## 3 Results and Discussion
### Effect of CNTs on Mechanical Properties  
Figure 5 plot the mechanical properties of Group 4 (as listed in Table 1) of the CNHONNs with different additions of CNTs \(\omega_{\text{CNT}}\), suggesting that the effect of CNTs strongly depends on deforming direction. In the out-of-plane direction, both the tensile and compressive mechanical properties increase  
Figure 4: (**a**) Young’s modulus \(E\) and (**b**) ultimate strength \(\sigma_{\text{u}}\) of HONNs with different relative density.  
with the increase of \(\omega_{\rm CNT}\). As compared to the HONNs with the same relative density, the increase of mass fraction \(\omega_{\rm CNT}\) of CNTs ranging from 1.28% to 5.22% can make the increase of the tensile modulus ranging from 2.2% to 8.8%, the tensile strength ranging from 1% to 5.1%, the compressive modulus ranging from 3.6% to 10.2%, the compressive strength ranging from 4.9% to 10.7%. But in the in-plane direction, the mechanical properties of CNHONNs cannot be strengthened or even may be weakened by the addition of CNTs.  
Figure 6 plots the average stress of the CNTs embedded in the CNHONNs with a \(\omega_{\rm CNT}\) of 5.22% with respect to strain. The stresses in the CNTs considerably depend on the loading directions. Compared to the in-plane tension and compression, Figure 6 shows that the CNTs can bear more loads during the out-of-plane loadings, resulting in a better reinforcement of CNHONNs in the out-of-plane direction due to the addition of CNTs. The interface between CNT and Ni is so weak that the load cannot be effectively transferred in the in-plane direction, resulting in defects at the interface, which is similar to the CNT-reinforced metallic glass nanocomposites [40]. This is why the in-plane mechanical properties of the CNHONNs are similar to those of the HONNs and sometimes they are lower than  
Figure 5: (**a**) Young’s modulus \(E\) and (**b**) ultimate strength \(\sigma_{\rm u}\) of CNHONNs with different \(\omega_{\rm CNT}\) of CNTs.  
those of HONNs, as evidenced by the result in Figure 5. The main reason for the difference in the in-pane and out-of-plane reinforcing effect of CNTs is the anisotropy of CNTs and the weak interfacial bonding between C and Ni.  
Moreover, the stress-strain curves of CNHONN are shown in Figure 7. As for the in-plane tension (see Figure 7a), it can be seen that as the strain increases, the stresses increase linearly for all samples at the initial stage up to peak stresses (i.e., the ultimate strengths) around a strain of 0.08 and then drop sharply owing to the fracture of Ni matrix. The toughness of the CNHONNs, except the \(\omega_{\text{CNT}}\) of 3.89%, is slightly higher than that of the HONNs. As for the in-plane compression (see Figure 7b), the stress-strain curves of all samples almost overlapped and reach a peak stress around a strain of 0.068. For out-of-plane tension (see Figure 7c), similar to the in-plane tension, the stresses reach peak values around a strain of 0.088 and then decrease dramatically. Particularly, the area under the curve between the 0.12 and 0.31 of strain values largely increases with the increase of \(\omega_{\text{CNT}}\) indicating that the endurance capability of the CNHONNs can be enhanced by the addition of the CNTs, even after the nickel matrix fractures. At around a strain of 0.31, the second sharp decline occurs in the stress-strain curves of the CNHONNs due to the failure of the CNTs. As for the out-of-plane compression (see Figure 7d), the stresses reach peak values around the strain of 0.05 and the plateau stresses generally increase with the increase of \(\omega_{\text{CNT}}\), which demonstrates that the energy absorption capacity of the CNHONNs can be improved by the addition of the CNTs.  
Figure 6: Stress contribution of CNTs in the CNHONN in the case of \(\omega_{\text{CNT}}\) of 5.22% along different deformation direction.  
Figure 7: _Cont._