The “nominal grain size” (average grain size) is generally applied to Hall-Petch relationship to evaluate grain refinement strengthening in polycrystalline materials. However, the steels with wide grain size distribution (duplex-grained structure) may not deform uniformly but yield preferentially from larger grains to finer ones. This phenomenon is called “micro-yielding”. In this study, the effect of duplex-grained structure on the yield stress was investigated by using some IF steels with different grain size distribution. As a result of tensile testing, the yield stress of duplex-grained steels could be conventionally plotted on the Hall-Petch relationship as a function of (nominal grain size)-1/2 in the range from 100 to 10 μm, even though the micro-yielding phenomenon occurred within the coarse grains at a lower stress than the macroscopic yield stress. When the volume fraction of grains with identical size is summed from larger-sized ones, the summated volume fraction (defined as the integrated volume fraction) always reaches 70-80 vol% at the nominal grain size irrespective of the difference in grain size distribution. These results suggest that polycrystalline materials including duplex-grained structure materials cause the macroscopic yielding when the grains of 70-80 vol% are micro-yielded.
