If I am doing functional testing of a web application, what are some attacks I can perform on input fields, forms, etc. that can cause the application to crash?
You should make more clear what you want to know because you mixed two things up.
Let me give you some hints. On the one hand you want to know, how to do functional testing, especially black-box testing, to crash a (web) application. To achieve that you should perform negative tests. In your case, if you want to manipulate input fields, forms etc. you define invalid input test data and use them as input for your application.
- For example you want to test an input field where the user should type in his/her age. Let's assume you define your valid input data from 18-120 years. That would mean, everything <18 and >120 are invalid inputs and useable for your negative tests.
So, you try to test the robustness of your application when manipulate it with invalid input test data.
On the other hand you mentioned security testing but this is non-functional testing. Simply, with security testing you test whether a system is secure or not. The way of doing it depends on many things like the domain, kind of application and so on. In your case, a collection of tasks for web application can be found here: Web Application Security Testing Cheat Sheet.