That tungsten ammo is only good for one use, while tungsten in a spinning bot weapon will have to last for thousands of impacts. The RioBotz team used tungsten counterweights on their one tooth drums very effectively, so it does a a place in bot building.
Tungsten penetrating spike.
Material of a penetrating spike on a robot doesn't matter that much. As Nick already wrote, doubling the speed does more than doubling the mass.
A solid mounted spike on a heavy has only 100 kg to concentrate with a speed up to 30kph. Even 15mm HDPE will accept that and avoid any serious damage.
Active spikes, for example a point on a very fast acting pneumatic ram, are even less powerfull.
Then the mass used is only the rod and point, on a big airspring, that isn't that fast either.
The only way I see tungsten as an advantage, is to make a smaller penetrating spike on a decent axe, and then the brittleness as well as cost will be "less than funny".
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