Beginner modeling question

I’ve broken apart a mesh (using rayfire) for the purpose of creating an animated explosion. While the original mesh looks fine, the fractured one shows “tears” where the sections fit together that flicker when you move around them.

I don’t know enough modeling terminology to find an answer with google, but hopefully this picture will give a better idea of the problem.

I’m guessing I need some sort of modifier on the meshes, but nothing I’ve tried has worked yet. Can anyone offer help for this stupid newbie?

That’s overlapping polygons. When rendered/compiled it won’t look like that (probably).

Yes it will.

Quick unscientific test: