Instead of a metal barrier I would use 40 mil plastic, buried 24-30" deep. You can find it at any quality nursery that sells bamboo. Actually, about anything is preferable over the turf, well except English ivy.

If you really want more turf install sod at the boundary of the yards, and overseed the rest. After the lawn is established a Weed-B-Gone type product (anything with 2-4-D) will kill the pachysandra.

I am sorry. I expressed myself poorly. I do not want to grow grass--actually tomatoes. I was just using the older colloquialism--turf, meaning terrain--poorly obviously.

I think the suggestion of a thick plastic barrier is perfect. I can staple it to the fence uprights to provide structure and rigidity. I assume 6-9 inches should be enough.

Thanks for the suggestion.

Ahh...TOMATOES! Now you're talking.

If you want to use metal, you can buy steel or aluminum flashing in widths from four to twenty inches at most large home building suppliers. I use it to line raised beds built out of treated lumber. It will last a long time.
Mrs H