Grain-size strengthening in terms of dislocation density measured by resistivity

Abstract

The effect of grain size on flow stress has been investigated in terms of dislocation density. The measurement of dislocation density was made for nickel having a high stacking fault energy, by means of electrical resistivity with which the dislocation density can be measured up to larger strains compared with transmission electron microscopy. It was found that the dislocation density for a given strain in specimens deformed in tension at 77 and 295 K increases in a linear manner with the reciprocal of grain size. It was also ascertained that the flow stress is proportional to the square root of dislocation density, irrespective of grain size, deformation temperature and the amount of plastic strain (ϵ). From the above two relationships, an equation between flow stress and grain size was obtained in a general form, which gives the Hall-Petch relation as the limited case at yield point or at small strains.