Have you noticed that Americans pronounce words like 'kitty' and 'kiddy' the same? The 't' and 'd' both become a lighter sound - they become a flap. This is called 't-flapping', and it happens when [t] and [d] are between vowels and at the end of a stressed syllable.
There's also th-stopping - this is when 'th' [θ] and voiced 'th' [ð] become harder sounds. Voiceless 'th' [θ] becomes a [t] and voiced 'th' [ð] becomes [d]. These sounds are still different from the normal 't' and 'd' founds in words like 'darn' and 'take' because these new sounds are dentals, made with the tongue hitting the back of the teeth and not the alveolar ridge.
Examples would be 'without' becoming 'wi[t̪]out' and 'there' becoming '[d̪]ere'.
Here's the fun part: when dental fricatives get t-stopped, they can even be flapped again. Here's an example from song:
This can happen across morpheme boundaries:
This particularly form of stopping is common in African American Vernacular English (which Denzel Curry speaks and which Ariana Grande and Vanilla Ice are trying to imitate).
In sung speech, I've even heard the flap fortitioned to [d]. This restores the [d] sound in a word like "pedal" (a Duke of York maneuver), but replaces "t" with "d" in words like "metal."
Just for fun, what if we combined all these processes... could we turn a voiceless th into a d?
Here are the rules in a VCV environment:
[θ] can become [t]
[t] becomes [ɾ]
[ɾ] can become [d]
One word that meets these constraints is 'toothache'.
So if we wanted to turn th into d, we'd need this sequence:
0. th.
We're starting with a 'th sound surrounded by two vowels.
too[θ]ache
1. [θ] becomes [t]
This t is usually a dental t and unaspirated, so it isn't the same as the alveolar aspirated [t] that is normally used. This should prevent mergers.
toothache -> too[t]ache 2. [t] becomes [ɾ]
This might be difficult if the t is dental - a dental flap doesn't sound all that easy to me. Perhaps the [t] can drift back towards the alveolar ridge, and make itself susceptible to tapping.
too[t]ache -> too[ɾ]ache
3. [r] becomes [d]
Another difficult one, since I've only encountered this in sung speech, but if you were to humor me:
too[ɾ]ache -> too[d]ache
So in an alternate universe, or a dialect-to-be, could you end up with 'toodache'?