Deformation profile and interface-mediated defect interaction in Cu/CuZr nanolaminates: An effective-temperature description

Both simulations and experiments have suggested that Cu/CuZr nanolaminates are stronger and more ductile than their individual constituents due to interface-mediated interactions between plasticity carriers. In this work, we use the effective-temperature theories of dislocation and amorphous shear-transformation-zone (STZ) plasticity to study amorphous-crystalline interface (ACI)-mediated plasticity in Cu/CuZr nanolaminates under mechanical straining. The model is shown to capture reasonably well the measured deformation response when strained either in tension parallel to or in compression normal to the amorphous-crystalline interface. Our analysis indicates that increasing CuZr or decreasing Cu layer thickness increases the maximum flow stress for both perpendicular and parallel loading cases. For the cases of parallel and perpendicular loading, the maximum flow stress values are 3.4 and $2.5\mathrm{GPa}$, respectively. Furthermore, increasing the strain rate for the parallel loading case decreases the slip strain in the amorphous and crystalline layers. For the perpendicular loading case, an increase in strain rate decreases the amorphous layer slip but increases the crystalline layer slip. In all slip strain analyses, maximum slip strain occurs at the ACI, thus indicating that plasticity carriers accumulate at the interface and are absorbed there. These findings indicate a significant anisotropy in strength with greater sensitivity to layer thickness for the case of tensile loading parallel to the ACI. Further findings signify that slip strain is more sensitive when the nanolaminate is compressed perpendicular to the ACI.

Figure 1

Our domain for modeling the nanolaminate. Through symmetry and the assumption that interactions between the layers do not vary along the ACI, we can model from the midpoint of the amorphous layer to the midpoint of the crystalline layer.

Figure 2

Parallel loading stress versus strain curve from the effective-temperature theory in Cu plotted over the Cheng (2016) result for Cu for an imposed strain rate of $\dot{\epsilon }={10}^8{\mathrm{s}}^{-1}$. The quantities ${\kappa }_1,\rho \left(0\right)$, and ${\chi }_c\left(0\right)$ are constrained through this comparison.

Figure 3

Parallel loading stress versus strain curve for sample set A (solid) plotted over the Cheng (2018) result (dashed) for thickness variations and an imposed strain rate of $\dot{\epsilon }={10}^8{\mathrm{s}}^{-1}$. Increasing the thickness in the amorphous layer increases the maximum flow stress. The parameters $D_a,D_c,{\epsilon }_0,{\epsilon }_Z$, and ${\chi }_a\left(0\right)$ are constrained through this comparison.

Figure 4

Parallel loading slip profile from the effective-temperature theory (solid) plotted over simulation data (dashed) for an imposed strain rate of $\dot{\epsilon }={10}^8{\mathrm{s}}^{-1}$. The maximum slip lies in the amorphous layer for both theory and simulation results suggesting that the nanolaminate's plastic flow is Cu dominated. This slip profile further validates our parameter values constrained from the stress versus strain comparisons. MD simulation results are taken from Ref. [2].

Figure 5

Parallel loading stress versus strain curve for sample set B and an imposed strain rate of $\dot{\epsilon }={10}^8{\mathrm{s}}^{-1}$. Similarly to sample set A, we find that increasing the $L_a/L_c$ ratio increases the maximum yield strength, further validating our parameter values.

Figure 6

Sample set A stress versus strain curve for perpendicular loading and an imposed strain rate of $\dot{\epsilon }={10}^8{\mathrm{s}}^{-1}$. We constrained our parameters with experimental results in parallel loading. The onset of plasticity is at a strain of around 0.02 and the ultimate strength is around 2.6 GPa. Also, an increased amorphous-to-crystalline layer thickness ratio gives rise to greater maximum flow stress similar to the case of parallel loading.

Figure 7

Sample set B stress versus strain curve for perpendicular loading and an imposed strain rate of $\dot{\epsilon }={10}^8{\mathrm{s}}^{-1}$ that is compatible with the observation that greater amorphous layer thickness gives rise to greater flow stress. The onset of plasticity is around a strain of 0.02 and the ultimate strength is around 2.6 GPa.

Figure 8

Slip profile prediction based from the effective-temperature theory applied to perpendicular loading for an imposed strain rate of $\dot{\epsilon }={10}^8{\mathrm{s}}^{-1}$. Most of the slip accumulates in Cu because this layer is weaker than the amorphous layer in terms of flow stress.

Figure 9

Parallel loading stress versus strain curves for an imposed strain rate of $\dot{\epsilon }={10}^8{\mathrm{s}}^{-1}$. The curves are nearly identical despite the amorphous and crystalline layer thicknesses doubling with maximum flow stress at 3.2 GPa.

Figure 10

Parallel loading slip profile for $L_a=2.5\mathrm{nm},L_c=5\mathrm{nm}$ (solid lines) against $L_a=5\mathrm{nm},L_c=10\mathrm{nm}$ (dashed lines) for an imposed strain rate of $\dot{\epsilon }={10}^8{\mathrm{s}}^{-1}$. Doubling the layers thicknesses increases the maximum slip strain in the CuZr layer. Note that the position in the slip profile for $L_a=5\mathrm{nm},L_c=10\mathrm{nm}$ is translated by 2.5 nm to the left.

Figure 11

Parallel loading slip profile for $16\%$ strain with varied thicknesses according to sample set A for an imposed strain rate of $\dot{\epsilon }={10}^8{\mathrm{s}}^{-1}$. Increasing the amorphous layer thickness increases the maximum slip in the amorphous and crystalline layers. Note that for $L_a=5\mathrm{nm},L_c=5\mathrm{nm}$, the slip profile is translated 2.5 nm to the left and for $L_a=7.5\mathrm{nm},L_c=5\mathrm{nm}$, the slip profile is translated 5 nm to the left.

Figure 12

Parallel loading slip profile for $16\%$ strain with varied thicknesses according to sample set B and for an imposed strain rate of $\dot{\epsilon }={10}^8{\mathrm{s}}^{-1}$. The thicknesses associated with the greatest slip strain is $L_a=2.5\mathrm{nm},L_c=2.5\mathrm{nm}$. Generally, the slip distance decreases as the crystalline layer increases except between $L_c=5\mathrm{nm}$ to $L_c=7.5\mathrm{nm}$.

Figure 13

Perpendicular loading stress versus strain curves for an imposed strain rate of $\dot{\epsilon }={10}^8{\mathrm{s}}^{-1}$. The curves are identical despite the amorphous and crystalline layer thicknesses doubling.

Figure 14

Perpendicular loading slip profile for $L_a=2.5\mathrm{nm},L_c=5\mathrm{nm}$ (solid) against $L_a=5\mathrm{nm},L_c=10\mathrm{nm}$ (dashed) for an imposed strain rate of $\dot{\epsilon }={10}^8{\mathrm{s}}^{-1}$. Doubling the layers thicknesses does not affect the overall slip strain for the nanolaminate.

Figure 15

Perpendicular loading slip profile for $16\%$ strain with varied thicknesses according to sample set A and for an imposed strain rate of $\dot{\epsilon }={10}^8{\mathrm{s}}^{-1}$. Increasing the amorphous layer thickness increases the maximum slip. The slip in the amorphous layer is minimal because it is stronger than the crystalline layer.

Figure 16

Perpendicular loading slip profile for $16\%$ strain with varied thicknesses according to sample set B and for an imposed strain rate of $\dot{\epsilon }={10}^8{\mathrm{s}}^{-1}$. The thicknesses associated with the greatest slip strain is $L_a=2.5\mathrm{nm},L_c=2.5\mathrm{nm}$. However, decreasing the layer thickness ratio by increasing the crystalline layer thickness generally decreases the slip distance except between $L_c=5\mathrm{nm}$ to $L_c=7.5\mathrm{nm}$.

Figure 17

Parallel loading stress versus strain for varied imposed strain rates and $L_a=2.5\mathrm{nm},L_c=5\mathrm{nm}$. As the strain rate increases, the maximum flow stress increases up to around 3.2 GPa at ${10}^8{\mathrm{s}}^{-1}$.

Figure 18

Parallel loading slip profile for $16\%$ strain and $L_a=2.5\mathrm{nm},L_c=5\mathrm{nm}$ with varied imposed strain rates. For imposed strain rates 10 through ${10}^3{\mathrm{s}}^{-1}$, the nanolaminate's plasticity is Cu dominant. At around an imposed strain rate of ${10}^8{\mathrm{s}}^{-1}$, the nanolaminate's plasticity begins to shift to CuZr dominant.

Figure 19

Perpendicular loading stress versus strain for varied imposed strain rates and $L_a=2.5\mathrm{nm},L_c=5\mathrm{nm}$. As the strain rate increases, the maximum flow stress increases up to around 2.6 GPa at ${10}^8{\mathrm{s}}^{-1}$.

Figure 20

Perpendicular loading slip profile for $16\%$ strain and $L_a=2.5\mathrm{nm},L_c=5\mathrm{nm}$ with varied imposed strain rates. Increasing the strain rate decreases the domination of Cu plasticity, and at ${10}^3{\mathrm{s}}^{-1}$, plasticity in the nanolaminate is dominated by CuZr.