Dislocation nucleation in Al single crystal at shear parallel to (111) plane: Molecular dynamics simulations and nucleation theory with artificial neural networks

We develop the theory of homogeneous nucleation of dislocations, which predicts plasticity incipience in FCC single crystal using material properties at elastic stage. In contrast to previous nucleation theories, we show that the work of shear stress is compensated by variation of the generalized stacking fault (GSF) energy during the loop formation. As a result, the energy barrier of nucleation includes only the line defect energy of the critical loop, which radius is defined by balance between all three contributions including the work of shear stress, the surface defect energy of the GSF and the line defect energy. This distinction is consequence of the difference between the mechanisms of the initial loop formation consisting in gradual shear along the protoloop area and the following growth by slip of bordering dislocation line. Calculation of the energy barrier requires material properties at elastic stage such as stress-strain relationship, the GSF and shear modulus. These data are determined from molecular dynamics (MD) simulations and approximated in the form of artificial neural networks (ANNs). We perform direct MD simulations of the dislocation nucleation for simple shear in different directions parallel to (111) plane in Al single crystal at initial pressures from -3 to +3 GPa. MD simulations show complex and nonlinear evolution of stresses at simple shear deformation even at elastic stage before the dislocation nucleation. Predictions of ANN-informed theory are in accordance with our MD simulations and with the literature data. The calculated nucleation threshold for shear along the Burgers vector of partial Shockley dislocation in [112] direction at zero initial pressure varies from 2.03 to 2.16 GPa at the strain rate increase from 1 to 109 s-1. The conditions for homogeneous nucleation are close to the states of matter in thin metal films under powerful sub-picosecond laser irradiation. It is shown that twins are nucleated at angles less or equal to 7.5? between the shear direction and [112] direction. Perfect dislocation loops formed by leading and trailing partial dislocations arise at larger angles. In spite of change in the final form of nucleated defect, the energy barrier of nucleation is well-described by the same theoretical expression. It is explained by the fact that the initial defect in both cases is the loop of leading partial dislocation with the stacking fault over the entire loop area. The formation of twin or perfect dislocation occurs after the nucleation and does not influence the nucleation threshold. The ANNs reveal themselves as an efficient tool for approximation of the complex and non-obvious dependencies, while one should be careful with using them for data extrapolation. The paper is supplemented by files with the parameters of the trained ANNs and description of their structure so that one can use them within the nucleation model or separately.

Automated summary

In this study, a theory on homogeneous nucleation of dislocations was developed to predict plasticity incipience in FCC single crystals. The energy barrier of nucleation was found to only include the line defect energy of the critical loop, emphasizing the importance of balancing various energetic contributions. Through molecular dynamics simulations and artificial neural networks, the theory was validated and shown to be applicable in predicting nucleation thresholds under different conditions.