Hi John, hard to pinpoint without seeing what you are doing. We can eliminate the horn because you say it happens on other horns as well. The best thing to do is start a few notes below the D, ones that you don’t have a problem with. Play nice long tones on these and keep the same air support and embouchure as you’re approaching the D. If you maintain the proper support, when you hit the D all should be good.
So, your exercise will look like this:
Play and hold B – play it loud, strong and long. Next same on C. Same on C#, then D, D#, E, F.
Also check to see if it makes any difference if you tongue the notes to start, or if it’s better not using your tongue at all.
Let me know how it goes.
thanks and good luck