Effects of grain size and microstructure rigid rotations on the bending behavior of nanocrystalline material beams

• In NcMs, a large volume fraction of atoms reside in interface regions.
• The inhomogeneity nature of NcMs affect their behavior in MEMS and NEMS applications.
• Grain size, grain rotation, and grain surface energy effects are investigated.
• A multi-phase RVE is proposed to detect the effective elastic properties of NcM beams.
• The modified couple stress theory is used to model effects of grains rotation.

Due to the intensive decrease in grain sizes of nanocrystalline materials (NcMs), a large volume fraction of atoms reside in the interface regions between crystals forming an atom-cloud phase with a distinct atomic structure. Moreover, the surface to volume ratio of the grain increases; thus its surface energy will significantly affect the mechanical properties of NcMs.Recently, nanocrystalline material (NcM) beams have shown effective performances in MEMS and NEMS applications. In the present paper, effects of the inhomogeneity nature of NcMs in addition to effects of the microstructure rigid rotations on the bending behavior of NcM beams are investigated. At first, a grain size-dependent multi-phase representative volume element (RVE) is proposed to detect the effective elastic properties of NcM beams considering the grain surface energy effects. Then, the modified couple stress theory is employed to capture the microstructure rigid rotation effects on micro/nano-Euler–Bernoulli beams. In this sense, the bending rigidity of the beam is adopted for the grain size effects and the microstructure rigid rotation effects.