## 3 Results and Discussion
### FEA-Supported Indentation Analysis  
The nanoindentation test curves were fitted with the aid of a developed finite element analysis process. Contact elements were used to define the interface between the indenter and the surface of the nanocomposite coatings. The nanoindentation experiments have been computer-generated when considering two load steps. The first step simulated the loading stage of the indenter penetrating into the Ni-P nanocomposites. During the second step, the relaxation stage, the indenter was gradually removed, leading to the material elastoplastic recovery. Previous work has shown [53; 54; 55; 58] that kinematic hardening leads to a rapid convergence in the corresponding FEM calculations, so this method was applied in the developed procedure. Figure 8: Calculated (**a**) hardness and (**b**) elastic modulus of as-plated Ni-P, Ni-P/SiC nanocomposites, and the heat treated coatings. During the loading stage the load-depth curve is digitized in order to generate the input for the developed computational model. Initially, the first pair of the applied force and the resulting penetration depth are processed. A first value is assumed for the first tangent modulus of the nanocomposite coating's stress-strain curve, which corresponds to the elastic modulus. In the FEA model, a depth is applied, and then a penetration force is determined and compared to the measured value. If the FEA force does not converge to the measured one then the value of the tangent modulus is estimated again and the finite element model has to be solved once more. For the solutions with computational force matching of the experimental force, the value of the tangent modulus is considered to be accepted and the next values of force and depth are applied to the model. The next calculation step starts with the previous indentation depth, while considering the already existing stress status as well as the previously obtained tangent modulus. This process is repeated until the last couple of force-depth values has converged and the loop ends. The results of the finite element model are demonstrated as an indentation load-depth curve, as presented in Figure 9, which displays the good correlation that was achieved between the measured indentation test and the computational curve in the case of the as-plated Ni-P coating. The potential to calculate materials' stress-strain curves that are based on the force-depth nanoindentation tests, for various SiC concentrations, enables the determination of coating constitutive laws through a Berkovich indenter. The corresponding stress-strain curves were determined while considering these nanoindentation results. The FEA results have revealed a precise estimate of the elasticity modulus for the neat Ni-P and Ni-P/SiC nanocomposite coatings. Table 1 demonstrates the differences between the FEA and the experimental results for all Ni-P samples. It has to be noticed that [PERSON] et al. [59] have also approached the indentation test with FEM, showing very good correlation results. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multicolumn{2}{c}{**Elastic Modulus [GPa]**} \\ \cline{2-3}  & **Nanoindentation Test** & **FEA** \\ \hline Ni-P & 70 & 76 \\ Ni-P HT & 95 & 100 \\ Ni-P/SiC & 114 & 120 \\ Ni-P/SiC HT & 125 & 140 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the elastic moduli of the nanocomposite coatings calculated from nanoindentation experiments and Finite Element Analysis (FEA) determined estimates. Figure 9: Comparison between FEA-determined and experimental nanoindentation tests. Figure 10 illustrates the FEM-extracted stress-strain laws of the Ni-P and Ni-P/SiC coatings, where higher yielding is observed for the heat-treated Ni-P/SiC coatings. When considering these results, it can be concluded that the SiC nanoparticles moderately affected the film's mechanical properties and their stress-strain overall behavior.