Nanoindentation of tungsten: From interatomic potentials to dislocation plasticity mechanisms

In this study, we employed molecular dynamics simulations, both traditional and machine learned, to emulate spherical nanoindentation experiments of crystalline W matrices at different temperatures and loading rates using different approaches, such as EAM, EAM with Ziegler, Biersack, and Littmark corrections, modified EAM, analytic bond-order approach, and a recently developed machine-learned tabulated Gaussian approximation potential (tabGAP) framework for describing the W-W interaction and plastic deformation mechanisms. Results showed similarities between the recorded load-displacement curves and dislocation densities, for different interatomic potentials and crystal orientations at low and room temperature. However, we observe concrete differences in the early stages of elastic-to-plastic deformation transition, revealing different mechanisms for dislocation nucleation and dynamics during loading, especially at higher temperatures. This is attributed to the particular features of orientation dependence in crystal plasticity mechanisms and, characteristically, the stacking fault and dislocation glide energies information in the interatomic potentials, with tabGAP being the one with the most well-trained results compared to density functional theory calculations and experimental data.

Figure 1

Average nanoindentation load as a function of the displacement at 77 and 300 K as determined by the tabGAP framework. The color region represents the range of minimum and maximum load obtained from all MD simulations. Temperature has a significant impact on the plastic deformation mechanisms modeled by different approaches, as indicated by the Hertz fit curve that defines the critical load, ${\mathrm{P}}_{\mathrm{crit}}$. The results at 77 K are scaled by a factor of 0.6 for visualization.

Figure 2

Average load displacement curves from nanoindentation test by using different approaches at sample temperature of 300 in (a) and 77 K in (b). Hertz fitting curve is added to show the pop-in event. Temperature effects on surface morphology are shown by the elastic part where the surface information is required in the interatomic potentials.

Figure 3

Evolution of average contact pressure, $p$, normalized to Young's modulus with normalized contact radius for (011) W by using different approaches at 300 K in (a) and 77 K in (b). Results follow the universal linear relationship as [20] $0.844/(1-{\nu }^2)a/R_i$, regardless of the employed interatomic potential.

Figure 4

Hertzian calculation of normalized maximum shear stress by the applied pressure, ${\tau }_{\mathrm{Max}}/P$, as a function of normalized depth at a temperature of 300 K in (a) and 77 K in (b). Surface information is needed in the interatomic potentials to model nanoindentation as observed in the range of 0.2 to 0.49 $z$/$a$. The vertical lines indicate the points where ${\tau }_{\mathrm{Max}}$ is not zero, which provides valuable surface information as demonstrated by the tabGAP simulations.

Figure 5

Average total, $1/2\langle 111\rangle$, and $\langle 100\rangle$ type dislocation density as a function of the normalized indentation depth during loading process at a temperature of 300 K in (a)–(c) and 77 K in (d)–(f), showing the differences of the description of W-W interaction by the MD potentials.

Figure 6

Visualization of the dislocation nucleation and evolution at depth $z=0.9a$.

Figure 7

Visualization of the dislocation nucleation and evolution at depth $z=1.22a$, using all approaches. Shear dislocation loops are nucleated at the maximum indentation depth in the case of all potentials.

Figure 8

Visualization of the formation of pileups and slip traces for the indented [001] W sample at the maximum depth (3 nm). The surface morphology for ABOP and tabGAP show fourfold slip traces on the $\left(1\overline{1}0\right)$ and (110) planes in good agreement with experimental findings [51].

Figure 9

Visualization of the von Mises strain mapping for the indented [001] W sample at the maximum depth, at room temperature. The W matrix is slid on the (011) plane for better visualization. BCC {112} twin boundaries are identified in our simulations as depicted in (f) by BDA method and are marked by white circles for the tabGAP simulations.

Figure 10

Evolution of $p/E$ with normalized contact radius at room temperature (a) and 77 K (b) showing the effect of load rate on the nanomechanical response of (001) W. The critical normalized pressure is identified as a deviation from the Hertz fitting and is marked in the figures. This deviation triggers early defect nucleation and is accompanied by the first hardness drop, $\mathrm{\Delta }p/E$, and a subsequent second one.

Figure 11

Generalized stacking fault energies for $\langle 111\rangle \left\{110\right\}$ in (a) and $\langle 100\rangle \left\{011\right\}$ in (b) computed for all approaches. Data for $\langle 111\rangle \left\{110\right\}$ is compared with DFT results from [24].

Figure 12

Screw in (a) and junction in (b) dislocation glide 1/2(111){110} energy of crystalline W by NEB method for different MD potentials. We compare to reported results by QM/ML calculations [59].

Figure 13

Defects in the plastic region beneath the indenter tip at the maximum depth of the (001) W sample were identified using the BCC defect analysis (BDA) technique.