How can I split my polygon file into "segements"? The lines should be broken up like this picture shows:

How can I split my polygon file into "segements"? The lines should be broken up like this picture shows:

In Grass, v.type.bl can be used to convert polygons to lines. You can follow it up by v.split to convert to line segments. The screens are from Qgis. Set max number of vertices to 2 in v.split as shown below.

Edit: The above method will not give you duplicates at d and f. If duplicate segments are required, you could probably replace the first step(v.type.bl) with the Qgis Polygons to Lines tool(Vector -> Geometry tools -> Polygons to Lines).
Edit#2 - "Any number of Points in a segment" seems a little confusing. You can specify the maximun segment length, or maximum number of vertices to refine your needs in v.split. But my gut feeling says that you only need v.type.bl. See the output of only v.type.bl below. It gives 6 segments for the three counties from California.
Edit#3 In GRASS / only the tool v.to.lines is needed to do the job!

I understand that you want to turn your polygons into individual line segments, and that your concern is that segments d & f will not be created as separate lines?
Vector | Geometry tools | Polygons to lines to split the polygons into two separate polylines, creating a new feature;Plugins | Split Feature and select the feature created in step 1.After running that procedure on two simple polygons, just as you show in your example, I ended up with 8 features, two of which are overlapping lines (corresponding to d & f); in the screenshot below, the 'id' refers to the original polygons, and each row is a separate line segment..
