Interwebs are huge to navigate
http://www.longrangehunting.com/forums/f17/carbon-wrapped-barrel-93657/#post662432
Speaking of sleeves, aluminum jacket for you, patent of 1932. somehow didn't fly, oh well
https://www.google.ca/patents/US2112144
Regardless, lets look at Christensen Arms ones
https://www.google.ca/patents/US8677670
https://www.google.ca/patents/US5804756
Lets read some of it, from the source so to speak:
One problem which has developed with barrels having a metallic liner surrounded by composite is that they often fail to maintain consistency when repeatedly fired. As a gun is fired several times in rapid succession, the heat generated from the firing of each bullet begins to accumulate in the bore. Because the metal liner and the composite materials generally have somewhat different coefficients of expansion when exposed to heat, a barrel heated by repeated firing can quickly loose its accuracy and consistency. This is due in large part to prior art lack of awareness or inability to form composite/metallic gun barrels, wherein the coefficients of thermal expansion are matched to those of the liner
They specifically claim this to be a problem, and they claim they solve it by different orientation of 2 layers of fiber - inner and outer and calculating an exact mix to match the thermal expansion of the barrel.
barrel temperatures in automatic weapons can exceed the melting point of the composite or epoxy resin
Hm, melting yeh? I was under the impression that you want magic coating on top if you plan to heat the barrels up. Well fine, those automatic weapons you know, belt fed probably.
Mr. Michael K. Degerness disagrees with Mr. Christensen
https://www.google.ca/patents/US6889464?dq=6,889,464&hl=en&sa=X&ved=0CB0Q6AEwAGoVChMI1sfGqaLGxwIVxxaSCh09eQU8
In some prior art composite gun barrels, the jacket has several layers with the tows in each layer having a different winding angle and/or some other different property or properties intended to enhance a particular characteristic such as bursting strength, torsional stiffness or bending stiffness..... This prior art type of gun barrel has several disadvantages such as for example: (1) its accuracy is reduced by excessive variations in the angle the muzzle is pointing at the moment of exit of the projectile caused by high amplitude vibrations at the muzzle end of the barrel; and (2) some embodiments are excessively susceptible to overheating during use. In the prior art, the muzzle angle is stabilized by trimming the length of the barrel to a point where the muzzle is at a node of low amplitude vibrations. However, this technique is time consuming and difficult.
Hm overheating, "excessively susceptible" pardon me. "time consuming and difficult" ok I guess so.
The prior art composite barrels commonly include a liner as the tubular member forming the bore of the firearm with its internal walls. The liner is usually too thin to be used alone as a barrel in the firearm without reinforcement. This type of composite barrel has the disadvantage of having poorer burst strength, poorer thermal conductivity along and through the barrel and wider vibrational swings of its muzzle end.
Poorer thermal conductivity? Who would imagine with thermal conductivity 50 of steel vs 8 of carbon fiber. I would never...
Well, to be honest, with fun aside, it seems to me that in fact the situation is even worse. Not only thermal performance is questionable, but also carbon wrapped barrel has issue with rates of thermal expansion of steel vs wrap, different vibration as sound wave travels through differently through steel and outer layers. Harder to manufacture and easier to screw up. And does not show significant performance advantage?
Not like I'm against the looks though - aesthetics are excellent, no argument.