Mr. Tom,
It seems that there is ALWAYS construction in AR. There is a major project on the last couple of miles of I-40 going east just before you get on the Memphis/Arkansas bridge. It's not that bad, just go slow and be careful.
Now the BIG problem is the I-240/I-40 interchange in Memphis going east towards Nashville. No matter how you do it, you have to go through this part of the interstate whether you take the north leg or the south leg..... they will meet up at this major construction project.
TDOT is building a new fly-over bridge that makes traffic come to a crawl (also becomes a parking lot). DO NOT attempt this route during rush hour (morning or evening), you will be parked for quite a while. And like always, there is some goofball that wrecks causing an even bigger headache.
Good luck,
MM.