Ductile or brittle

They can be identify quite easily as the following:

If there is a very long section after yielding point, which we call the plastic deformation section, existing in the curve then it is ductile.

If the curve is basically just a short section of straigth line obeying Hooke's law followed by a small, short curve indicating the breaking point or UTS, then it is brittle.

 

Just keep in mind that the actual micromechanism of fracture is not always that straightforward to identify from a force-displacement curve, in a case where several coexist (for example brittle failure can result after quite extensive plasticity). Typical formula would be those typically related to stress-strain curves or then fracture mechanical ones (usually the former, but don't know the "level" of your problem).