## 6 Self-Healing Metals
### Liquid State Healing Mechanism  
The most commonly method for self-healing of metals is the embedding of healing agent into the metal matrix [173]. When the metal is subjected to heating, the matrix becomes liquid, and thus the healing agent becomes able to heal the damage. In addition, damage can be healed in different lifetimes of metals due to the availability of the liquid healing agent. Many investigations were carried out on self-healing mechanisms using SMA [174; 175; 176]. Figure 18 illustrates the liquid state healing mechanism. When the metal composite is subjected to tensile stress resulting in crack formation, interfacial debonding will occur by crack due to the low strength at the interface of and high strength of SMA. The crack in the metal composite is supposed to heal when the SMA is subjected to high temperature.  
Several numerical models were developed to predict the behavior of liquid state healing mechanism. In [177], the authors developed a numerical model to describe the thermomechanical behavior in the interface SMA-matrix. Two-dimensional elasto-plastic model was applied on the matrix and one-dimensional material model was applied on the SMA wires using material subroutine implemented in the software package Abaqus (Version 6.3, 2002, Pawtucket, RI, USA, Hibbitt, Karlsson & Sorensen, Inc., 7.9.3-3). The model shows its ability to describe the behavior of SMA wires at different temperature levels. The authors in [175; 176] developed a model that analyzes the relationship between the strength of matrix, stress of SMA wires, and volume fraction of reinforcement. In [178], [PERSON] et al. developed a three-dimensional model of metal-matrix composites reinforced by SMA. The self-healing mechanism was modelled based on pre-strained SMA wires. In addition, micromechanical approaches were also proposed by many researchers in order to demonstrate the healing efficiency of SMA-based  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Elastic Strain Equivalence**} & \multicolumn{2}{c}{**Elastic Energy Equivalence**} \\ \hline
**Phase** & **Elastic Modulus** & **Variable** & **Elastic Modulus** & **Variable** \\ \hline Damage & \(E_{\varphi}=\bar{E}\left(1-\varphi\right)\) & \(\varphi=\frac{\bar{E}-E_{b}}{\bar{E}}\) & \(E_{\varphi}=\bar{E}\left(1-\varphi\right)^{2}\) & \(\varphi=1-\sqrt{\frac{E_{\varphi}}{\bar{E}}}\) \\ Healing & \(E_{h}=\bar{E}\left[1-\varphi\left(1-h\right)\right]\) & \(h=1-\frac{\bar{E}-E_{h}}{\varphi\bar{E}}\) & \(E_{h}=\bar{E}\left[1-\varphi\left(1-h\right)\right]^{2}\) & \(h=1-\frac{\sqrt{1}-\sqrt{E_{h}}}{\sqrt{E}}\) \\ Super healing & \(E_{sh}=\bar{E}\left[1+\left(R-1\right)\varphi\right]\) & \(R=\frac{\bar{E}_{sh}-\bar{E}}{\varphi\bar{E}}+1\) & \(E_{sh}=\bar{E}\left[1+\left(R-1\right)\varphi\right]^{2}\) & \(R=\frac{\sqrt{E_{sh}-\bar{E}}}{\sqrt{E}}+1\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Elastic modulus in the damaged, healed, and super healed material states using the hypotheses of elastic strain equivalence and elastic energy equivalence.  
composite structures [179; 180; 181]. The effectiveness of the description of the microstructure behavior is high. Nonetheless, it is not an easy task to be applied at the specimen level. For more information on the different mechanisms of self-healing metals in fine scale and structural scale, the reader can refer to [182].