The phrase "partial rupture" means when something is partially broken or damaged. It is not completely torn or ruptured, but it has suffered some damage. Full definition
Angle between the patellar ligament and tibial plateau in dogs with partial rupture of the cranial cruciate ligament. (kyon.ch)
With partial ruptures of the ligament, most dogs have an intermittent weight bearing lameness that is often worse after exercise or after lying down for long periods of time. (vrc-nova.com)
Now, the data suggest that several partial ruptures were more complete than previously thought, and that complete ruptures occur slightly more than half the time. (sciencedaily.com)