On several occasions we've actually seen the Hulk damaging or breaking vibranium artifacts. In Ultimate Avengers II Vibranium was shown to be largely useless against the Hulk because it becomes brittle when exposed to Gamma radiation (which he emits when he becomes especially angry).
Vibranium can also cut the Hulk due to the same reasoning as Adamantium -- they are two of the strongest metals in the world. The one thing to note is that when Hulk gets angrier, his skin becomes more durable and can then withstand even these metals.
In the canon Earth-616 depictions of the Marvel Universe, the Hulk has never destroyed Captain America's shield. And unless something about his power profile changes, he never will.
Though the Hulk did manage to rip apart Adamantium, it is not established that it was the same metal that Wolverine's skeleton is laced with. It might have been a different and cheaper alloy, which allowed the green monster to rip it apart.
In Age of Ultron, concentrated energy blasts of sufficient heat and power are also shown to be effective against Vibranium. Thor's lightning, Vision's Mind Stone lasers and Iron Man's repulsor beams were able to melt Ultron's body when used in combination, meaning that high enough temperatures can break Vibranium down.
The fact that Thanos possesses enough power to beak vibranium is a testament to the strength of the Mad Titan, but more importantly, the weapon itself. Although the origin of the sword is unknown, the evident force and qualities of the blade reveal clues to its composition.
But you can heat the metal to a soft red point, and it can also be melted. So Superman could melt vibranium with his heat vision. Superman heat vision has been shown capable of cutting through something that was said to be as powerful as the event horizon of a black hole.
The amazing thing about the Hulk is that unlike nearly every other superhero ever created, the Hulk's strength has absolutely no upper limit.
Wolverine manages to do some damage, though, actually making the Hulk bleed.
The two brawlers have fought beyond these two encounters, but these two fights establish a few hard facts: the Hulk can be overpowered by the Juggernaut; the Hulk cannot consistently stop the Juggernaut; and most importantly, the Hulk's strength, even at maximum, cannot harm the Juggernaut at his maximum power.
The Avengers found that a certain lullaby, typically said by the Black Widow, was able to calm the Hulk and help him revert back to Banner, when the Hulk's strength was no longer needed.
There aren't many things in the universe capable of cutting the Hulk's skin, but one that has always been able to slice and dice him has been Adamantium. That miraculous metal has seen its fair share of Hulk blood over the years thanks to the constant scuffles between the Hulk and Wolverine.
Hulk's inability to break Wolverine and his adamantium claws isn't an indictment of the green monster's strength but more shows how strong Wolverine's metal-coated bones really are. If the Hulk can't snap his claws, then it's unlikely many other heroes or villains could do so, either.
Due to the gamma radiation that birthed him, his skin is nearly indestructible and takes massive force to break. Throughout Hulk's many on-screen fights, he has only bled twice, and both circumstances prove it takes a unique set of variables to accomplish that.
But they didn't seem to be much use after he wielded the Infinity Stones, as his arm was left forever scarred. Well, Endgame directors the Russo brothers have explained just why the powers didn't work, admitting that the power of the Stones was just too great.
The Hulks are iconic green monsters. Their skin is green. They bleed green. Even their feces are green.
The Hulk's skin is impervious to conventional blades, Adamantium and Vibranium being strictly the few known metals that can effectively pierce and penetrate his skin. The Hulk was even able to remove Adhesive X from his body without any injury.
During the time Bruce Banner lived in Rio de Janeiro, he worked in the Pingo Doce Bottling Plant. After Banner was cut, his gamma-irradiated blood dripped into one of the bottles where it was eventually drunk by the Watcher Informant in Milwaukee.
Supporting and rising up despite being weighed down with a force equal to the weight of a star capable of going nova (It carries enough kinetic energy to destroy a solar system). If the star's weight was equivalent to the weight of Sol, the Hulk is capable of lifting 2 octillion tons.
The Hulk's name is practically synonymous with strength, but just how much can the angry green giant bench? Believe it or not, there is actually an answer: 150 billion tons (at least).
Vibranium. Unlike adamantum, Magneto cannot manipulate vibranium – not if it's pure. Vibranium is a rare, extraterrestrial metallic ore.
Even the most powerful substances have their weaknesses, and Vibranium is no exception. The Wakandan metal, although near indestructible, is shown to be able to melt under the heat produced by the Mind Stone, when coupled with a single lightning bolt, courtesy of Thor's (Chris Hemsworth) Mjølnir.
He can phase through anything. Nanosuit or Vibranium shield… he can phase through all of them.