This will need to be setup with your Destructible and how much damage it can take. Setting up an accumulated damage will help with this. It will not calculate how much time has passed when it was first hit to be destroyed. If you set it up to take accumulated damage this could work.
If you’re talking about having the chunks that break off disappear there are a couple of ways you could do this. 1 you could use Debris Timeout that will make all chunks disappear after a specified time, but this will make them all disappear at the same time. That is intended with debris timeout. 2 you could set up a GPU particle to spawn debris meshes that can hit the ground, disperse and than disappear independently of the others.
Destruction elements can be complicated to get right but testing things in PhysX Labs and trying out different settings can get you the look you want. There is no silver bullet to get the exact look you have in your mind as everyone has different ideas for what they want. We can point you in the right direction but you’ll need to iterate and tweak to get exactly the look and feel you want. 
Destruction meshes are a lot of fun and feel free to ask questions anytime! 
Tim