Yes, there is. You can find some on various fanfiction websites. Just search for 'tmnt raphael and april love fanfiction' and you'll likely come across several stories.
One common theme is the struggle with their different natures. Raphael being a mutant turtle and April being human. Another could be the protection aspect, where Raphael is always ready to protect April.
One reason could be to create a contrast. Raphael is often seen as a tough and strong character. By writing about him being abused, the writer might be aiming to show his vulnerability and how he overcomes it. Maybe they want to explore the idea of how trauma can shape a character and how he can still be a hero despite it. However, it's important to note that this is a rather heavy and potentially disturbing topic to write about.
One common theme is the 'opposites attract' idea. Raphael is often portrayed as a tough and sometimes hot - headed character. So, when paired with the reader, there can be a dynamic where the reader's more calm or gentle nature complements his. For example, in some stories, the reader might be able to soothe Raphael when he's angry.
I'm not aware of any 'abused' fanfictions in a positive or promoting way as abuse is a serious and negative topic. Fanfictions should generally focus on positive, creative and healthy storylines rather than such disturbing themes. However, if there are some that deal with this in a way to show how to overcome abuse or something similar, they would be hard to single out without extensive searching through the TMNT fanfiction community.
Well, in such a fanfiction, maybe the other Turtles would have to take on a more protective role. They'd need to figure out how to take care of baby Mikey, like feeding him pizza mush or something. And Splinter would probably be super strict about their babysitting skills.
One possible scenario could be that Pikachu is exposed to a strange type of energy. This energy mutates its genetic structure, slowly transforming it into a human form. At first, Pikachu might be confused and scared, not understanding its new body. But as time passes, it starts to learn about human ways, like walking on two legs and using its hands to pick things up.
One idea could be that the little human sister discovers the Tmnt's lair by accident. Maybe she was exploring the sewers for a school project on urban infrastructure. Once there, she befriends the turtles and helps them out with some human - world tasks like getting supplies or finding information on their latest enemy.
One great tmnt human high school fanfiction is 'The Turtles in High School Chaos'. It has an interesting plot where the turtles try to blend in with human students while also dealing with their ninja duties.
Splinter might be the main helper. He has raised the Turtles, so he has experience with taking care of young ones. He could teach the other Turtles the proper way to hold baby Mikey, how to soothe him when he cries, and give them advice on how to keep him clean and healthy. Splinter's wisdom would be really important in this situation.