An attachment fitting and a method for connection to a tubular duct comprising at least one ply of armors, the armors having a free end respectively defining an outer surface, the attachment fitting comprising a bushing and a sleeve having an attachment part and a connection part with a reception portion, the sleeve being mounted on the duct by spreading the free ends of the armor perpendicularly to the reception portion, the armors comprising a widening device, the bushing being mounted about the connection part and forming an annular chamber for receiving a flow of a mass-curing material for encapsulating the free ends of the armors. The widening device connected to the free outer surface of the free ends of the armors.