Rationalizing the Grain Size Dependence of Strength and Strain-Rate Sensitivity of Nanocrystalline fcc Metals
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is well known that grain size can significantly influence the mechanical properties of polycrystalline metals and alloys.[1] The conventional plasticity mechanism in coarse-grained (CG) face-centered-cubic (fcc) metals, mediated by the nucleation and gliding of dislocations in the grain interior,[2] is expected to become increasingly difficult with reduction of grain size down to the nanometer regime characterized by the abundant grain boundary (GB) atoms.[3] Studies[4–6] have shown that grain refinement in the ultrafine-grained (UFG) or nano-grained (NG) regimes leads to an obvious strengthening effect, which appears to follow the well-established Hall-Petch (HP) relationship[7,8] originally proposed to describe CG metals, i.e., ry ¼ r1 þ kd1=2
½1
where ry is the yield stress, r1 is the stress at which yielding occurs at very large grain sizes, k is the slope, and d is the average grain size. Such an empirical equation has been explained mostly by dislocation-based models including (i) stress concentrations induced by dislocation pileups[7,9] and (ii) Taylor’s pffiffiffi relation ry / q together with the assumption of q /
Y.Z. LI and M.X. HUANG are with the Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China and also with the Shenzhen Institute of Research and Innovation, The University of Hong Kong, Shenzhen, China. Contact e-mail: [email protected] Manuscript submitted November 10, 2018.
METALLURGICAL AND MATERIALS TRANSACTIONS A
1=d where q is dislocation density.[10,11] However, these explanations suffer from the fact that metals either without pileups or exhibiting the starvation of dislocations[12] nevertheless obey this HP form. This contradiction naturally leads to a new view that the hardening of nanostructured metals may be induced by an additional deformation mechanism associated with numerous GBs. Molecular dynamics simulations[2,13,14] indicate that the GB-mediated plasticity (e.g., GB sliding[15,16] and/or diffusion[3]) serves as the cooperating/competing mechanism to the conventional dislocation slip when grain sizes are reduced below a critical value. Although direct experimental observations for such a transition are lacking, indirect experimental evidences based on the rate behavior of UFG/NG fcc metals hint at this GB mechanism.[17] The strain rate sensitivity (SRS) index m, which serves as a signature of deformation mechanism,[18] is typically 0:005 0:01 for CG fcc metals such as Cu,[19] Ni,[20] and Al.[21] Although m is generally insensitive to grain size in the micrometer regime, it has been discovered that further refining microstructures to nanometer regime will lead to an elevated m. In particular, the m value at d 30 nm is measured to be 0.02 for NG-Ni[20] and 0.035 for NG-Cu.[22,23] Yet, these values are still much lower than that corresponding to the GB-mediated plasticity (m ¼ 0:5 1), and this often leads to the claim from some investigators[20,23] that GB activities are not important even in NG metals. Given such a controversy between simulation
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