I don't see why not. Crack may appear if local stress is high enough, no matter which shape the body has. Structures with sharp corners, as in your figure, have lower cracking threshold because of stress concentration near the tips.

And stress may be caused by gravity of course.

Thanks for your helpful comments! Dr. A. M. Lomonosov.

If crack appear, how to decribe it? how to determine the location of fracture face? and which yiled criteria is applicable in this case?

only one way, enhance the craked location. make it stronger. such as reinforcing rib.

it will happened at the farthest point from the section center.

for my opinion, the third and fourth theory are both OK for your object. maximum distortional strain energy is more suitable.