A process of upsetting the ends of the pipes, i.e. the area at the end of the pipe with thicker walls and external and/or internal diameters that are different from the diameter of pipe bodies obtained by hot pressing. Upsetting may be external (when the external upsetting diameter is larger than the diameter of a pipe body), internal (when the internal upsetting diameter is smaller than the diameter of a pipe body), or integrated (when the external upsetting diameter is larger and the internal diameter is smaller than the diameter of a pipe body).