In all explosive cladded samples, an Incoloy 825 plate was claded on an X65 steel plate. Before welding, the Y-groove is processed, and multilayer and multi-pass welding is carried out using an ER/E CrNiMo-3 welding wire/electrode. The cladding layer is welded by argon arc welding (GTAW), and the substrate is welded by shielded metal arc welding (SMAW). The bimetal pipe welded joint was machined into a size of Φ 610mm × (22 + 3) mm as the experimental material according to the API 5ld standard. The chemical composition of the Incoloy 825 cladding, X65 substrate, and filler metal is shown in Table 1.

The sampling diagram of the bimetal pipe welded joint with a size of 10 mm × 10 mm × 3 mm for the immersion corrosion test is shown in Figure 1. The corrosion solution is NACE-B solution, and the composition is shown in Table 2. Before immersion, the sample is ground using sandpaper to 1,1500 mesh and cleaned with acetone and anhydrous alcohol. The morphologies and composition of corrosion products in the bimetal pipe welded joint were analyzed using a scanning electron microscope (SEM, JSM-7200F), a three-dimensional topography instrument (Contour X), an energy dispersive spectrometer (EDS, X-Mas50), and an X-ray diffractometer (XRD-6100).

The test time was 30, 60, and 180 days, respectively. The corrosion resistance of welded joint samples was analyzed by comparing the size and quality of samples before and after corrosion in each period.

The corroded weld sample was sanded to 2,500 mesh first and then polished with 0.5 μm polishing paste. Aqua regia (hydrochloric acid–to–nitric acid volume ratio of 3:1) was used to corrode the surface of the samples. The microstructure and composition of welded joint samples were analyzed using a metallographic microscope, SEM, and EDS.

Four fundamental elements are included in a complete CA process: cells, cell space, neighbors, and evolution rules. The cells, also known as the units, are the most basic component of a CA. The cell space is a set of grid points with different boundary conditions such as the periodic boundary, reflective boundary, and fixed value boundary. The evolution rules are the transfer relationships that determine the state of the cell at the next step based on the current state of this cell and its neighbors. According to the experiment, the main components of the welded joint sample are Ni, Cr, and Fe, which account for more than 99% of the total welded joint weight. The atomic diameters of Ni, Cr, and Fe are about 0.248, 0.254, and 0.250 nm, respectively. We define each cell of the CA model as a square of 0.25 μm, representing 1,000 atoms. The weld material with a thickness of 75 μm was simulated with a 300 × 300 cell space in the CA model. The cell type and state are shown in Table 3, and the cell position relationship is shown in Figure 2. The state of each cell depends on the state and configuration of neighbors in the cell. In the simulation, we choose the von Neumann neighborhood, that is, the cell will have four neighbor cells in the upper, lower, left, and right positions. If the cell is represented as (0,0), its neighborhood can be represented as (0,1), (1,0), (1,0), and (0, −1).

J. Saunier (Saunier et al., 2004) analyzed the initial stage of cellular automata simulating corrosion and put forward the relevant formulas of the cell size and timescale, such as Eq. 1, as follows: Δ h = A N t 0.5 , (1) where A is the scale coefficient, Δ h is the cell size, and N_t is the time scale. In this simulation,   A = 2.46 × 10 − 7 c m 2 / s .   Δ h = 0.25 μ m and N t = 0.12   d can be determined. Thus, the unit of corrosion time must be translated from 30, 60, and 180 days to 250, 500, and 1,500 time steps, respectively, with the definition of the CA model.

The CA model algorithm is programmed using MATLAB software. Cellular reaction rules can be divided into five categories according to Eqs 2–6. A, B, X, M’, and W are solution cells that can move randomly. When cell A moves toward cell M, cell M’ will replace the position of cell M with p_corr probability (Equ. 2), cell W occupies the position of cell A, and corrosion occurs on the weld (Figure 3A). The occurrence and dissolution of the passivation film have a great influence on the development of pitting corrosion. It is assumed that the passivation layer P dissolves in the form of M’ in an acidic medium. In addition, Cl⁻ and S²⁻ have an autocatalytic effect on the corrosion pit after entering it. Rules related to the formulation of the passivating film are shown in Figures 3B–D. When cell B moves toward cell M’, cell P occupies the position of cell M’ with probability of p_pas (Eq. 3), cell W occupies the position of cell B, and passivation occurs on the weld surface (as shown in Figure 3B). When the number of cell A in the neighborhood of cell P is greater than the number of site B in the neighborhood, the location of cell P will be occupied by cell M’ with a probability of p1 (Eq. 4), and depassivation will occur (as shown in Figure 3C). Cell X moves toward cell P, and cell P is depassivated with a probability of p2 (Eq. 5) and becomes cell M’, while cell B occupies the position of cell X (as shown in Figure 3D). When cell A moves toward cell P, cell P will be replaced by cell M’ with probability p3 (Eq. 6), cell W occupies the initial position of cell X, and depassivation occurs (as shown in Figure 3E). If the weld metal site is not in contact with the corrosive electrolyte, the M cell does not change, in which case the weld retains its original properties and does not change. C Ms + C H → C Ml + C N , (2) C Ml + C O H → C P + C N , (3) if num ( A ) > num ( B )   P → M ′ , (4) C Cl + C P → C W + C O H , (5) C P + C H → C M l + C W . (6)

Cellular automata are simulated on a mesoscopic scale, and appropriate boundary conditions are selected to make the simulation results conform to the actual situation. Figure 4 shows the initial state of cellular automata. The simulation boundary condition of the CA model is that the left and right boundaries can be connected end to end, which is the closest to the infinite space. Thus, the simulation results are more consistent with the actual corrosion situation. The Brownian motion of the cell is prior to the chemical reaction, so there is no chemical reaction in the Brownian motion. The diffusion velocities of eight kinds of cells are set to be the same so as to simplify and reduce the number of parameters according to the reference of Caprio and Stafiej (2011). In order to simulate local pitting of weld metal, a passivation layer composed of three layers of passivation cell P is set above the metal cell M before simulation. The metal covered by the passivation film is exposed to the corrosive medium at the 14-cell width position in the central area of the passivation film. The corrosion rules of the passive film set in this experiment conform to the definition of passive cell corrosion rules in Evolution Rules.

According to the ion concentration and simulation requirements of the welding seam immersion experiment in Immersion Corrosion Test, the concentration, corrosion probability, passivation probability, and depassivation probability of each cell are set as shown in Table 4.

Figure 5 shows the weld microstructure, in which a, b, c, and d are the metallographic microstructure of the backing bead, the interface area of the bead, the filler bead, and the cover bead, respectively. It can be seen that the microstructure of the weld specimen is composed of fine primary dendrites of the austenitic γ phase (dark phase) and the interdendritic eutectic phase (light phase). The microstructure is shown in Figure 5A is dendritic due to the argon arc welding technology adopted in the backing welding, which has a small heat input and is not preheated by the front weld pass during welding. As a result, the grain size is fine, and obvious directional growth occurs in the grain size during cooling. As the welding process goes on, the latter bead has the effect of heat treatment on the previous bead, while the previous bead has the effect of preheating, and the dendrite will change into cellular crystal and cellular dendritic crystal, as shown in Figure 5B. In Figure 5B, zone 1 and zone 2 are the microstructures of the latter and the backing bead, respectively. Figure 5C shows the metallographic microstructure of the middle pass, which is similar to the metallographic microstructure in zone 2 of Figure 5B. After preheating by the previous pass, the microstructure changes into cellular crystal. Figure 5D shows the metallographic microstructure of the cover welding pass, which is cellular dendritic or cellular crystal, but the microstructure is thicker than that in Figure 5C. The main reason is that the cover welding, as the last weld in the welding process, will not be subjected to the heat treatment of the back weld, so it is unable to regulate the coarse and large dendritic structure.

Figure 6 shows energy spectrum surface scanning in the weld zone. The results show that the second phase, which is randomly dispersed in the interdendritic region, is enriched in the plateau sublevel elements (such as Mo and Nb). Element segregation occurs in dendritic and interdendritic regions. According to the analysis of the relevant reference, the secondary phases generated during welding are Laves phases (Gill et al., 2013). Among them, the Laves phase is a common precipitate, which existed in the weld solidification microstructure (Cieslak et al., 1989).

The Laves phase is an irregular band distributed in the center of the interdendritic region. Therefore, different positions in the figure were selected for EDS point analyses, and the average value of the element content in the Laves phase was calculated. According to the element distribution of element point analysis results as shown in Figure 7 and Table 5, the contents of Ni, Cr in the Laves phase are significantly lower than those of ER/E CrNiMo-3, while the contents of Nb and Mo are to the contrary. Ni and Cr are important corrosion-resistant alloy elements. Therefore, the content of Ni and Cr in the Laves phase is low, which indicates that the corrosion resistance of welded metal is lower than that of the base metal.

The typical area morphologies of weld samples after 30, 60, and 180 days of corrosion were observed using a 3D morphometric, respectively. Figure 8 shows the appropriate X and Y paths to scan the corrosion pit and obtain the contour morphology of the corrosion pit. It can be seen that the maximum depth of the corrosion pit is 2.46 μm after 30 days, 4.54 μm after 60 days, and 10.94 μm after 180 days.

Komp proposed (Ahn et al., 2019) a relationship between corrosion depth and corrosion time, which is in accordance with Eq. 7 as follows: C = A t β , (7) where C is the maximum corrosion depth, μm; t is the corrosion time, day; and A and β are the parameters determined by the regression analysis of experimental data. The experimental data of 30, 60, and 180 days were fitted to get A = 0.158 and β = 0.816 . Therefore, the corrosion depth and corrosion time of the weld in the NACE-B solution will conform to the formula of C = 0.158 t 0.816 in 180 days. The experimental and fitting relationship between corrosion depth and time is shown in Figure 9.

The SEM morphology image and XRD pattern of the weld sample after 180 days of corrosion are shown in Figures 10, 11, respectively. As can be seen from Figure 10, some pits and deep trenches appear on the surface when the weld is corroded. According to XRD analysis, the corroded weld sample is mainly composed of Ni–Cr–Fe, CrO₃, and MoO₃. Among them, the peak corresponding to Ni–Cr–Fe is the strongest, which corresponds to the austenite phases in the weld matrix. In addition, the weak peak related to the CrO₃ and MoO₃ phases is the generated corrosion product. Mo usually appears in the form of MoO₄ ²⁻ in corrosion products, and Chou (Chou et al., 2010) believed that the formed MoO₄ ²⁻ is thermodynamically unstable and tends to precipitate as MoO₃.

Figures 12, 13 show the surface and line scan of EDS of the weld sample after 180 days of the corrosion immersion test. The results show that the contents of Cr and Ni are lower in the corrosion pit area due to the segregation, while the contents of Mo and Nb between dendrites are less, so the interdendritic area is easy to be corroded. It can be inferred that the Mo and Ni elements in the filler metal possess a strong segregation trend during the welding process of the bimetal clad pipe, which leads to the precipitation of the Laves phase enriched in Nb in the interdendritic region. The precipitation and segregation of the second phase indirectly reduce the content of Cr, Ni, and other corrosion resistance elements in the interdendritic region; thus, the corrosion resistance of the weld metal is reduced.

The simulation results of cellular automata corrosion under different time steps are presented in Figure 14. According to the definition of the cell size and timescale in Cell Space and State, the results are the corrosion morphology of simulated actual corrosion for 60–300 days. It can be seen that the pit depth and the surface roughness increase gradually, with the extension of corrosion time. The pitting depth after CA simulation is shown in Figure 15. The pitting development rate in the middle area is much higher than that in the edge area.

Figure 16 shows the comparison of experimental and simulated corrosion morphologies of 250 time steps and 30 days, 500 time steps and 60 days, and 1,500 time steps and 180 days, respectively. As can be observed, there is a high similarity between the simulation results and the experimental results.