I have driven a lot of miles on I40 in between Willmington and Memphis
within the last few years and driven most of this section recently.
Moving West to east here are my observations.

West Memphis Arkansas through Memphis can be crazy.  I am currently
staying in Memphis and the traffic is very bad every afternoon on
sections I40 and I240.  Avoid the section of 240 that runs directly
north and south (the west side of memphis near downtown) as it is down
to one lane under heavy construction.

It seems like going straight through Nashville (not taking the
recommended bypass) is quicker.

Knoxville can have very bad rush traffic.  I have gotten stuck there
for hours on multiple occasions.  Avoid peak hours if possible.

Just east of the Tennessee line a section of east bound I40 washed
away.  Last time I passed through all traffic was routed over the west
bound lanes for a couple of miles at this point.  Speeds averaged 40
to 45 through this section.  Reconstruction of the center barrier has
been progressing further east of this washout and you should
experience a few miles of one lane interstate here as well. Sesonal
and Weekend traffic can be very thick from Knoxville to Asheville, and
I have seen some bad backups around the spots mentioned above and
around the I40 and I26 intersection.  The I40 and I26 intersection is
usually backed up at least a bit around 5:00 and going south on I26
(really I26 east) can be a real pain.

If you want to bypass all of the nonsense in the smokies you can go
north to Johnson City and then come down the new section of I26 to
Asheville where you rejoin I40 east of all of the problems unless
there is severe snow on the continental divide just east of Black
Mountain (rarely is a problem).  This route doesn't add much time at
all even when there aren't a lot of backups, and the new interstate is
amazing.  Johnson City to Asheville is beautiful, be sure to do this
in daylight.

Around Raleigh I40 is undergoing some construction in a few places and
is probably still down to one lane fairly close to Raleigh.
Greenesboro etc. has gotten a lot better lately but the Raleigh
section can be tough.  I have driven it late at night with pretty good
luck.

Hope this helps,,

Jonathan Poole