If you're going to smother tough grasses like wiregrass, torepedo grass, bahiagrass, Bermuda, the smother must be strong, block the light, and stay in place for at least 6 months. All of these grasses are in our yard and it takes forever for a smother to truly work.
The other important element that must be done in conjunction with the actual smother is severance. Going around the edges of the to-be-smothered area to several all connections from the "grass" under the smother to anything outside. Without doing that, no matter now long the smother is in place, anything under there that is still connected to healthy plant material outside of the smother area will stay alive indefinitely until the conditions permit growth again. And will never stop creeping until it finds the edge of the smother to reappear on the other side. Don't bother if this step won't be included.
My fav thing to use is corrugated cardboard under at least 4" of heavy material, anything organic, whatever's available, from "dirt" moved from elsewhere, mulch, leaves, kitchen scraps, yard trimmings, pine needles, any combo of these. Using all organics means nothing needs to be moved later to use, and while waiting the soil is improving in tilth, fertility, drainage.
Make sure there are no sharp sticks or stumps that will puncture the smother.
Uncovering a small area for a month or so to test if it's been long enough for death to truly occur is always a good idea.
This is not for those in a hurry, but for those who want to invest initial waiting and the efforts described above in a plot that will be used indefinitely, improving with time, as more organic material is added as needed to maintain a layer on the surface to protect soil from wild temp and moisture fluctuations.