Ok, the astronauts were smiling because they had no clue of what had gone on the night before. There had been similar issues in earlier flights, but again, the astronauts did not know about those either. Allan McDonald and others tried to stop the launch. They failed due to people in charge at Marshall SFC refusing to believe McDonald and Eberling and others regarding the weather.
To try to explain all the ins and outs of the STS-51L accident, it is more beneficial for you to actually read the report than for me to attempt to explain it all to you in this forum. To this day Arnie Aldrich, who was vocally against stopping the launch ("Good God Thiokol, when do you expect me to launch, next April") to this day refuses to bear any responsibility for his role in approving the launch after being told that it was not a great idea.
The first evidence of a problem with the seal was at 0.687 seconds after launch, where a plume of black smoke was seen coming out of the lower field joint at the 270 degree to 310 degree part of the SRB. There were a few more puffs of smoke and then they stopped. The educated assumption is that as the aluminum melted, it formed an in-situ seal that temporarily sealed the burn through. About a minute later, the Shuttle got hit by a wind gust as it passed through the jet stream, as evidenced by the exhaust distortion as seen shortly after the explosion. The force was within technical limits, but the fragile in-situ seal was disrupted and the o-ring started up again and proceeded to a burn through. The bottom of the SRB came detached from the external tank and swung around, bashing a hole in the ET hydrogen tank. The release of pressure then pushed the O2 tank up through the top of the tank and when the H2 and LOX mixed, they combusted (known as a hypergolic reaction). At that point the shuttle was destroyed due to exceeding aerodynamic limits from the force of the explosion. It is believed that all 7 crew members survived the initial explosion but died of hypoxia, as the crew cabin continued upward to about 60,000 ft, then hit the water at roughly 200 mph and sunk in about 100 ft of water off the coast of Cape Canaveral.
Now, that was all from memory. I still recommend reading this
https://history.nasa.gov/rogersrep/v1ch1.htm along with the Challenger mini-series available on Netflix.
If you'd like to know more, there's plenty out there.