## 4 Modeling of the Hardening of an Aluminum Metal Matrix Composite Reinforced with CNTs
The weakening of the base texture due to the addition of hybrid reinforcement favorably affected the ductility; however, the weakening of the base texture also compensated to some extent for the effects of hardening [136]. In [147], [PERSON] et al. carried out molecular dynamics (MD) modeling study of the mechanical behavior of an aluminum composite reinforced with CNTs with different diameters. Stress-strain curves under tensile loading were obtained, and variations in the curves were analyzed using MD images, which allow a detailed analysis of the behavior of atoms. It is shown that Young's modulus and impact strength increased significantly as the reinforcement of CNTs increased. In [137], [PERSON] et al. studied the mechanical behavior of MMCs reinforced with Ni-coated CNTs by MD simulation. The results show that the Young's modulus of Ni-coated SWCNT/Mg is obviously larger than that of uncoated SWCNT/Mg. The results also show that the interfacial bonding of an SWCNT-Mg composite can be dramatically increased by adding a Ni coating to improve the wettability of the nanotube surface and the Mg matrix. In addition, the effect of the amount of Ni coating on the interfacial bonding characteristics of SWCNT-Mg composites was studied. In [148], Meguid S.A., by MD method using the LAMMPS software package, CNT pulling tests from a matrix are simulated to determine the effect of various parameters that affect the strength of the interfacial shear of metal matrices reinforced with CNTs. The study focuses on the influence of cell size, cell geometry, and potential features assumed in MD simulations. In [149], [PERSON] et al. estimated the influence of the choice of a representative element, the division of a representative element into finite elements, and the interface layer near inclusions on the deformation curves of the metal composite. It is shown that simplified models can be used in estimation calculations (the calculation error, in this case, is no more than 2%). In [67], the experimental data for CNT-Al composites were compared with the data of MD and the modified rule of mixtures (see Figure 9). Due to dispersion problems observed in experiments, experimental data are given for CNT volume fractions up to 10%. Experimental data showed a large scatter, as the manufacturing process and distribution of CNTs affected the mechanical properties. However, the MD data are generally consistent with experimental data. In [103], [PERSON] et al. studied the effect of Ni-plated carbon tubes on the strength and deformation properties of a metal composite with an aluminum matrix. It is shown that the main mechanisms of hardening are Orowan dispersion hardening, which is due to the small diameters of CNTs (8 and 15 nm), hardening generated by a mismatch in the coefficients of linear expansion, as well as hardening due to redistribution of the load between the matrix and reinforcing elements. It has been established that the aspect ratio of CNTs plays the most important role in the strengthening of composites in terms of the ratio of length to transverse dimension. Hardening analysis was based both on a micromechanical model and the finite element method. The review by [PERSON] et al. [150] provides an analysis of publications devoted to modeling the properties of metal composites reinforced with CNTs. The sensitivity of the simulated properties to several factors is expected, such as the curvature and orientation of CNTs, the presence of reaction products at the interface, changes in the length of CNTs, etc. To compare the calculated properties with experimental ones, a three-dimensional microstructure of the composite is required, which is impossible due to the small size of CNTs. display using available tomography methods. It is shown that the presence of aluminum carbide Al\({}_{4}\)C\({}_{3}\) slightly increases Young's modulus of the composite.