When did Iron Man's front plate change?

The Mark VI (6) with the triangular chest plate is created after (drunk) Stark and Rodey fight. The Mark IV (4) is a bit banged up, but nothing a quick fix won't handle. (The Mark V (5), the suitcase model is destroyed at the Grand Prix).

The next day, Nick Fury gives Stark his father's old data. The very next day, he synthesizes a new element. In his basement. In less than 24 hours. And finishes the Mark VI (6). And he saves the Expo the same night. Yes, this is canon. Everything from Iron Man 2, Thor & The Incredible Hulk happen in 1 seven day week, called "Fury's Big Week". sigh.

The Triangle shape was specifically due to the new Arc Reactor being Triangular in shape.

Anyway, since we don't see an Iron Man factory setup like we do in Iron Man 3, we can't assume he built the suit from scratch. (He doesn't go into full production mode until after The Avengers, where he's up to Mark 46 at the start). It was either part of a prototype already in progress, or in my opinion, simply a modified Mark IV suit.

The Mark VI and IV are identical except for the power source, the new Arc Reactor. A new chest plate for the new reactor is all that would be needed, aside from the repairs. The suit he uses at the end of The Avengers,the Mark VII (7) is based on upgrades from the Mark V and new reactor, not an improvement on Mark IV (4) or VI (6). The Mark II (2) was upgraded to the current War Machine armament in 2 days by the Air Force as well.

Of course, the real reason Stark goes to the triangle is out-of-universe. It's a design choice by the movie production. Which the new director quickly decided to drop. Because Joss Whedon thinks "the triangle is ass".

Across both the core Iron Man films as well as others in the MCU, Tony has designed a number of suits to suit various mission needs and protocols.

As such, the triangular design of the Mark VI armor you're asking about could have simply been an aesthetic choice for this particular suit, and not because the power core in his chest changed.

Note that the Mark VII armor, which comes after the model you're talking about, sees a return to the circular unibeam shape.

However, as shown when Tony activated the "House Party Protocol" in Iron Man 3, and early in Age of Ultron when we see a facility in the Avenger's tower manufacturing robots and suits, Tony has become quite paranoid since his battle in the first Avengers movie (which took place between Iron Mans 2 and 3), feeling it's up to him to protect the planet the only way he knows how: with a suit of armor, or in this case several suits of armor around the planet.

Tony is constantly upgrading and modifying his suit, as any gearhead is want to do. Given the Mark V (aka, the Briefcase Suit) was damaged early in Iron Man 2, and it's possible there was still damage to the Mark IV due to his drunken antics at his party, where he got into a fight with Rhodey who was wearing the Mark II suit, the only one available at the time was the Mark VI, which simply happened to have a triangular unibeam chest plate.

Other suits have had different unibeam centers on their chest plates, an extensive number of which can be seen here.

Most are circular, but some have vertical and horizontal rectangles, others are triangular and even have triangles with flattened corners, and even the size of the unibeam emitter changes depending on the suit and its intended purpose.