircraft carrier, and if even 1 hits the fuel storage, the kinetic energy alone may be enough to ignite it.