Martin (1992: 222):
As far as non-concessive consequential relations are concerned, distinctively internal resources are very limited; for the most part the same conjunctions are used to code internal and external relations. A few unmodalised causals are regularly internal: consequently, hence and in conclusion. And there is one conjunction, after all, which is only used internally; it introduces reasons which are so obvious as to require a mild apology for being mentioned.
[4:144] It might be objected that people could not possibly remember information about all the social contexts for individual linguistic items, given that the term includes lexical items as well as constructions and more general patterns.
After all, even a monoglot must know tens of thousands of linguistic items, so the burden on his memory would be very great.
 This continues the misunderstanding of the distinction between internal and external relations.
 In SFL theory, consequently and hence are markers of causal-conditional enhancement, whereas in conclusion may mark summative clarifying elaboration or, in the sense of lastly, conclusive temporal enhancement.
 The phrase after all is neither a conjunction nor a conjunctive Adjunct and, therefore, does not express any conjunctive relation between the messages in the text.
Rather, it functions interpersonally as a comment Adjunct: speech-functional: unqualified: persuasive: concession, like to be sure (Halliday & Matthiessen 2004: 130).
The likely realisation of after all is as a tone4 tonic, giving it the KEY of 'reserved statement' (see Halliday & Matthiessen 2004: 142).