Size Effect in the Uniaxial Compression of Polycrystalline Ni Nanopillars with Small Number of Grains

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growing interest in nanocrystalline (NC) materials for their superior mechanical properties including high strength, toughness, and superplasticity.[1,2] Unlike coarse-grained (CG) materials where dislocation glide is the primary source of plastic deformation with grain boundaries (GBs) acting as barriers, for the NC materials, both dislocation glide and GB sliding have significant influence on the deformation.[3] Consequently, in the deformation plasticity of NC materials, both the grain size (intrinsic) and the specimen size (extrinsic) are found to play vital roles in the mechanical response of the material. In the Hall–Petch relation[4,5] of polycrystals’ plasticity, the grain boundaries act as dislocation barriers, and the yield and flow strengths of the material vary as the inverse square root

LIN YUAN, CHUANLONG XU, DEBIN SHAN and BIN GUO are with the School of Materials Science and Engineering, Harbin Institute of Technology, No.92 West Dazhi Street, Nan Gang district, Harbin, 150001, China and also with the National Key Laboratory for Precision Hot Processing of Metals, Harbin 150001, China. Contact e-mail: [email protected] RAJIV SHIVPURI is with the Department of Integrated Systems Engineering, The Ohio State University, Columbus, OH 43210. Manuscript submitted October 13, 2018. Article published online July 2, 2019 4462—VOLUME 50A, SEPTEMBER 2019

of the grain size. However, at the nanoscale, the strength no longer follows the Hall–Petch relation. GB-driven softening becomes the primary driver of plastic straining with the yield stress decreasing with the grain refinement (inverse Hall–Petch relation).[6,7] That is to say, with the decreasing grain size of NC materials, there exists a transition in the plastic deformation drivers, from the one that is governed entirely by dislocation-mediated processes to the one that includes both the intergranular and the intragranular mechanisms.[8,9] Since both these mechanisms are dependent on the dimensions of the grain as well as the specimen, considerable attention has been paid to the effect of size on the mechanical behavior of NC materials. The effect of dimensions (size effect) has been the focus of many previous studies in the area of microforming.[10–15] One explanation proposed by Greer and Nix[16,17] is based on ‘‘dislocation starvation’’ with the GBs acting as dislocation sinks, resulting in unexpected strengthening at the nanoscale. An alternate hypothesis, to explain the size effect, is proposed by Parthasarathy and Rao,[18–20] which states that the hardening is not from dislocations starvation but from the repeated motion of dislocations around internal pinning points. These single-arm Frank-Read sources are activated by critical resolved shear stress (CRSS), with the dislocation length depending on the diameter of the pillar. With the advancement in computational modeling, simulation methods based on MD have been applied to the observance of size effects at smaller dimensional METALLURGICAL AND MATERIALS TRANSACTIONS A

scales.[6,7,9,21–23] For example, Xu