The tires that equip airplane wheels have elastomer treads from which a piece may detach and damage a zone of the airplane. Shredding means, situated between wheel and another part of the airplane, shred the piece of tread, which detaches from the tire and is projected onto the other part of the airplane, into several small pieces. These shredding means, such as a grid with blades that can cut the tread material, are arranged so as to disperse the pieces. A process reinforces the tolerance of an airplane to impacts of a detached piece of the tread, by shredding the piece into several small pieces between the instant when the piece is detached and the instant when the piece would have struck airplane.