Here is a non destructive technique I like to use that works for simple cases, when you don't want to break the model apart or need to separate into different objects.
- Add an Edge Split modifier to your base mesh
- Solidify it a desired distance
- Now add a Bevel modifier and limit it to Angle
- Enter Edit Mode, select and the desired edges
- Press Ctrl + E and Mark Sharp
- Adjust Bevel distance as desired, if necessary disable Clamp