[en] Total reaction cross-sections with H.I. from 30 to 100 MeV/nucleon are measured by means of the associated 4π-γ-ray detection method. The results cover a wide span of targets for various stable and neutron-rich beams. The validity of the method is shown in a combined systematics including also the results of beam transmission-type experiments. The data are confronted to the predictions of low-energy and high-energy models. The authors also show that they are well described by the empirical formula developed by KOX et al. The method is applied to secondary neutron-rich fragment beams produced by a 44 MeV/n ²²Ne beam on ¹⁸¹Ta target and transported by the Ganil Lise spectrometer to interact with a Cu target. The measured σ_R are discussed in terms of the reduced strong absorption radius r₀ and compared with other experimental results