According to many google hits they speak about work in "parts"...

http://www.bgc.bard.edu/degree_programs/degree_phd.shtml


Dissertation Proposal
The process of selecting a dissertation topic and writing the dissertation proposal has three parts. The student begins the process by meeting with the director of doctoral studies

I doubt there is a particular technical, official term.

I would use Transcrit's proposal ("parts"), and if that turns up to be too vague or weak in the context, I would use the more specific "dissertation parts".

If "delarbete" just refers to a piece of work (e.g. research, writing, experiments, etc.), "part" should be all right.

If, in your context, it refers specifically to the written result which results from such work (a paper that is part of a wider dissertation) - which seems to be the case here -, then "dissertation part" might be better.
Thus: "...in a doctoral dissertation in the form of 3 to 5 dissertation parts..."

On the other hand, I think it is pretty clear from the context that these are parts in the sense of parts of a dissertation, wherefore I suppose just "parts" should be sufficient.

It appears to be regarding a Ph.D. by coursework and thesis, in which case the coursework would include a number of "modules", which would be assessed in written assignments.

Eg. Lancaster University, PhD in Applied Linguistics by Thesis and Coursework
'Assessment for the taught part of the programme is based on 5000-word assignments for the Applied Linguistics modules, and 5000/2500-word assignments for research projects for the Research Methods modules. You are required to pass all the coursework, but the final award of the PhD depends entirely on the thesis. The thesis length is 70,000 words.'

(If the degree is by thesis only, the correct term would be "chapter" but if seems a bit odd that a dissertation would be assessed as several parts rather than a whole. )