I am currently trying to make a cylinder out of chipboard(the cardboard that notebooks are typically made out of). However, whenever I try to bend it, parts of the chipboard start to tear. How do I bend chipboard without tearing it apart?
I'm going to run with the assumption that you're referring to paperboard or a thin hardboard.
Think of the paperboard as being like a sausage: it has a skin on it that keeps the good bits in, but if you bend it too far, that skin will tear.
Your best option (steam would probably damage the board, as Matt mentioned) would be to score the board at intervals. This will allow you to control where the skin breaks. From here, you'll probably want to coat the gaps with glue or something to prevent them from becoming easy points of failure.
This will mean that your cylinder will not be perfect, it will be somewhat angled at each score line. A smaller distance between scores will help hide this.
Another option: laminated layers of posterboard/thin paperboard
If this doesn't work for you, you could try laminating instead: use a thin paperboard that's easy to use. Make a cylinder with that (You probably want to use a center form to get the diameter right, try circles made of wood). Then glue the outside and roll another piece of paperboard over that, adding successive layers until it's the desired thickness. This lamination method is likely a better option for you: it will be more durable than simple hardboard and will be under less stress. Additionally, you can overlap seams so there won't be a single weak point.
If you're using thin paperboard rather than posterboard, I would leave a small gap at the final seam and use epoxy to give it a secure seal that's unlikely to peel away from the cylinder.
Aside from wetting it, you will have better success (probably) by treating it like wood-bending - provide a tension support on the outside when bending, rather than bending it around a form on the inside. When bending around a form, the outside needs to stretch, so it tears. When bending inside a form the inside compresses - it may wrinkle a bit, but it won't tear.
Something like a sheet of aluminum flashing might make a suitable tension support for stiff cardboard (chipboard has a different connotation over here - oriented strand board, a plywood like substance glued up from chips of wood.)
In wood bending both a strap and form are used, commonly. Here's an image to show the general idea from "Model T forum"
For paperboard running the material over a hard edge with a little tension will put some curvature in the board. The more you pull the board over an edge like the side of a bench or table saw, the tighter the radius of the curve will be. Depending on the size, you can keep going until the two edges meet up, forming your cylinder.
Another approach would be to place a flexible but firm backer on both sides of the paperboard. A thin plastic sheet from a folder or package would work. Clamp them together, and then bend the 'sandwiched' materials, which would keep the paperboard from folding. join the edges when they meet, and then the paperboard will hold its shape.