The instant invention concerns the use of at least one polymer P obtained by radical copolymerization of a mixture of (i) acrylic acid; (ii) methacrylic acid; and (iii) at least one monomer of formula: for treating a metallic surface intended to be coated by a paint, a varnish or an adhesive, for example intended to be adhesive-bonded to another surface, in order to impart a resistance to the adhesive failure to the resulting bonding.