When I was doing a work up for Africa in 2014, among other things I did was to test some big aluminum arrows (23/64" dia). I learned that they didn't get as much penetration as the carbons. My belief is that the cross sectional density was lower with the aluminum arrows even though the overall weight was higher.
That said, two things: (1) the difference wasn't a major factor. (2) black bear are relatively easy to kill at any rate, only requiring the same arrow you would use for whitetail deer.
For myself, I ended up using Gold Tip Traditional carbon, 300 spine arrows so I could add to the point weight.
Good luck. Bear hunting is a blast! You'll have a great time.