Can anybody tell me how thick the plastic is on a typical hard case lipo battery? I'm designing a homebuilt touring car and wondering how much protection the cases can be expected to provide I'm interested in abrasion rather than impact resistance.

It depends on the lipo. Anywhere from 1.x to 3mm thick in my experience. They're thinner along the seams. It's a fairly resilient plastic, a few of mine have been ejected from the car and dragged along the track or sent sliding along the asphalt/concrete surface with only cosmetic damage. (label torn off, hella scratches)

Avoid the lipos with the carbon fibre look case. Those tend to be thinner and more fragile, once again IME.

the case nearly no protection.

1 to 3mm seems a surprising about of variation. Thanks for the info.