## 4 Discussions  
The reinforcement and matrix of MIMC composites are regarded as two interpenetrating pore structures or network structures, which are shown in Figure 10a. Owing to that one kind of metal phase is interpenetrated by another metal phase, the mechanical models of the network structure of MIMC composites does not follow the brittle fracture mode which is shown in Figure 10b, it follows the elastic plastic mode which is shown in Figure 10c, and this deformation mode is the main failure mode of MIMC composites [31,32]. Considering the linear elastic elements, the elastic modulus of interpenetrating composites is estimated as Equation (1), according to the mixing rule  
\[E_{C}=E_{M}V_{M}+E_{R}V_{R}, \tag{1}\]  
where \(E_{C}\), \(E_{M}\), and \(E_{R}\) are, respectively, the elastic modulus of composites (C), matrix (M), and reinforcement (R), and \(V_{M}\) and \(V_{R}\) are, respectively, the volume fraction of matrix and reinforcement. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Materials**} & **Tensile Strength** & **Yield Strength** & **Elongation** \\  & **(MPa)** & **(MPa)** & **(\%)** \\ \hline Fe–18 Cr–9 Ni & 893 & 824 & 36 \\ Ti–6 Al–4V & 790 & 710 & 21 \\ Al–5 Mg–3 Zn & 542 & 520 & 11 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The mechanical properties of the three network reinforcements. Figure 9: The mechanical properties of AZ31, MISC, MITC, and MIAC: (**a**) UTS; (**b**) YS; (**c**) E.  
Considering the elastic modulus influence, the constitutive mechanical mode of MIMC is proposed according to mixture law of composites, as shown in Equations (2) and (3). \[\text{Upper limit model}:\ E_{C}X_{C}=\sum_{i=1}^{n}E_{i}X_{i}V_{i}, \tag{2}\]  
\[\text{Lower limit model}:\ \frac{E_{C}}{X_{C}}=\sum_{i=1}^{n}\frac{E_{i}V_{i}}{X_{ i}}, \tag{3}\]  
where \(X_{C}\) represents the mechanical properties of composite materials, and \(X_{i}\) and \(V_{i}\) represent the mechanical properties and volume fractions of different composite phase, respectively. For two phases interpenetrating composites, the mechanical properties, such as tensile strength, yield strength, and elongation, are rewritten as Equations (4)-(7), according to the above equations,  
\[E_{C}\sigma_{C}=E_{M}V_{M}\sigma_{M}+E_{R}V_{R}\sigma_{R}, \tag{4}\]  
\[\frac{E_{C}}{\sigma_{C}}=E_{M}\frac{V_{M}}{\sigma_{M}}+E_{R}\frac{V_{R}}{ \sigma_{R}}, \tag{5}\]  
\[E_{C}\delta_{C}=E_{M}V_{M}\delta_{M}+E_{R}V_{R}\delta_{R}, \tag{6}\]  
\[\frac{E_{C}}{\delta_{C}}=E_{M}\frac{V_{M}}{\delta_{M}}+E_{R}\frac{V_{R}}{ \delta_{R}}, \tag{7}\]  
where \(\sigma\) and \(V\) represent, respectively, the tensile strength or yield strength and volume fractions of the matrix (M) and reinforcement (R), and \(\delta\) represents the elongation of the matrix (M) and reinforcement (R). Combining Equation (1) to Equations (4)-(7), the following Equations (8)-(11) are obtained:  
\[\text{Upper limit model}:\ \sigma_{C}=\frac{E_{M}}{E_{M}V_{M}+E_{R}V_{R}}V_{M} \sigma_{M}+\frac{E_{R}}{E_{M}V_{M}+E_{R}V_{R}}V_{R}\sigma_{R}, \tag{8}\]  
\[\text{Lower limit model}:\ \frac{1}{\sigma_{C}}=\frac{E_{M}}{E_{M}V_{M}+E_{R}V_{R}} \frac{V_{M}}{\sigma_{M}}+\frac{E_{R}}{E_{M}V_{M}+E_{R}V_{R}}\frac{V_{R}}{ \sigma_{R}}, \tag{9}\]  
Figure 9:0  
Figure 9:1  
According to the above mathematics model, the relationship between volume fraction and tensile strength of magnesium matrix composites interpenetrated by different reinforcement is shown in Figure 9:2 The results show that as the volume fraction of reinforcement increases, the continuous improving trend of tensile strength is more obvious. Similarly, the yield strength and elongation also  
Figure 9:3 The mechanical model of network structure: (**a**) the unit model; (**b**) the brittle model; (**c**) the elastic plastic model. have the same regularity. Compared with the tested results in Figure 9, the results of the mathematics model are the same.