Anelasticity in thin-shell nanolattices

Abstract

In this work, we investigate the anelastic deformation behavior of periodic three-dimensional (3D) nanolattices with extremely thin shell thicknesses using nanoindentation. The results show that the nanolattice continues to deform with time under a constant load. In the case of 30-nm-thick aluminum oxide nanolattices, the anelastic deformation accounts for up to 18.1% of the elastic deformation for a constant load of 500 μN. The nanolattices also exhibit up to 15.7% recovery after unloading. Finite element analysis (FEA) coupled with diffusion of point defects is conducted, which is in qualitative agreement with the experimental results. The anelastic behavior can be attributed to the diffusion of point defects in the presence of a stress gradient and is reversible when the deformation is removed. The FEA model quantifies the evolution of the stress gradient and defect concentration and demonstrates the important role of a wavy tube profile in the diffusion of point defects. The reported anelastic deformation behavior can shed light on time-dependent response of nanolattice materials with implication for energy dissipation applications.

Keywords: 3D nanostructures; anelasticity; nanoindentation; nanolattices.

Fig. 1.

Schematic of the indentation test. In Stage I, a load with constant loading rate is applied on the nanolattices and results in elastic deformation and stress gradient in the elements. The load is then held constant to allow the diffusion of the defects across the stress gradient, resulting in the anelastic deformation shown in Stage II. In Stage III the load is removed, and the stress gradient induced by the elastic deformation is removed. This stage is held for an extended amount of time to allow the defect to diffuse back to a uniform profile and enabling the recovery of the anelastic deformation in Stage IV.

Fig. 2.

SEM images of the nanolattice cross-sections. (A) Fabrication process of the nanolattices. (B) 30 nm Al₂O₃ nanolattices. (C) 40 nm Al₂O₃ nanolattices. (D) 75 nm ZnO nanolattices.

Fig. 3.

Nanoindentation results of Al₂O₃ thin-shell nanolattices. (A) Force and displacement profiles over time of Al₂O₃ nanolattices. (B) Representative force–displacement indentation profiles. (C) The anelastic deformation ratio α_d over time during the holding period (after loading). (D) The anelastic recovery ratio α_r over time during the holding period (after unloading). In (C) and (D), the dashed curves are simulation results and all the solid curves are experimental results.

Fig. 4.

(A) Nanolattice model in COMSOL with the highlighted tube further analyzed. (B) Comparison between experiment and simulation in force versus displacement curves during nanoindentation. (C) Sequence of images showing tube deformation and defect concentration levels during the holding period from 0 s to 120 s. The unit for the defect concentrations shown is number/m³.

Fig. 5.

Defect concentration distribution at different locations. (A) Defect concentration distribution across the tube thickness at A and B sections. (B) Defect concentration along the height of the tube external shell. (C) Defect concentration around the internal and external circumferences of the tube at section A. (D) Defect concentration around the internal and external circumferences of the tube at section B.