There are multiple issues to work out, threading the aluminum sleeve is the one that is most iffy.

I'll assume you are considering a .223 chambered AR barrel.

Do you know if this piece of stock is heat treated?  Do you have a piece of material on hand already, or is this something you found by searching on line?

Barrels get hot enough for the difference in the coefficient of thermal expansion for each piece is not negligible.  The aluminum will grow almost 50% greater than the steel liner.  If they are bonded together, then the bond line stress should be examined.

For containing the chamber pressure, I would want to do an analysis of the thin liner to find the wall thickness required. The commonly used "thin wall pressure vessel" formula will not yield the correct stress to size this part; in case someone directs you to that equation.

The difference in CTE between titanium and steel is closer.

Rough numbers:
13(10^-6) in/in/F for aluminum
7(10^-6) for 4340 steel
5(10^-6) for Ti-6Al-4V


I've wanted to fool with tensioned and damped barrels.  I still think it's an opportunity to improve accuracy.  But the work needs to be done in conjunction with the barrel to action joint to make worthwhile gains.

Ti-6Al-4V is a poor conductor of heat, and steel likes to hold onto heat, so that will cause the barrel temp to rise.  Whether it got high enough to create a problem I don't know off hand.