The present invention provides a rolled steel sheet, for press hardening, for which the chemical composition includes, with contents expressed by weight, 0.24%≦C≦0.38%, 0.40%≦Mn≦3%, 0.10%≦Si≦0.70%, 0.015%≦Al≦0.070%, 0%≦Cr≦2%, 0.25%≦Ni≦2%, 0.015%≦Ti≦0.10%, 0%≦Nb≦0.060%, 0.0005%≦B≦0.0040%, 0.003%≦N≦0.010%, 0.0001%≦S≦0.005%, 0.0001%≦P≦0.025%, it being understood that the titanium and nitrogen content satisfy: Ti/N>3.42, and that the carbon, manganese, chromium and silicon content satisfy: 2.6 ⁢ C + Mn 5.3 + Cr 13 + Si 15 ≥ 1.1 ⁢ % , with the chemical composition optionally including one or more of the following elements: 0.05%≦Mo≦0.65%, 0.001%≦W≦0.30%, 0.0005%≦Ca≦0.005%, with the remainder made up of iron and inevitable impurities coming from preparation. The sheet includes a nickel content Nisurf at any point of the steel near the surface of said sheet over a depth Δ, such that Nisurf>Ninom, where Ninom designates the nominal nickel content of the steel, and such that Nimax designates the maximum nickel content within Δ: ( Ni max + Ni nom ) 2 × ( Δ ) ≥ 0.6 and such that: ( Ni max - Ni nom ) Δ ≥ 0.01 , with the depth Δ expressed in microns and the Nimax and Ninom contents expressed in percentages by weight.