Dependence of the yield stress of metals on grain size

Abstract

1. It is shown that, for iron, brass, and zinc, the best agreement with experiment is given by the Hall-Petch dependence of yield stress on grain size, which is of the form σ = σ0 + kd−1/2, where σ0 and k are constants having definite physical meanings. This relationship well represents the experimental data for lower yield stress at small strains as well as for flow stress at high levels of deformation (≈0.15–0.20). 2. The relationship σ = σi + 25 (ed−1/2)1/2 proposed by Conrad is only valid for iron and then only for strains greater than 0.02. In addition, both the constant σi, as well as the numerical multiplier of the term (ed−1/2)1/2, vary as a function of the amount of strain. For the lower yield stress of iron at small strains, a linear relation is observed between (σ − σi) and d−1/2, i.e., the Conrad equation reduces to one of the Hall-Petch type. 3. Even for large strains (0.15 to 0.20), the experimental data for brass and zinc do not produce a linear relation between σ and (ed−1/2)1/2, and thus, for these metals Conrad's relationship is inapplicable. Baldwin's formula σ=k1d−1/3, is a gross approximation, and empirical; its use is therefore not recommended. 4. In light of the above, it is finally concluded that, for the brittle fracture case, Conrad's equation is inappropriate, since the amount of strain is approximately zero. Thus, the notions previously advanced in [4, 5] are correct.