# Crack Extension Analysis of Atmospheric Stress Corrosion Based on Peridynamics
## 2 Materials and Methods
### Atmospheric Stress Corrosion Coupling Model with Peridynamics
#### 2.1.4 Atmospheric Corrosion-Fracture Coupling Model with Peridynamics  
In this part, the mechano-chemical coupled kinetic model for near-field kinetic ASCC is introduced. In the previous sections, the PD fracture model, the air corrosion process, and the anodic dissolution model were covered briefly. In the fracture model, the nodes carry information about the displacement (\(u\)) and mechanical strain damage index (\(d_{s}\)); in the atmospheric corrosion mechanism, they carry information about the liquid film thickness (\(\lambda\)) and corrosion mechanism (\(c_{i}\)); and in the anodic dissolution model, they carry information about the concentration (\(C\)) and corrosion damage index (\(d_{c}\)). Figure 3 illustrates the links between them.  
Figure 3: Schematic of the coupled peridynamic atmosphere corrosion–fracture model.  
Starting from the top of the figure, environmental changes lead to changes in the electrolyte film thickness, where the film thickness is updated according to Equation (15) and the corrosion mechanism is determined according to Equation (26). Starting from the corrosion evolution and moving in a clockwise direction: electrochemical corrosion leads to a phase change in the corrosion front of the metal according to Equation (23); then, the corrosion damage index is updated, the displacement and bond strain are updated according to Equation (2) under the current load, and finally, the microsolubility is updated according to Equation (30). In the counterclockwise direction: alterations in the corrosion process's progression lead to the distribution of metal displacement under a mechanical force, and when the bond stretch exceeds the critical bond strain, mechanical damage occurs, and according to the corrosion damage connection in Equation (21), the cumulative mechanical damage accelerates corrosion.  
We numerically simulated atmospheric stress corrosion cracking using the algorithm shown in Figure 4. It refers to the algorithm reported by [PERSON] et al. [36]. There were two main differences: the hydrogen atoms were involved in the anodic dissolution type of SCC and atmospheric stress corrosion cracking was formulated through the thickness variation of the electrolyte liquid film.  
Solution steps: The region in the defined material was discretized with a uniform grid and the relevant parameters were entered for modeling. The initial concentration \(C\), the initial liquid film base thickness \(\lambda_{b}\), the relevant atmospheric parameters were set, and the initial damage d and the initial liquid film thickness \(\lambda\) were calculated. Equation (1) was solved using the mechanics solver step and \(k^{s}_{diss}\) was found using Equation (30). For the AD diffusion solver: the diffusion of metal ions at each time step was solved using the near-field kinetic diffusion model (Equation (20)), and the concentration \(C\) and the damage index \(d\) of the metal ions were updated. For the mechanics solver: when the metal ion diffusion step cycle was completed, the displacement of the material point was solved using Equation (1) and the damage \(d\) at the material point was updated.