Is it possible to get a raspy voice like that of Chad Kroeger of Nickeback? Are there any exercises or techniques that can help me with this?
You can add rasp to your voice safely. Proper vocal rasp (and screaming) involve the use of your false cords (bigger things above your vocal cords). It takes a lot of trial and error to control them, but once you master it you can add varying levels of rasp to your singing. I've been screaming and doing raspy singing almost every day for about 6 years and i've never had any vocal problems.
The idea is that while your vocal cords produce a pitch, your false cords also vibrate together and produce a grit. It does increase the wear on your voice, but its similar to how your voice will wear out faster if you sing at the top of your range or the top of your volume for a while. You may end up coughing or blowing your voice out for a day while learning, but the idea is that you should only practice it for 5-10 minutes at a time while learning so you don't actually hurt yourself.
To actually answer your question on 'exercises', its not so simple. You really have to look up examples on YouTube to hear all the 'examples' people present. Generally someone will tell you to make a certain sound (like a frustrated sigh, or grunt'). Then they will tell you to maintain strong diaphragm pressure, and visualize something. Its a very subjective thing that is very hard to teach, because you can't look at someones vocal cords, and then mimic it with your vocal cords (at least not realistically, maybe some day).
I would just look up articles and video's on YouTube, try it out, and work slowly. I personally teach screaming and raspy vocals on my YouTube channel (look up Andrew Southworth on YouTube and my videos will come up), but you don't need to learn it from me. Watch a few different people and see what teaching style makes it click. I watched dozens of different teachers on YouTube while I was learning and it didn't click until I found one particular screaming tutorial and mimicked the sounds they made.
Good luck, and have fun!
Andrew is correct, it CAN be done safely - but there is a real risk of doing harm to your instrument. Be very careful when attempting to mimic other singers. Your raspy or screaming-type sound will sound different from other people. You're a different person, your voice will sound different. You should keep in mind that this type of sound is also very dependent on a sound system. The complete effect is achieved by the use of the microphone, often enhanced with either natural or artificial distortion. I know you're probably thinking of harder rock examples, but it's worth noting that a particularly raspy pop singer, Michael Bolton, who approaches a 'scream tone' in his higher range, actually sings quite softly. The mic does most of the work. Learning to use your microphone will go a long way in approaching this technique safely. That being said, if it ever hurts, STOP, and try a new approach. It won't hurt and you shouldn't ever lose your voice if you're doing it "correctly". (unless you're singing too much in general). I highly recommend you look for a seasoned vocal coach familiar in this area.