# Analysis of Interaction between Interior and Exterior Wall Corrosion Defects

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Establishment of FEM Model

#### 2.1. Establishment and Parameters of the Geometric Model

#### 2.2. FEM Model

#### 2.2.1. Model Constraints

#### 2.2.2. Application of Load

#### 2.2.3. Failure Pressure Solution

#### 2.3. Failure Criterion

#### 2.4. Verification of FEM Results

#### 2.5. Critical Distance Calculation Method

_{d}of the double defect pipe model was calculated using the above solution method. By comparing it with the failure pressure P

_{s}of the single defect pipe model, the following formula was used to determine whether the interference effect had occurred. When the critical influence factor was less than 5%, it was considered that there was no interference effect between the two defects in this case and that no interference phenomenon occurred, so then both defects can be considered separate defects [38].

_{d}is failure pressure of the double defect pipe model calculated using FEM, MPa; P

_{s}is the failure pressure of the single defect pipe model calculated using FEM, MPa.

#### 2.6. Example of the Critical Distance Calculation

_{1}/t = 0.6 and the defect depth of the right exterior wall a

_{2}/t = 0.5. The defect spacing was 80, 120, 160, 200, and 240 mm. The calculated failure pressure and the critical influence factor are shown in Table 3. The influence of defect spacing on critical influence factor is shown in Figure 2. The specified critical impact factor ω = 5% is the standard and the critical distance is 155.35 mm.

## 3. Results of the FEM Analysis

#### 3.1. Geometric Model and Stress Nephogram of Different Double Defect Pipe Models

#### 3.2. Impact of Defect Depth on the Critical Distance

_{1}/t and the right defect depth a

_{2}/t are 0.4, 0.45, 0.5, 0.55, and 0.6, respectively. Using the judgment criteria and the critical distance calculation method in Section 2.6 the impact of the defect depth a

_{1}/t and a

_{2}/t on the critical distance of the double defect pipe models based on the exterior wall, the interior wall, and the interior and exterior wall can be obtained, as shown in Figure 5. It can be concluded that the defect depth a

_{1}/t and a

_{2}/t vary from 0.4 to 0.6 for the different types of double defect pipe models, and the critical distance varies from 65 to 193 mm for the double defect pipe model based on the exterior wall; for the double defect pipe model based on the interior wall, the critical distance varies from 47.5 to 183 mm; for the double defect pipe model based on the interior and exterior wall, the critical distance varies from 40 to 178 mm; and the critical distance of different types of double defect pipe models increases with the increase in the defect depth.

#### 3.3. Impact of Defect Length on the Critical Distance

_{1}/β and the right defect length b

_{2}/β are 0.6, 1.2, 1.8, 2.4, and 3.0, respectively, and β = (Rt)^0.5 = 80 mm. Using the judgment criteria and the critical distance calculation method in Section 2.6, the impact of defect length b

_{1}/β and b

_{2}/β on the critical distance of the double defect pipe models based on the exterior wall, the interior wall, and the interior and exterior wall can be obtained, as shown in Figure 6. It can be concluded that the defect lengths b

_{1}/β and b

_{2}/β vary from 0.6 to 3 for the different types of double defect pipe models, and the critical distance varies from 124 to 247.5 mm for the double defect pipe model based on the exterior wall; for the double defect pipe model based on the interior wall, the critical distance varies from 111 to 243.5 mm; for the double defect pipe model based on the interior and exterior wall, the critical distance varies from 81 to 232.5 mm; and the critical distance of the different types of double defect pipe models increases with the increase in defect length, but its growth rate gradually decreases.

#### 3.4. Critical Distance Fitting Formula of Different Types of Double Defect Pipe Models

_{1}= a

_{1}/t, M

_{2}= a

_{2}/t, N

_{1}= b

_{1}/β, N

_{2}= b

_{2}/β are introduced in the establishment of the function; using MATLAB software, the formula of polynomial function for the critical distance of the three double defect pipe models based on the exterior wall, the interior wall, and the interior and exterior wall is established as follows, and fit:

_{lim}= c

_{1}M

_{1}

^{3}+ c

_{2}M

_{1}

^{2}+ c

_{3}M

_{1}+ c

_{4}M

_{2}

^{3}+ c

_{5}M

_{2}

^{2}+ c

_{6}M

_{2}+ c

_{7}N

_{1}

^{3}+ c

_{8}N

_{1}

^{2}+ c

_{9}N

_{1}+ c

_{10}N

_{2}

^{3}+ c

_{11}N

_{2}

^{2}+ c

_{12}N

_{2}+ c

_{13}

_{lim}is the critical distance of the double defect pipe models based on the exterior wall, the interior wall, and the interior and exterior wall, mm; c

_{1}-c

_{13}are undetermined parameters of the polynomial; M

_{1}is the dimensionless parameter of the defect depth on the left side of the double defect pipe models based on the exterior wall, the interior wall, and the interior and exterior wall; M

_{2}is the dimensionless parameter of the defect depth on the right side of the double defect pipe models based on the exterior wall, the interior wall, and the interior and exterior wall; N

_{1}is a dimensionless parameter of the defect length on the left side of the double defect pipe models based on the exterior wall, the interior wall, and the interior and exterior wall; N

_{2}is a dimensionless parameter of the defect length on the right side of the double defect pipe models based on the exterior wall, the interior wall, and the interior and exterior wall.

_{lim}= f

_{M1}+ f

_{N1}+ f

_{M2}+ f

_{N2}− 327.8239

_{M1}= 1010.0170M

_{1}

^{3}− 2378.8767M

_{1}

^{2}+ 2003.6000M

_{1}

_{M2}= −2982.3355M

_{2}

^{3}+ 3839.5536M

_{2}

^{2}− 1324.3389M

_{2}

_{N1}= −4.0200N

_{1}

^{3}+ 17.4092N

_{1}

^{2}+ 18.2857N

_{1}

_{N2}= −8.5298N

_{2}

^{3}+ 49.5147N

_{2}

^{2}− 63.7467N

_{lim}= f

_{M1}+ f

_{N1}+ f

_{M2}+ f

_{N2}− 317.5405

_{M1}= −2414.5138M

_{1}

^{3}+ 2579.2806M

_{1}

^{2}− 490.0823M

_{1}

_{M2}= 401.7664M

_{2}

^{3}− 1027.7096M

_{2}

^{2}+ 999.3139M

_{2}

_{N1}= −7.9146N

_{1}

^{3}+ 37.7637N

_{1}

^{2}− 8.0452N

_{1}

_{N2}= −10.3097N

_{2}

^{3}+ 55.2761N

_{2}

^{2}− 62.4469N

_{2}

_{lim}= f

_{M1}+ f

_{N1}+ f

_{M2}+ f

_{N2}+ 452.3709

_{M1}= −3547.8828M

_{1}

^{3}+ 4359.6350M

_{1}

^{2}− 1258.5208M

_{1}

_{M2}= −4902.2457M

_{2}

^{3}+ 7282.7058M

_{2}

^{2}− 3215.4372M

_{2}

_{N1}= −7.9146N

_{1}

^{3}+ 37.7637N

_{1}

^{2}− 8.0452N

_{1}

_{N2}= −10.3102N

_{2}

^{3}+ 53.1496N

_{2}

^{2}− 50.3494N

_{2}

_{M1}represents the impact of the defect depth on the critical distance on the left side of the double defect pipe models based on the exterior wall, the interior wall, and the interior and exterior wall; the parameter f

_{M2}represents the impact of the defect depth on the critical distance on the right side of the double defect pipe models based on the exterior wall, the interior wall, and the interior and exterior wall; the parameter f

_{N1}represents the impact of the defect length on the critical distance on the left side of the double defect pipe models based on the exterior wall, the interior wall, and the interior and exterior wall; the parameter f

_{N2}represents the impact of the defect length on the critical distance on the right side of the double defect pipe models based on the exterior wall, the interior wall, and the interior and exterior wall.

_{1}-c

_{13}in the critical distance fitting formula model of different types of double defect pipe model, the sum of squares (R

^{2}) and the mean square error (RMSE) are calculated, respectively, to verify its precision: for the double defect pipe model based on the exterior wall, R

^{2}= 0.9755 and RMSE = 7.2750; for the double defect pipe model based on the interior wall, R

^{2}= 0.9634 and RMSE = 9.9727; for the double defect pipe model based on the interior and exterior wall, R

^{2}= 0.9579 and RMSE = 11.4171. It can be concluded that, for the parameters c

_{1}-c

_{13}in the critical distance fitting formula of different types of double defect pipe models, the R

^{2}approaches one, which shows that most of the data obtained exists in the fitting curve, and the fitted formula model can accurately reflect the relationship between the critical distance and the geometric elements of the double defect pipe model based on the interior and exterior wall.

#### 3.5. Comparative Analysis of Defect Interaction in Different Types of Double Defect Models

#### 3.5.1. Comparative Analysis of the Critical Distance of Defect Depth

_{2}/t is 0.5; a

_{1}/t is 0.4, 0.45, 0.5, 0.55, 0.6; and the defect length b is 80 mm. The defect width is the width displayed after 15° deflection of the left and right sides of the axis of symmetry of the pipe vertex as the center line, a total of 15 sets of data, and the comparative analysis of the critical distance of defect depth of different types of double defect pipe models is shown in Figure 8. It can be concluded that when the defect depth increases, the critical distance grows, whether it is the double defect pipe models based on the exterior wall, the interior wall, or the interior and exterior wall; under the same defect depth, the critical distance of the double defect pipe model based on the exterior wall is the largest, the critical distance of the double defect pipe model based on the interior wall is the second largest, and the critical distance of double defect pipe model based on the interior wall is the smallest; from the growth rate in the figure, the growth rate of the pipe model based on the interior and exterior wall is the largest, the double defect pipe model based on the interior wall takes the second place, and the double defect pipe model based on the exterior wall is the most gentle.

#### 3.5.2. Comparative Analysis of the Critical Distance of Defect Lengths

_{2}/β of each type is 1.8; b

_{1}/β is 0.6, 1.2, 1.8, 2.4, and 3; and the defect depth a/t is 0.5 (that is, the depth is 10 mm). The defect width is the width of the defect displayed after the left and right deflections of 15°, with the axis of symmetry of the pipe vertex as the centerline. A total of 15 sets of data, and the comparative analysis of the critical distance of the defect length of different types of double defect pipe models, are shown in Figure 9. It can be concluded that when the defect length increases, the critical distance grows, whether it is the double defect pipe models based on the exterior wall, the interior wall, or the interior and exterior wall; under the same defect length, the critical distance of the length of the double defect pipe model based on the exterior wall is the largest, the second largest is the interior wall, and the shortest is the interior and exterior wall; from the growth rate of the broken line, the growth rate of the double defect pipe model based on the interior and exterior wall to the double defect pipe model based on the interior wall and then to the double defect pipe model based on the exterior wall is gradually flat.

#### 3.6. Applicability Analysis of the Critical Distance Fitting Formula for Different Pipe Models

#### 3.6.1. Conservative Analysis of the Three Models

#### 3.6.2. Error Analysis of the Three Models

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Geometric model of different types of double defects: (

**a**) the exterior wall; (

**b**) the interior wall; (

**c**) the interior and exterior walls.

**Figure 4.**Stress nephogram of different double defect pipe models: (

**a**) the exterior wall; (

**b**) the interior wall; (

**c**) the interior and exterior wall.

**Figure 5.**Diagram of impact of defect depth on the critical distance: (

**a**) the exterior wall; (

**b**) the interior wall; (

**c**) the interior and exterior wall.

**Figure 6.**Diagram of impact of defect length on the critical distance: (

**a**) the exterior wall; (

**b**) the interior wall; (

**c**) the interior and exterior wall.

**Figure 7.**Critical distance regression fitting curve of different pipe models: (

**a**) the exterior wall; (

**b**) the interior wall; (

**c**) the interior and exterior wall.

**Figure 10.**Critical distance ratio K of the three models: (

**a**) the exterior wall; (

**b**) the interior wall; (

**c**) the interior and exterior wall.

**Figure 11.**Relative error analysis of the three models: (

**a**) the exterior wall; (

**b**) the interior wall; (

**c**) the interior and exterior wall.

Material | Yield Strength (MPa) | Tensile Strength (MPa) | Modulus of Elasticity (GPa) | Poisson’s Ratio |
---|---|---|---|---|

X100 | 690 | 760 | 210 | 0.3 |

Number | D (mm) | t (mm) | a (mm) | b (mm) | Burst Pressure (MPa) | FEM (MPa) |
---|---|---|---|---|---|---|

1 | 1320 | 22.9 | 11.5 | 1110 | 15.4 | 14.5 |

2 | 1320 | 22.9 | 11.5 | 1013 | 15 | 14.2 |

3 | 1320 | 22.9 | 11.4 | 609 | 18.1 | 16.5 |

Defect Spacing (mm) | P_{d} (MPa) | P_{s} (MPa) | Critical Influence Factor ω (%) |
---|---|---|---|

80 | 24.03 | 26.27 | 9.32 |

120 | 24.59 | 26.27 | 6.85 |

160 | 25.09 | 26.27 | 4.69 |

200 | 25.42 | 26.27 | 3.35 |

240 | 25.71 | 26.27 | 2.15 |

Model Category | Mean Relative Error | Mean Absolute Error |
---|---|---|

exterior wall | −0.0029 | 0.0373 |

interior wall | −0.0059 | 0.0625 |

interior and exterior wall | −0.0080 | 0.0864 |

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## Share and Cite

**MDPI and ACS Style**

Wang, Z.; Long, M.; Li, X.; Zhang, Z.
Analysis of Interaction between Interior and Exterior Wall Corrosion Defects. *J. Mar. Sci. Eng.* **2023**, *11*, 502.
https://doi.org/10.3390/jmse11030502

**AMA Style**

Wang Z, Long M, Li X, Zhang Z.
Analysis of Interaction between Interior and Exterior Wall Corrosion Defects. *Journal of Marine Science and Engineering*. 2023; 11(3):502.
https://doi.org/10.3390/jmse11030502

**Chicago/Turabian Style**

Wang, Zhanhui, Mengzhao Long, Xiaojun Li, and Zhifang Zhang.
2023. "Analysis of Interaction between Interior and Exterior Wall Corrosion Defects" *Journal of Marine Science and Engineering* 11, no. 3: 502.
https://doi.org/10.3390/jmse11030502