Abstract: A blind rivet assembly comprising a body made with an insertion head at one end and having a setting concave face at the other end, and an axial thread hole in which a screw is located, the screw having a head at one end and a break-away stem at the other end. A deformable, cylindrical socket, or sleeve, with a two-step axial hole is installed on the screw between its head and the setting concave face of the body, the step with the larger inside diameter being located at the side of the body. In order to prevent damage to the composite materials which are being joined and the tearing-off of the screw by limiting assembly loads, the axial hole of the cylindrical sleeve has an additional step with the smallest inside diameter located at the side of the screw head, a predetermined ratio of the thickness of the walls of the additional step and the second step adjacent being provided, the thickness of the wall and the length of the second step also having a predetermined range.