Recently, the surface of carbon fibre composite tiles of the toroidal pump limiter of Tore Supra has been analysed by scanning electron and atomic force microscopies. In regions where fibres are perpendicular to the surface, a specific erosion pattern has been observed. It is constituted of a striation oriented with an angle oblique with respect to the magnetic field. The characteristic wavelength of this structure is micrometric, and similar to the fibre size. Modelling has been undertaken to reproduce this micrometric pattern. It is shown to originate from the carbon composite structure, for which it has been found by measurement using laboratory plasma that the erosion rate of the fibres is different from that of the surrounding matrix. Modelling emphasizes the effect of the impinging flux angle distributions of deuterium ions and carbon impurities that are preliminarily determined from computation of the magnetic sheath. In the case of deuterium the sheath is shown to have little effect on the particle trajectories for the simulation parameters considered here, although when impurities are included the sheath deflection is significant. Furthermore this study shows how the fibre organization in the composite influences the striation direction and points out the importance of the angular dependence of the sputtering yield.