My yard is a conglomeration of bermuda, crabgrass, clover and other weeds. When I moved here in early February I laid out the first veggie beds and blueberry patch and put down cardboard (leftover from moving). I also added some dried molasses and a small amount of compost under the cardboard, and pine straw on top of the aisle sections. I put compost and topsoil in the raised beds. I can report that it helped, but certainly didn't smother the bermuda, which keeps popping up everywhere. Interestingly enough, one of the two raised beds has much more of an invasion, although they are only 4 feet apart. I'm going to plant a dense winter cover crop to try and get rid of this stuff.
In my blueberry patch I ended up digging out the sod by hand, putting more cardboard down and topping that with a combination of cedar mulch and hardwood mulch. That seems to be working fairly well, so far.
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Recently, I tried another approach for a new, adjacent bed area. Bought some cheap black plastic and spread it over the new area, also over the existing aisle areas that were becoming weedy. This has been down about a month, and really seems to be working like a champ. Right away, I had a lovely smell of dying, rotting vegetation coming from under the plastic, and when I peeked under the plastic after a week or so, no greenery remained. I put dried molasses here, too, under the plastic. I've read that it needs to be left in place for anywhere from 6 weeks to several months. I'm planning to leave it for 6-8 weeks, then plant some kind of cover crop to finish the job for fall planting. I'll let you know how it all works. I'm planning to do much more of this method, as it's easy, cheap and effective. I have a lot of bermuda and weeds to replace with something that doesn't require mowing.
Good luck!