Suppressed Rage

Alice is upset. She hasn't told Bob this, but he has a hunch. Maybe it's because she's chopping those carrots a little too hard. Maybe it's because she's pressing down on that pen so hard it's torn through the paper. Or maybe it's because she just gave her coworker a broken jaw when he asked how she was.

In short, this is where a character cannot or will not express their feelings, so they try to let it out a bit by being... overenthusiastic about whatever they're doing.

This may be because the person annoying them is their boss, or if they are trying to appear professional in, say, a law court to avoid Courtroom Antics. Alternately, our hero could be taunted by a villain who would gain from his anger, such as a certain Mr. Palpatine

Not exactly like Tranquil Fury. There, someone is being angry in a very calm way. Here, someone is trying to appear calm by suppressing their anger (though it is not necessarily anger; it can be any kind of emotional distress that causes destructive feelings), but doesn't quite succeed.

Related to Yanderes and Cute and Psycho characters, who look nice but are completely insane on the inside rather than simply upset, though they can have moments of this when the cracks in their nature start to show. Stepford Smilers have this long term and are much better at hiding their feelings.

Anime and Manga
"Ringo: Angry? I'm not angry. Why do I care if Ikki wants to hang out with some skank?"
 * In Air Gear, Ringo is upset that Ikki has a crush on Simca. She says the following line while furiously chopping carrots.

Film
"Greg: *writing in the diary* So what if Rowley has a new friend, it's not like I can't make new friends, as if I even ca-*his pencil breaks*."
 * My Super Ex-Girlfriend: When Matt first mentions "needing space", his girlfriend's OK with it... until he mentions dating other people, when she slams the knife she is chopping carrots with into the board.
 * The Diary of a Wimpy Kid film:

Literature

 * In the sixth Harry Potter book, Hagrid is said to be chopping some things up "as if each had done him a great personal wrong" because he's angry about Harry et al (and everyone else) dropping his class,
 * One of Hercule Poirot's short stories: A rich man was murdered in his study and people from his house were suspected. The wife, who was a bit of a loony, and had a violent argument with her husband on the night of his death, kept putting the blame on the man's Butt Monkey assistant, but couldn't quite tell how. Finally, she was hypnotised and then she remembered seeing him write, while his employer ranted, trying to look calm but pressing the pencil so hard it broke.

Live Action TV

 * In Combat Hospital, Bobby gets cut off mid-procedure by fellow surgeon and has to suppress his anger. It boils over very strongly later on in the episode.

Web Comics

 * In Gunnerkrigg Court, Antimony did this the first time she heard a disparaging remark about her father (it's a very sore spot for her) from his ex-friend and ex-rival. A little girl perfectly controlled her fury and instantly devised a pretty awesome comeback. Her mother is said to be like this too. When Annie failed to rein in her fiery nature, it was not so well. She wildly overreacted, snapped at her friends and felt bad later.

Western Animation
"Homer: Okay, I've thought this through. I will send Bart the money to fly home. Then I will murder him."
 * Homer Simpson pulled a funny one once. Bart was stuck across the country after renting a car without permission and Lisa had to tell Homer, but first she makes him promise not to get mad. After she explains, Homer manages to say "My, that is quite a pickle" calmly, as a Luminescent Blush formed on his face... until he excuses himself, puts on the mask of his hazmat suit, and starts ranting and raving incoherently until the mask is all fogged up. Then, when he's finished he says (completely deadpan);


 * The Tick (animation): The Superman Expy is frequently angry with The Tick while in his Clark Kentish disguise, constantly quietly crushing typewriters in annoyance.