GuruGle says:
"Yes, tungsten ammo can damage a shotgun barrel. Tungsten is very hard and can scratch barrels, even smoothbore barrels.
"(Rifles/Pistols) After many rounds, the barrel may not seal well to additional rounds of the same caliber. Some calibers are more likely to be stripped than others.
"Tungsten Super Shot can also cause scratches, rubmarks, or scoring in gun barrels and chokes. Some recommend using a gun with interchangeable or replaceable barrels.
"Some say that Tungsten Matrix is safe to use in older guns and produces good patterns. The HEVI-XII load uses flaxseed as a buffer to protect barrels and choke tubes from the tungsten shot."