In TMNT(2014), there is a point near the climax where Raphael hesitates saving Leonardo because his shell is cracked and tells Donatello to duct tape it. However, it's never shown in the movie when his shell is actually cracked. Even early in the movie, his shell has duct tape on it. So when does Raphael have his shell cracked and what actually cracks it?
Although Raphael does have duct tape on his shell throughout the movie, the crack that Donatello is referring to was received in the fight with Shredder just moments before.
While April and Vern attempted to free the other turtles, Raphael tried to fight Shredder on his own and was less than successful. He ended up face-down on the concrete with Cyber-Shredder forcefully stepping on his back shell. Not only does Raphael nearly scream in pain during the scene, but there are also notable cracking noises heard. In addition, certain versions of the film even note "cracking noises" in the subtitle text. Afterwards, Shredder is seen walking off with Raphael lying on the floor defeated.
Here's a clip of the fight. The cracking occurs around the 1:30 mark:
I am thinking the duct tape is covering injuries in Raphael’s shell from when the tunnel fell on him. It collapsed on top of him when he pushed the fan out of the way. This was when the footclan claimed he was dead, when the other 3 were first captured.