# Analytical Model and Numerical Analysis of Composite Wrap System Applied to Steel Pipeline

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## Abstract

**:**

## 1. Introduction

## 2. Applied Methodologies

#### 2.1. Standards ASME PCC-2 and ISO/TS 24817

#### 2.2. Analytical Approach

#### Procedure to Find the Thickness t_{c} Based on the Developed Approach

#### 2.3. Finite Element Analysis

_{i}is insignificant and the numerical pressurization becomes slow. The calculation process stops when one of the two failure criteria is satisfied. These two criteria are the rupture criterion of the composite and the burst criterion of the pipe steel. The pressure obtained at the end of the calculation process is considered the maximum burst pressure.

## 3. Limit Load and Experimental Validation

## 4. Composite Repair Sleeve Sizing at Design Pressure

## 5. Results and Discussion

## 6. Conclusions

- The composite overwrap sizing calculated according to ASME PCC-2 and ISO/TS 2481 standards is conservative with respect to the obtained sleeve thickness and results in unnecessary repairs of the steel pipe wall thinning, particularly for small depths of material losses. For a medium depth of metal losses, ranging from 50% to 65% of the tube wall, in the case of the new developed solution, the sleeve thickness was reduced as follows:
- -
- by 96% to 42% compared to the results of ASME PCC-2,
- -
- by 97.5% to 54% compared to the results of ISO/TS 2481.

- For the deepest pipe wall metal losses, starting from 70% of wall thickness, the applied sizing algorithm reduces the wrap thickness as follows:
- -
- by 32% to 4% compared to the results of ASME PCC-2,
- -
- by 43% to 8.4% compared to the results of ISO/TS 2481.

- The presented methodology takes into consideration an effect of the external pressure surrounding the tube, as in the case of offshore pipelines, in which the thickness of the fiber-glass sleeve is even less.
- The proposed approach predicts the burst pressure of the defected pipes repaired with a composite overwrap system for practical applications. Due to this fact, the authors are going to conduct experiments to validate the burst pressure of steel tubes repaired with the use of the developed sleeve sizing procedure.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

${D}_{ext}$ | Outside diameter of the steel tube |

${P}_{recovered}$ | Pressure to be recovered |

${P}_{d}$ | Internal design pressure of the pipeline |

${P}_{live}$ | Live pressure |

${P}_{i}$ | Actual internal pressure |

${P}_{ext}$ | External pressure |

${P}_{c,j}$ | Contact pressure at the location j |

${P}_{f}$ | Burst pressure of the steel pipe |

${t}_{c}$ | Minimum required thickness of the composite sleeve |

${t}_{s}$ | Remaining thickness of the pipe wall in the corroded zone |

${t}_{0}$ | Thickness of the steel pipe |

${\u03f5}_{c}$ | Composite allowable strain |

$S$ | Specified minimum yield stress of steel |

$n$ | Strain hardening exponent |

$K$ | Material strength coefficient |

${R}_{0}$, ${R}_{1},{R}_{2}\mathrm{and}{R}_{3}$ | Internal radius of the steel tube, internal radius of corrosion defect, external radius of steel tube, and internal radius of composite repair |

${\alpha}_{0},{\alpha}_{1},{\alpha}_{2}\mathrm{and}{\alpha}_{3}$ | Dimensionless geometric ratio |

${\sigma}_{y}$ | Actual yield stress |

${\sigma}_{\theta ,i}^{j},{\sigma}_{a,i}^{j}\mathrm{and}{\sigma}_{r,i}^{j}$ | Stress components, respectively, in hoop, axial, and radial directions. The indices i and j denote, respectively, the contact pressure location and the material type |

${\u03f5}_{\theta ,i}^{j},{\u03f5}_{a,i}^{j}\mathrm{and}{\u03f5}_{r,i}^{j}$ | Strain components, respectively, in hoop, axial, and radial directions. The indices i and j denote, respectively, the contact pressure location and the material type |

${E}_{\theta}^{c},{E}_{a}^{c}\mathrm{and}{E}_{r}^{c}$ | Elastic moduli of the composite, respectively, in the circumferential, axial, and radial directions |

${v}_{ra}^{c},{v}_{a\theta}^{c}\mathrm{and}{v}_{r\theta}^{c}$ | Composite material Poisson’s ratio |

${G}_{ra}^{c},{G}_{a\theta}^{c}\mathrm{and}{G}_{r\theta}^{c}$ | Shear moduli of the composite, respectively, in the circumferential, axial, and radial directions. |

${v}_{p}$ | Putty Poisson’s ratio |

$c$ | Corrosion defect half length |

$w$ | Corrosion defect width |

$d$ | Corrosion defect depth |

$z$ | Normalized defect length |

$M$ | Folias factor |

$FET$ | Safety factors |

MAWP | The maximum allowable working pressure |

MOP | The maximum operating pressure |

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**Figure 5.**FEA predicted radial stress, steel and composite hoop stresses at the center of the 50% pipe wall loss axisymmetric defects, ${P}_{burst}=43.29\mathrm{MPa}$ (full expansion).

**Figure 6.**(

**a**) FEA predicted radial stress, steel and composite hoop stresses at the center of the 60% pipe wall loss axisymmetric defects, ${P}_{burst}=28.32\mathrm{MPa}$, (

**b**) comparison of the FEA predicted rupture zone with the experimental one performed by [23].

**Figure 7.**Evolution of circumferential stress and strain through the thickness for 50% wall loss axisymmetric defects.

**Figure 9.**FEA predicted hoop strain at the design pressure: (

**a**) outer surface of the pipe (middle of corrosion feature), (

**b**) inner surface of the composite repair system.

Reference | [18] | [23] |

Steel grade | A106 Gr B | GOST 8731-74 |

External diameter ${D}_{ext}$ (mm) | 152.3 | 220 |

Pipe wall thickness $t$ (mm) | 7.11 | 6.0 |

Yield stress${\sigma}_{y}$ (MPa) | 300 (0.2% offset) | 305 (0.2% offset) |

SMYS (MPa) | 241.3 | 241.3 |

Poisson’s ratio${v}_{s}$ | 0.30 | 0.30 |

Hollomon true $\sigma -\u03f5$ model | $823.33{\u03f5}^{0.1813}$ | $697{\u03f5}^{0.136}$ |

Reference | [18] | [23] |

Polymer-based laminate | Carbon fiber/epoxy | Glass fiber/epoxy |

Modulus in the hoop direction ${E}_{\theta}$ (MPa) | 49,000 | 48,470 |

Modulus in the axial direction ${E}_{a}$ (MPa) | 23,400 | 6770 |

Modulus in the radial direction ${E}_{r}$(MPa) | 5500 | 6770 |

Poisson’s ratio ${v}_{ra}$ | 0.45 | 0.4 |

Poisson’s ratio ${v}_{a\theta}$ | 0.07 | 0.099 |

Poisson’s ratio ${v}_{r\theta}$ | 0.45 | 0.099 |

Shear modulus ${G}_{ra}$ (MPa) | 690 | 1670 |

Shear modulus ${G}_{a\theta}$ (MPa) | 2960 | 3200 |

Shear modulus ${G}_{r\theta}$ (MPa) | 690 | 3200 |

Failure stress in hoop direction (MPa) | 576 | 678 |

Composite thickness ${t}_{c}$ (mm) | 3.1 | 6 |

Filler Material | ||

Young’s Modulus ${E}_{p}$ (MPa) | 1740 | 3300 |

Poisson’s ratio${v}_{p}$ | 0.45 | 0.37 |

Defect Type Length (mm) × Width (mm) | Flaw Depth d/t (%) | Burst Pressure, MPa (Unrepaired) | EXP Burst Pressure, MPa (Repaired) | FEA Burst Pressure, MPa (Repaired) | ANA Burst Pressure, MPa (Repaired) | Reference |
---|---|---|---|---|---|---|

Intact steel pipe (Unflawed) | 0% | 45.85 | N/A | N/A | N/A | [18] |

Axisymmetric | 50% | 29.99 | 43.80 | 43.29 | 44.15 | |

152.4 × 152.4 | 50% | 30.34 | 43.10 | N/A | 44.15 | |

Intact steel pipe (Unflawed) | 0% | 27.59 | N/A | N/A | N/A | [23] |

133 × 102 | 60% | 13.8 | 29.06 | 28.32 | 46.4 |

Polymer-Based Laminate | |
---|---|

Modulus in the hoop direction ${E}_{\theta}$ (MPa) | 23,800 |

Modulus in the axial direction ${E}_{a}$ (MPa) | 24,500 |

Modulus in the radial direction ${E}_{r}$(MPa) | 11,600 |

Poisson’s ratio ${v}_{ra}$ | 0.071 |

Poisson’s ratio ${v}_{a\theta}$ | 0.107 |

Poisson’s ratio ${v}_{r\theta}$ | 0.1 |

Shear modulus ${G}_{ra}$ (MPa) | 2600 |

Shear modulus ${G}_{a\theta}$ (MPa) | 4700 |

Shear modulus ${G}_{r\theta}$ (MPa) | 3600 |

Laminate allowable strain ${\u03f5}_{c}$(mm/mm) | 0.003 |

Filler Material | |

Young’s Modulus ${E}_{p}$ (MPa) | 1.740 |

Poisson’s ratio${v}_{p}$ | 0.45 |

P_{d} [MPa](Equation (49)) | $\frac{\mathit{d}}{\mathit{t}}\text{}[\%]$ | $\frac{{\mathit{P}}_{\mathit{f}}}{\mathit{M}\mathit{A}\mathit{O}\mathit{P}}$ | ${\mathit{t}}_{\mathit{c}}\text{}\left[\mathbf{mm}\right]$ | ||||
---|---|---|---|---|---|---|---|

ASME PCC-2 (S = SMYS) | ISO/TS24817 (S = 0.72 SMYS) | $\mathbf{Developed}\text{}({\mathit{P}}_{\mathit{e}\mathit{x}\mathit{t}}=0\mathbf{MPa})$ | $\mathbf{Developed}\text{}({\mathit{P}}_{\mathit{e}\mathit{x}\mathit{t}}=2.5\mathbf{MPa})$ | $\mathbf{Developed}\text{}{\mathit{P}}_{\mathit{e}\mathit{x}\mathit{t}}=5\mathbf{MPa}$ | |||

14.68 (Pressure ${P}_{i}$ to be recovered) | 10 | 1.86 | 0 | 1.73 | 0 | 0 | 0 |

15 | 1.79 | 0 | 2.60 | 0 | 0 | 0 | |

20 | 1.73 | 0 | 3.46 | 0 | 0 | 0 | |

25 | 1.66 | 0 | 4.33 | 0 | 0 | 0 | |

30 | 1.59 | 0.48 | 5.19 | 0 | 0 | 0 | |

35 | 1.52 | 1.68 | 6.06 | 0 | 0 | 0 | |

40 | 1.45 | 2.88 | 6.92 | 0 | 0 | 0 | |

45 | 1.37 | 4.08 | 7.79 | 0 | 0 | 0 | |

50 | 1.30 | 5.29 | 8.65 | 0.22 | 0 | 0 | |

55 | 1.22 | 6.49 | 9.52 | 1.83 | 0 | 0 | |

60 | 1.14 | 7.69 | 10.38 | 3.47 | 0.44 | 0 | |

65 | 1.05 | 8.89 | 11.25 | 5.16 | 2.01 | 0 | |

70 | 0.97 | 10.09 | 12.11 | 6.89 | 3.61 | 0.67 | |

75 | 0.88 | 11.29 | 12.98 | 8.66 | 5.25 | 2.2 | |

80 | 0.79 | 12.49 | 13.84 | 10.47 | 6.93 | 3.76 | |

85 | 0.69 | 13.70 | 14.71 | 12.34 | 8.65 | 5.36 | |

90 | 0.59 | 14.90 | 15.57 | 14.26 | 10.42 | 7.00 |

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**MDPI and ACS Style**

Djahida, D.; Tewfik, G.; Witek, M.; Abdelghani, M. Analytical Model and Numerical Analysis of Composite Wrap System Applied to Steel Pipeline. *Materials* **2021**, *14*, 6393.
https://doi.org/10.3390/ma14216393

**AMA Style**

Djahida D, Tewfik G, Witek M, Abdelghani M. Analytical Model and Numerical Analysis of Composite Wrap System Applied to Steel Pipeline. *Materials*. 2021; 14(21):6393.
https://doi.org/10.3390/ma14216393

**Chicago/Turabian Style**

Djahida, Djouadi, Ghomari Tewfik, Maciej Witek, and Mechri Abdelghani. 2021. "Analytical Model and Numerical Analysis of Composite Wrap System Applied to Steel Pipeline" *Materials* 14, no. 21: 6393.
https://doi.org/10.3390/ma14216393