Quantifying the influence of grain boundary activities on Hall-Petch relation in nanocrystalline Cu by using phase field and atomistic simulations

Abstract

It has been shown experimentally that the Hall-Petch relation of nanocrystalline (NC) metal will be broken down when the average grain size (d) is below a critical value, but the mechanism behind this remains to be quantitatively analyzed. In order to capture the subtle evolution of grain boundaries (GBs), we recently developed a novel algorithm by using moving least-squares (MLS) interpolant. Moreover, the phase field model is used to build NC copper with more natural and physical GBs for molecular dynamics (MD) tensile simulation. The results show that the variation of stress at GBs (σGB) and at grain interiors (σGI) in the elastic stage are in good agreement with previous study. The σGB exhibits periodic vibration, while σGI shows a linear behavior. From the stress distribution, we find that the increased σGB in one cycle can make the σGI increase. The microplasticity of GBs occurs when σGB increases to a peak value, which attenuates the stress concentration and then leads to the decrease of the σGB. Therefore, the σGI can be affected by the frequency of vibrated σGB. The fast Fourier transform (FFT) results show that the dominant frequency for the model with d of 13.8 nm is larger than that for other models, which causes a larger Young's modulus in the model. The GBs and GIs supplement each other during deformation: GBs providing an extra stress to GIs, GIs supplying the space for microplasticity of GBs. Besides, the fraction of deformed GBs and rotated GBs in the model are also large. GB activities are the results of overall microplasticity before σGB = σGI and deformation during the plastic stage. The rotated GBs results in the emission of many Shockley partial dislocation (partials) from GBs since they create larger paths for dislocation movement. Thus, many twinning boundaries (TBs) are generated in the model with d of 13.8 nm by partials gliding on the successive plane of adjacent stacking faults (SFs) structures, which plays an important role in work hardening of NC Cu.