Velocity is only one factor, however important. Bullet construction is another. M193 and M855 fragment because the bullets have thin copper (actually "gilding metal," which is a copper alloy of roughly 90% copper and 10% zinc) jackets that are further weakened by a cannelure. It cannot be assumed that all bullets will fragment, or will fragment at the same velocity.
Czech-made Sellier & Bellot (S&B headstamp) ammo uses bullets with thicker jackets made of mild steel which have been copper-plated. From the outside, they appear just like M193 bullets, but due to the jacket material and construction, they do not fragment.
Winchester 64gr Power Point ammo is loaded with a soft-point (SP) bullet with a thick copper jacket and no cannelure. It was specifically designed for hunting medium (deer) sized game and was designed to expand, but not fragment.
M995 Armor Piercing ammo has a solid tungsten-carbide core. Tungsten is denser than lead, but much harder, and it won't fragment.
Some time ago 7.62 NATO rounds manufactured in West Germany also had fragmenting properties. NATO standards do not specify jacket material or jacket thickness. The West German 7.62 round used copper-plated steel in the jacket, but their US counterparts used gilding metal alloy around .032 inches (.8mm) thick at the cannelure. The West German jacket is only about .020 inches (.5mm) thick near the cannelure. As a result of the differences, particularly the weaker jacket, the West German round yaws after 8cm or so in tissue before breaking in half at the cannelure. The nose, comprising just over half of the bullet's weight, generally remains intact, and the remaining mass of the lower half fragments. The result in tissue is predictably devastating.
Many people wrongly assume that any ammo loaded with a 55gr FMJ bullet is the same as M193 ammo. This is false. Unless the ammo meets M193 specs, including both muzzle velocity and bullet construction, it can not be counted on to perform like M193.
The same applies to 62gr ammo. Not all 62gr ammo is M855/SS-109.
Counter Opinion: Fackler's 2700fps rule for M193 is more like 2600fps.
Though the dramatic fragmentation seen over 2700 fps in M193 and M855 is clearly an effective wounding mechanism, the lesser fragmentation seen at 2600 - 2650 fps in M193 is still impressive. Wound channels from rounds at 2650 fps are certainly not as devastating as 2700+ fps but they are still larger than from controlled expansion rounds. Really, we should not be discounting the performance of M193 until its under 2600 fps. This should extend M193 fragmentation standards out to slightly over 200 meters from a 20" barrel and 150-175 meters from a 16" barrel.
A M193 round with cannelure indicated
A West German 7.62 round (left) and the American counterpart (right)