So if there is no one on the other end you would stutter?  If you have a somewhat consistent stutter here and there since you said it doesn't relate to high stress situations, it may be easier to test it.  I did it with friends before.  Can simply chat on the phone but ask them to hang up when they hear you stutter but you must continue and finish the sentence.   You mention you stutter on R's and that gave me a suspicion that it could be a self fulfilling prophecy for you.  When I used to stutter on the word "stutter" I thought I stuttered on "s" so I noticed every time I stuttered on other s words and among other letters I began to notice.  What I didn't notice was all the times I said words with those letters in the beginning just fine.  I used to also stutter on my name but now it's one of the most reliable words I can say.  But I could have developed a fear of words that start with the same letter all the same.   Take it for what you will but I have always found it empowering knowing that I can say anything a thousand times over in one situation but maybe get hung up in another.  It reminds me not to think of any particular word or sound as the cause so to speak.  Heck I remember over the phone where it didn't matter what I was going to say, I couldn't start saying anything without hard blocking the moment I heard them pick up.  Even after all the pep talk I used to give myself back then as it rang.  But even that reminded me that how can it be a particular word or sound that's the issue when people can ask us to repeat a word we said just fine a moment ago and we'd stutter on it.  I think it's how we feel about it in the situation and otherwise we can say it a thousand times over elsewhere.  For instance, I never had an issue saying the word food until it was a part of the name of the company I worked for and I had to pick up the phone and say that name.  Foodex, couldn't say it for the life of me for a while.