I imagine that you intended to compare these alternatives:
No one died, but four people were injured and had to be taken to hospital after the plane was crashed near the airport.
No one died, but four people were injured and had to be taken to hospital after the plane had been crashed near the airport.
I agree with this comment:
Neither of your alternatives are idiomatic, because the passive form
implies something was deliberately done to the plane by an external
agency (the pilot, terrorists, or whatever). Native speakers would
just say after the plane crashed. – FumbleFingers
In other words, native speakers would say "No one died, but four people were injured and had to be taken to hospital after the plane crashed near the airport."
But I think that the sense of the particular example about crashing airplanes might be obscuring your grammatical question.
If the plane did crash because of a terrorist attack, I would prefer Sentence 1.
In my opinion the construction in Sentence 2 is fancier and is reserved for subtler points. For example:
- It would be suitable where the timing of events is important to your point, and you perceive one event as ongoing and another as brief: “The plane had been crashed an hour before ambulances arrived on the scene.”
- It could be used to emphasize the order of recent and remote past: “The plane that was crashed on Tuesday was larger than the four planes that had been crashed in the previous six years.”
It’s hard to think of a natural way to express that kind of point after the word “after.” But I think that this has something to do with the meaning of the specific example. It’s hard to think of a plane crash as anything but sudden.
All of these sound fairly natural:
- The airport only resumed normal operations after the surrounding roads had been clear of wreckage for three hours.
- The airline began to comply with federal regulations only after they had been fined repeatedly for lapses.