The pinning process within a hard superconductor in a two-component configuration was experimentally studied under a cycling transport current. The axial component of the magnetic moment of polycrystalline Y-Ba-Cu-O cylinders was directly measured in a SQUID magnetometer under longitudinal currents and simultaneously applied stationary parallel magnetic fields. The effect on the axial magnetization of the current cycling (i.e. the azimuthal field cycling), shows a strong pinning which reduces the shielding capability of the superconductor. Additionally, two different types of behaviour were found. For moderate current amplitude of the cycle (depending on the field penetration regime at a given temperature and applied field strength), the magnetization decreases in each cycle. In contrast, when the current amplitude is relatively high, 'butterfly' loops are observed. This evidence indicates that the cutting and cross-flow of nonparallel flux lines occur in the weak link regime of high-T c superconductors; the results can be analysed in the framework of a generalized critical state model.