Here's a fuse that didn't take 35A to blow. 35A would have blown it instantly. One of the commenters said the fuse would blow at the rated current when given time. I am of this sentiment. Going beyond the rated current will merely speed up the blow.
I think you are still not clear on the terminology. Nobody is saying it takes 35A to blow. What we are saying is 35A is the MAXIMUM current that particular style of fuse can interrupt safely. If it is subjected to a fault current greater than 35A that it may fail in a catastrophic way and/or it may fail to break the circuit.
The rating of a fuse is the current that the fuse will carry indefinitely without failing. The higher the current is above that rating then the faster it will open BUT there is a max current that the designer has said is safe for that given fuse - its breaking capacity. In the case of a glass fuse this is usually 35A. Subject it to a fault current bigger than 35A and it may not play nicely.