I flew with a captain once who had a severe hydraulical failure in flight and landed -offcourse- with much delay at his destination (our homebase). He then rushed to his next flight ('cos he was late already) and after all the stress to get this next show on the road and after the gear was up he noticed himself trembling all over, whereafter he decided that if anything severe would happen in the cockpit in the future he would take the day off, because he considers himself unfit to fly afterwards.
I think it is good airmanship if you reckognize that you are a bit shocked due to what happened and that it might be better to go home and relax. I don't see the need to play the tough guy if you're not.
Offcourse in 411A's post I understand the crew wanted to get home (how quickly did they repair the engine btw?? no duty-time problems there?!), but if at the homebase, I'd call it a day.
From my own little bag with experiences since I took up flying I can recall an approach into MUC, with a heavy windshear on final, which -offcourse- resulted in a go-around, during which we were hit by lightning 2 times and all our pax threw up due to the turbulence, combined with some heacy icing etc etc. Here, just as in the small story above, offcourse we arrived late, then got on to the next flight with some stress due to our late arrival, and afterwards during climb out, after switching on the AP I first realized that I actually had needed some time to think and talk about what actually had happened.
We offcourse may call to be relieved, I didn't do that, first because I didn't think of it, secondly -I can say afterwards- even if I had thought about it, I think I would have made the decision to keep on flying. On the other hand I wouldn't feel ashamed at all to call in as unfit to fly. Even pilots are humans
!!
P77
Oh now I forgot about your question
In my company you can call it a day after an heavy inflight event, but that does not happen automatically. There even is a special team of specialists ready to help you get on with your normal life if needed.
P77