[AngelicaDeAlquezar]

These are very different verbs.
"Volverse" is to grow into becoming something that will be perceived as an inherent trait of your personality.
"Ponerse" is rather to happen to become something that will change as soon as the circumstance that provoked the change ends.

- Juan se volvió loco cuando falleció su esposa. -> He has never been the same and acts crazily ever since.
- Juan se puso loco cuando falleció su esposa. -> He did crazy things like breaking things, not washing himself or whatever a mad behaviour would look like, but as soon as he accepted the fact, his behaviour was the usual before the sad event.

- Karla se volvió nerviosa desde que robaron en su casa. -> She became a nervous person since she was robbed at home.
- Karla se puso nerviosa durante el asalto. She was nervous when she was being robbed.

- Los perros se volvieron agresivos en la casa donde los maltrataban. -> They are aggressive dogs, and probably that will not change.
- Los perros se pusieron agresivos cuando entró el gato. -> As soon as the cat goes away, they'll go back to normal.

- ¿Pero por qué te volviste así? -> Something happened to your personality and you've changed.
- ¿Pero por qué te pones así? -> There is something right now that is making you act differently to your behavior a moment ago.

Of course, they can't always be used with the same adjective, but I used these examples for contrast.