Abstract
The Hall-Petch relation, developed originally for single-phase alloys, has been extended to alloys containing two ductile phases. The extended Hall-Petch relation can separate the contributions from the different kinds of boundary to the overall efficiency of grain and phase boundaries as obstacles to dislocation motion. The overall friction stress and the overall Hall-Petch coefficient for the two-ductile-phase alloys have been derived as functions of the Hall-Petch constants of the different constituent phases and their microstructural parameters. The extended Hall-Petch relation has been applied to α-β Ti-Mn alloys, α-β Cu-Zn alloys and α-γ Fe-Cr-Ni stainless steels to evaluate the efficiency of the phase boundaries as obstacles to dislocation motion. It is concluded that phase boundaries are not always the strongest obstacles to dislocation motion as in the case of α-γ Fe-Cr-Ni stainless steels.
