Crash is somewhat a bit too strong, generally.
And although it isn't as exciting, the equation that mat catastrophe alluded to with the "k" generally predicts a gentle slowdown in growth and then slow fall in population. A crash is, unfortunately, another possiblity depending on how fast the population grew and why it broke it's carrying capacity: if it's a lack of land for mating ground or habitation, the population will slow and stabilize. Lack of food, well, you can run into famine. The equation generally associated is:
dN/dt = rN (K-N/K) Where
- K= Carrying Capacity
- r= Reproductive Rate or Growth Rate
- t= Change in or Delta
- N= Original Population Size
This shows that the closer the actual population size gets to the carrying capacity, the slower it (theoretically) grows. Unfortunately, human ability to make the best of the situation will likely result in a crash unless human common sense, dreadfully close to it's carrying capacity it seems, finds a solution. | 
