The sentence in question is,

"Hardening timescales are plotted against separation in Fig.2, broken down by hardening mechanism."

It was suggested that I change this to "hardening mechanisms". I'm pretty sure this is incorrect, and the interwebs seem to agree (although this is a difficult topic to search for). See: http://alt.usage.english.narkive.com/f3XfjY8U/in-a-breakdown-by-singular-or-plural,
http://www.indiana.edu/~wts/pamphlets/proofing_grammar.shtml (has example using singular).

1) Is there a name / description for this type of situation / problem? Are there other constructs it is analogous to?

2) Which is correct, singular or plural? And why (i.e. what is the general rule)?

  • Consider this analogous phrasing: "200 years ago, a school was often a single room, where all the students attended.  Now (except, perhaps, in the tiniest or most impoverished areas) students are separated by age." (not "by ages") – Scott May 21 '16 at 19:01

You are quoting the name of the measurement or category, 'hardening mechanism'. It doesn't need to change.

Not a grammarian's answer, but consider that if you wrote it as

"Hardening timescales are plotted against separation in Fig.2, each broken down by its hardening mechanism."

It's clear that this should not be pluralised.

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