# Crack Extension Analysis of Atmospheric Stress Corrosion Based on Peridynamics
## 2 Materials and Methods
### Atmospheric Stress Corrosion Coupling Model with Peridynamics
#### 2.1.2 Atmospheric Corrosion Model  
The atmospheric corrosion of metals is a phenomenon that is prevalent in nature; it is very different from the corrosion of metals in their native solution, with the main difference being the thickness of the electrolyte liquid film on the surface of the metal. According to the thickness of the liquid film, atmospheric corrosion is divided into three categories:  
1. Dry atmospheric corrosion: There is no liquid film coating on the metal surface. It is mostly generated by pure chemical reactions and its corrosion efficiency and destruction are often modest. 2. Humid atmospheric corrosion: There is a 10 nm-1 um liquid film coating on the metal surface. This thin liquid film is generated on a metal surface via capillary action, adsorption, or chemical condensation. Atmospheric oxygen travels considerably more readily through the water film on the metal surface than through the liquid layer when totally submerged. 3. Wet atmospheric corrosion: There is a 1 um-1 mm liquid film coating on the metal surface. It is broadly compatible with the electrochemical corrosion mechanism in the body solution. The anodic reaction of atmospheric corrosion is  
\[M\longrightarrow M^{n+}+ne^{-} \tag{9}\]  
When the electrolyte layer is very thin, the cathodic process is dominated by the oxygen reduction reaction, and the hydrogen precipitation reaction can be disregarded. The cathodic process is  
\[O_{2}+2H_{2}O+4e^{-}\longrightarrow 4 OH^{-} \tag{10}\]  
For a higher electrolyte thickness of \(\lambda_{0}\), the oxygen reduction reaction is blocked and hydrogen precipitation begins to occur in the cathodic process:  
\[2H^{+}+2e^{-}\longrightarrow H_{2} \tag{11}\]  
[PERSON], N et al. [14] proposed a dynamic electrolyte film corrosion model based on the continuous medium assumption, i.e., the assumption that the liquid film on the metal surface is continuous. The model estimates the dynamics of the liquid film thickness with environmental changes by providing an initial liquid film thickness \(\lambda_{B}\); it is based on a fundamental condensation/evaporation model of standard heat and mass transfer, it is driven by the known evolution of temperature and relative humidity with time, and it takes into account the effect of hygroscopic salts. The model uses the heat and mass transfer equation shown below:  
Heat transfer equation:  
\[q_{conv}=h(T_{s}-T_{\infty}) \tag{12}\]  
Mass transfer equation:  
\[\dot{m}=k_{m}(w_{\infty}-w) \tag{13}\]  
Linking the heat and mass transfer coefficients through Lewis' constant:  
\[\frac{h}{k_{m}}=\big{(}C_{p,air}+wC_{p,water}\big{)}Le^{2/3} \tag{14}\]  
where \(q_{conv}\) is the heat flux at the surface/air interface, W/m\({}^{2}\); \(h\) is the mass transfer coefficient; \(T_{s}\) is the temperature of the film surface, \(K\); \(T_{\infty}\) is the temperature of the air, \(\dot{m}\); \(\dot{m}\) is the mass flux of water toward or away from the film surface; \(k_{m}\) is the mass transfer coefficient, kg/(m\({}^{2}\) - s); \(w_{\infty}\) and \(w\) are the absolute humidity and absolute saturation humidity of the air at the film/air interface, respectively, kg/m\({}^{3}\) : \(C_{p,air}\) is the heat capacity of air, J/(kg \(\cdot\) K); \(C_{p,water}\) is the heat capacity of water, J/(kg \(\cdot\) K); and \(Le\) is the Lewis constant. When \(w_{\infty}-w>0\), the film thickness will increase; otherwise, the film will become thinner. By using the mass flux \(\dot{m}\), the metal surface area \(S\)(m\({}^{2}\)), the mass density \(\rho\), and the substrate thickness \(\lambda_{B}\), the transient average liquid film thickness of the metal surface can be estimated from the following equation:  
\[\lambda=\lambda_{B}-\frac{\dot{m}}{S\rho} \tag{15}\]  
Under the hygroscopic effect of hygroscopic salts or mixtures, the model describes the effect of the hygroscopic effect on the liquid film thickness by correcting the partial pressure of water due to the activity of water.