Is it ok to put black plastic under a tree to kill the weeds?

I have an apple tree, when I planted it last year, I had put weed block cover at the base, but all the crab grass seemed to have thrived under it. Now I have removed this weed block and tried to hand weed around the base of my apple tree, but I want to do a better job at removing these crab grass.

Whenever I drive by a farm, I see black plastic covering the dirt, and the plant is springing out in an opening. And the vegetables are doing great.

So, would it be possible to do the same for a tree, covering the base with black plastic? Or has anyone done this and damaged their tree?

I would mulch about 3-4 inches around the tree. Don't mulch up to the trunk though, leave a little space. It will greatly reduce weeds and improve the soil over a few years. Spot treat weeds by hand pulling (best) or Roundup (only if necessary).

use cardboard if you want to be "green" about it.

Just completely surround the tree with overlapping pieces of of cardboard. Put some mulch on top of the cardboard to keep it in place and hide it.
by the time the cardboard breaks down into mulch itself, the weeds should be gone.

This way there is nothing to remove and dispose of.

Wouldnt the black plastic warm the soil (year round)....