Transfer case

I had a clinging sound off and on when turning. After a about a month I was driving and heard a big clunk that came from driver side. My vehicle slowed down and got stuck in gear. It would not budge out of first gear. Pulled over and switched to 2wd instead of auto. It drove fine until about seven weeks later I hear clunking sound. Driver side tire was taken off and there is a huge crack all the way around where the axle goes into. I do not know what this part is called I have been told it is the transfer case, but it is not for sure it is. I have pictures of it and no one is able to identify the part. Vehicle drives fine, but noise is awful. Can someone please tell me what part this is? It is the round bigger part.