Multiscale Simulations Of Crystal Instability During Nanoindentation Of Perfect Metallic Crystals

As one of the most fundamental topics in materials science, the instability of crystals has been studied extensively in simulation and experiment. However, due to the limitations on the length scales and time scales, there are significant differences between material simulations and experiments. The recent rapid development of multiscale materials modeling offers opportunities to close the gap between simulations and experiments. Interatomic potential finite-element model（IPFEM） provides a seamless connection between atomistic simulation and finite-element simulation, which is based on the Cauchy-Born rule, hyperelastic constitutive relation and interatomic potentials. In this work, the application scope of the IPFEM was expanded from simple crystals to complex crystals by modifying the original IPFEM model. Furthermore, the lattice dynamical finite-element model（LDFEM） was constructed by embedding the soft phonon analysis into finite-element simulations, to further improve the prediction accuracy of crystal instability. The IPFEM, LDFEM and molecular dynamics（MD） methods were used to investigate the nanomechanical properties of HCP Co, L10-ordered γ-Ti Al, L12-ordered Fe Ni₃, and Ni₃ Al metallic crystals.The modified IPFEM model was applied to investigate the nanoindentation-induced incipient instability of L12-ordered Fe Ni₃ crystal. In cylindrical nanoindentation, the load-displacement curves, indentation-induced stress fields and active slip systems obtained from IPFEM simulations are consistent with those obtained by MD simulations. In spherical nanoindentation, the crystal instability sites and stress fields are associated with crystallographic orientations. Several critical parameters required for crystal instability are interpolated on an inverse stereographic triangle as a function of crystallographic orientations, including the critical load, critical mean contact pressure, indentation modulus and critical resolved shear stress. Furthermore, MD simulation results demonstrate that the critical load required for dislocation nucleation and the nucleation processes are strongly dependent upon crystallographic orientations. The pop-in behaviors observed in nanoindentation are associated with dislocation generation and reactions. The first pop-in event indicates the homogeneous nucleation of 1/6<1 1 2>-type partial dislocations. Activated partial dislocations can transform into dislocation locks through complex dislocation reactions.The orientation-dependent crystal instability of L10-ordered γ-Ti Al crystal was investigated using the IPFEM model. Simulation results show that the load-displacement curves, critical indentation depth and critical load for crystal instability, as well as indentation modulus are all associated with surface orientations. The active slip systems and the location of crystal instability in five typical nanoindentations are analyzed in detail, i.e.（0 0 1）,（1 0 0）,（1 0 1）,（1 1 0） and（1 1 1） crystal surfaces. The predicted crystal instability sites and the active slip systems in the IPFEM simulations are in good agreement with those in MD simulations.The LDFEM was applied to study the lattice instability of γ-Ti Al crystal. The simulation results show that the lattice instability of γ-Ti Al crystal was significantly influenced by loading modes and crystallographic orientations. In uniaxial loading, γ-Ti Al crystal exhibits tension-compression asymmetry in crystal instability. The stress-strain curves and the active slip systems obtained from LDFEM simulations are in agreement with the MD simulation results. In nanoindentation, surface orientation plays an important role in stress field, lattice instability and dislocation nucleation. The LDFEM accurately predicts the location of lattice instability and the active slip systems.The LDFEM was also used to investigate the phonon instability of Co crystal in uniaxial tension and nanoindentation. Simulation results show that the lattice instability of Co crystal is associated with loading modes and crystallographic orientations. The LDFEM model can exactly reflect the mechanical behavior of Co crystal under uniaxial tension. In nanoindentation, the load-displacement curves and stress distribution obtained from LDFEM simulations are coincided with those obtained from MD simulations. The crystal instability of Co leads to dislocation nucleation on basal plane. Six symmetric instability sites appeared in the spherical nanoindentation of the（0001） crystal surface.Furthermore, the nanoindentation-induced incipient plasticity of Ni₃ Al crystal was investigated by performing MD simulations. Simulation results reveal that the incipient plasticity of Ni₃ Al crystal was originated from the homogeneous nucleation of Shockley partial dislocations. The critical load, critical contact pressure, dislocation nucleation site and active slip system were significantly affected by crystallographic orientations, interatomic potentials, model sizes, indenter radii and temperatures. The indentation modulus and the depth of nucleation sites increase with increasing indenter radius but the maximum shear stress decreases. The maximum shear stress and indentation modulus decrease linearly with increasing temperature, reflecting the stress-assisted and thermally activated nature of dislocation nucleation.