Single carbon fibers are deformed in bending by forming loops with varying radius. Position-resolved x-ray diffraction patterns from the bent fibers are collected from the tension to the compression region with a synchrotron radiation nanobeam of 100 nm size from a waveguide structure. A strain redistribution with a shift of the neutral axis is observed. A significant increase of the misorientation of the graphene sheets in the compression region shows that intense buckling of the nanosized carbon crystallites is the physical origin of different tensile and compressive properties.