Abstract: The invention relates to a blind riveting member of the type comprising a tubular sleeve (1) and a mandrel (2) passing through said sleeve. The stem portion (5) of the tubular sleeve (1) comprises successively along its length, a first articulation zone (5a), an inclined portion (5b), a second articulation zone (5c) and an end portion (5d). These zones or portions are arranged in such a manner that the sleeve is subjected to a double folding during setting of the rivet which causes the inclined portion to expand and fold back upon itself toward the materials being assembled, forming a continuous rest surface at the periphery of the hole which contains the riveting member. The invention is applied in particular for assembling fragile materials such as composite materials. It permits providing a good vibration resistant holding for these materials without risk of damaging the same.