No, your size and distance did not wear out the crankarm, I say that but you should shortly hear how I am wrong from someone. However, it may have been stripped due to not having enough torque on it and it comming loose.

If it is indeed that bad the bottom bracket spindle may be damaged also.

Make sure it's as tight as it should be and take it from there. BTW, there are quite a few posters in the "Bicycle Mechanics" that could tell you for sure.......after you make sure you have it tightened to spec first.