# Crack Extension Analysis of Atmospheric Stress Corrosion Based on Peridynamics
## 1 Introduction
Most of the existing numerical models for simulating crack emergence and expansion in materials are based on the finite element method (FEM). In the conventional finite element method, the displacement field discontinuity generated by the crack expansion is corrected by redefining the object. That is, the crack is defined as a boundary and the mesh needs to be re-defined after each crack extension. It is also necessary to provide mathematical expressions for the kinetic relationships that control crack growth for the simulated fracture method to describe how the crack expands under local conditions. Considering the above factors, it is difficult to solve the multi-crack problem with multiple interactions and a complex expansion mode using the traditional finite element method. The extended finite element method (XFEM) [28] is one of the ways to solve these challenges by introducing additional nodal degrees of freedom and local strengthening functions on top of the standard finite elements. These reinforcement functions contain discontinuous displacement fields and can simulate the growth of cracks and fractures without the need to divide the mesh. However, this approach requires the reintroduction of external criteria. Meanwhile, the XFEM model performs poorly in terms of crack sprouting and fracture. Molecular dynamics simulation (MDS) [29] uses interatomic forces to simulate crack sprouting and extension, and is a detailed and realistic method for predicting material fracture. However, because of computational capacity constraints, the time and size scales that can be studied in simulations differ greatly from those required in real-world engineering applications. Peridynamics (PD) was proposed by [PERSON] et al. [30], who constructed new elastodynamic equations based on space integral equations and the idea of nonlocal action. The theory has unique advantages when dealing with damage and fracture problems by solving spatial integral equations to simulate mechanical behavior. It also has a strong ability to capture complex phenomena. Examples include crack nucleation, crack spreading, multi-crack joining, and crack halting in both isotropic and non-isotropic materials [31]. In PD theory, cracks can naturally sprout and expand freely without imposing a restriction criterion on crack expansion [32]. PD theory has been widely used in the simulation of crack initiation and extension in a variety of materials. PD corrosion models were shown to be a reliable and flexible tool for simulating corrosion damage and were used for damage evolution in pitting and intergranular corrosion in a variety of alloys [33; 34; 35; 36]. [PERSON] et al. [36] coupled a PD corrosion model with a PD mechanics model to simulate the mechanochemical effects of stress on the anodic dissolution rate. [PERSON] et al. [31] proposed a numerical multi-physics field near-field kinetic framework for simulating the stress corrosion cracking of adsorbed hydrogen based on the AIDEC mechanism. [PERSON] et al. [37] proposed a PD model of stress corrosion that was dominated by an anodic dissolution mechanism. [PERSON] et al. [38] simulated the hydrogen embrittlement of AISI 4340 steel. However, their simulation and experimental models were conducted by submerging the samples in an electrolyte solution and did not consider the stress corrosion cracking of metallic materials in an atmospheric environment, i.e., ASCC. Meanwhile, in their PD models, hydrogen embrittlement or anodic dissolution was singled out as the only mechanism for the occurrence of the stress corrosion of metals. However, according to relevant studies, anodic dissolution and hydrogen embrittlement do not exist in isolation when SCC occurs. The effects of anodic dissolution and hydrogen atoms are simultaneous and interact during stress corrosion [39; 40; 41; 42; 43; 44], and the dominant mechanism of stress corrosion may also change when the environmental medium is changed [45; 46; 47]. [PERSON], [PERSON] et al.