Abstract
In the present work, a multiscale Hall-Petch relation is derived from a new multiscale model and applied for all ranges of grain sizes. The derived multiscale Hall-Petch relation has a superior over the previous models represented by its direct applicability on any material without the need for prior knowledge of grain size distribution. The new multiscale relation applicability is tested with three elements Mg, Zn, and Fe due to their importance in industrial applications. The comparison among the coefficients of different materials suggested a criterion to predict the reverse Hall-Petch relation.
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