As noted in the entry on how voiced stops became spirants in Quenya, medial d usually became “a weak untrilled r or đ-like sound”. This lexicon denotes this sound as [ð] for consistency with other spirantalizations, but it eventually developed into a sound like [ɹ] (English untrilled “r”) which Tolkien denoted as ř. In the Ñoldorin dialect of Quenya, this ř sound ultimately became a normal trilled r [r], merging with primitive r and the r that developed from z. Tolkien described similar changes in both the Outline of Phonetic Development (OP1) from the 1930s and the Outline of Phonology (OP2) from the 1950s:

d ... medially between vowels it would appear to have been slightly retracted and to have become a weak untrilled [r], distinct from original r. The two sounds have distinct letters in early PQ spelling; but the distinction disappeared already in the classical period, a lightly trilled [r] being used for both (OP1: PE19/32).

d ... medially between vowels it appears to have been somewhat retracted, and to have become at first a weak untrilled r or đ-like sound distinct from original r. The two sounds have distinct letters in earlier Quenya spelling, which may be represented by r (original) and r̃ (derived from d). 7 = r, 6 = ř. In classical PQ spelling 8 (s) or k [z] was used for product of s, 6 for product of d, and 7 for original r (OP2: PE19/69-70).

In OP1, this phonetic development occurred in Parmaquesta [PQ] and was common to all dialects, and the same was true in the original draft of OP2 (PE19/70 note #9). But Tolkien revised this section in green ball point pen (used for revisions around 1970) so that the development to r was a Ñoldorin-only change, and the Vanyarin development was to z:

In the event this sound generally fell together with the z-product of (voiced) s. In Van[yarin] pronunciation both ř and z > z. In N[oldorin] ř and z > ř, and this later to r (same as original r). The spelling of both V. and N. (6) was thus normally used for products of medial d and s, and the special z-letter k both used. The N. (only) tended to use 6 for products of r (7), but this was considered incorrect by loremasters (OP2: PE19/70).

The full [d] > [ð] > [ɹ] > [r] phonetic development was described by Tolkien in notes on the history of ar “and”, probably from the mid-1960s:

Ad went through four stages of development: (1) archaic before records ad (2) early weakening ađ (3) retraction to ař, an untrilled spirantal r (as commonly heard in English “dry”), (4) assimilation to normal r (PE17/71).

This phonetic development is also reflected in Tolkien’s description of the tengwar in The Lord of the Rings Appendix E:

Thus [tengwa] 21 [6] was often used for a weak (untrilled) r, originally occurring in Quenya and regarded in the system of that language as the weakest consonant of the tincotéma ... [Tengwa] 25 [7] (in origin a modification of 21) was used for “full” trilled r (LotR/1120-1).

In attested tengwar samples, 7 tended to be used for initial r and for r before vowels, whereas 6 was used for final r and for medial r before consonants, regardless of origin. In fact, the name of 6 (óre) was probably chosen because it had a medial r, as opposed to name of 7 (rómen) which had an initial r. The r in the word óre was not derived from d, so the name must have been coined after d > ð > r. The name óre makes more sense in the earlier OP1 scenario where this phonetic development occurred in PQ and may be a remnant of that idea, though in the Feanorian Alphabet documents from the 1940s the name of 6 was either rómen or rana, whereas 7 was ráma (PE22/22, 50).

In the 1950s, Tolkien mentioned that d > r before the semi-vowels y and w as well: “d became r, as between vowels, before y, w (OP2: PE19/94 note #123)”. This is reflected in examples from The Etymologies of the 1930s:

• ᴹ√MAD > ᴹQ. marya “pale, fallow, fawn” (Ety/MAD).
• ᴹ✶nidwō > ᴹQ. nirwa “bolster, cushion” (Ety/NID).

He modified this rule in green ball point in OP2 around 1970, so that medial dy > ly, as discussed in the entry on how [dj] became [lj]:

d became r, as between vowels, before w ... Phonetically dy > ly (owing to greater tensity[?] of d + y), cf. initial ly < dy or < gy (OP2: PE19/94).

The only example of medial dy > ly was written around the same time: ✶kwenedyā > Q. †quenelya, an archaic adjective with the same meaning as Quenderin (OP2: PE19/93 note #116).

In other combinations, d/ð was often modified, such as being unvoiced when combined with voiceless sounds or in combination with other stops, remaining a stop after nasals, or restopping after liquids. Thus d > ð > r primarily between vowels and before semivowels w and (sometimes) y.

Conceptual Development: In the 1910s these developments were complicated by the fact that đ [ð] was part of the phonetic inventory of Primitive Elvish. Nevertheless, Tolkien had medial d > r in Early Qenya (PE12/15-16), but in the 1910s it passed through z in the process: “đ > z > r everywhere, except ... [with exceptions similar those listed above] (PE12/24)”.

As noted above, d > ð > r was a change in PQ in the 1930s, and remained so in the first draft of OP2 from the early 1950s. It is not clear exactly when Tolkien decided this was a Ñoldorin-only sound change in TQ, but he mentioned it in a discussion of omentielmo vs. omentielvo, so it must at least predate the publication of the second edition of The Lord of the Rings:

In this respect EQ [Exilic Quenya] represented the recognition of sound-changes which had begun among the Noldor before the Exile and had already caused Noldorin Quenya to diverge from the language of the Vanyar. The principal of these were: 1. the change of both z (from s) and ř (from d) to r ... (PE17/129).