After changing the bed, I would fall asleep quickly.

更换床单后，我会很快入睡。

《柯林斯英汉双解大词典》

He still didn't fall asleep.

他仍然没有入睡。

youdao

I can't fall asleep tonight.

今夜我无法入睡。

youdao

Last August,a study in the journal Sleep Medicine said children who go to bed after nine o'clock took longer to fall asleep and slept less.

VOA: special.2010.06.09

Sleep thought" is the sort of thing you get typically before you fall asleep and it's like "did I take the garbage out, ??

半睡半醒的想法是指那些,你睡着前所想到的东西,例如“我倒垃圾了吗？

耶鲁公开课 - 心理学导论课程节选

For those of you who don't realize it, it's now about 12:00 in the evening tomorrow in Beijing Yeah, so anyway, I'll probably fall asleep by about 10:30.

对那些没有注意到的人，请于明晚12点左右联系我,不管怎么说，我会在10点半左右睡觉。

麻省理工公开课 - 固态化学导论课程节选

They stressed that the drugs may not necessarily have caused the patients to fall asleep.

BBC: Parkinson's patients face sleep danger

"We've had some people fall asleep the second they sit back, " Ms. Sahatqija said.

WSJ: Face Facts: Treatment Not So Bad

They also tend to fall asleep immediately on the massage table because they are so shattered.

CNN: What Comes Next?