# Numerical Modeling of Damage Caused by Seawater Exposure on Mechanical Strength in Fiber-Reinforced Polymer Composites

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Material and Experimental Methods

^{2}) glass fiber and Biresin

^{®}(Sika Services AG, Zurich, Switzerland) CR122 epoxy resin with the Biresin

^{®}CH122-3 hardener. The amount of hardener was 30% of the resin’s total weight, as suggested by the manufacturer. The laminates were placed in a vacuum bag and compressed with a load of 2.5 kN for 12 h to preserve the original thickness. During the first 4 h, the vacuum bag remained connected to a vacuum pump to eliminate air bubbles. The post-cure was conducted in agreement with the manufacturer in an oven at 60 °C for 8 h. The laminates were composed by 12 plies distributed according to the layout [0°, 45°, 90°, 45°, 0°, 90°] s and had an overall dimension of 330 mm × 330 mm × 2.3 mm.

## 3. Failure Criterion and Proposed Seawater Exposure Damage Model

#### 3.1. Puck’s Failure Criterion

_{21}, τ

_{31}and τ

_{23}are shear stresses.

#### 3.2. Constitutive Relation and Progressive Failure Theory

#### 3.3. Proposed Model for Seawater Damage

## 4. Finite-Element Based Implementation

## 5. Results and Discussion

## 6. Conclusions

- The linear relation between the weight gain and the wet volume was adequate to model the diffusion process. The maximum errors between the fitted function and the experimental results were lower than 9%.
- The first principal strain fields near the hole surface simulated with the proposed methodology were quite similar to those measured in the experiments for the different loading cases with digital image correlation;
- The model predicted both the maximum stress and the strain at failure with good accuracy, irrespective of the immersion time. In the absence of seawater, the results were more accurate;
- The stress–strain plots exhibited a nonlinear behaviour. However, this non-realistic behaviour only occurred in the early stage of the loading process. After a certain stress level, the numerical simulations and the experimental results behaved similarly;
- A power relationship between the stress at failure and the immersion time was found. Most of the damage caused by the exposure to seawater occurred in the first three months;
- The model can help designers to identify the areas where the application of impermeable coatings can improve the resistance to seawater exposure. The cases analysed showed gains in maximum stress higher than 10%.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Comparison of Fick’s law for predicting the seawater absorption and the experimental results for the tested laminate.

**Figure 4.**Comparison between the first principal strain (ε

_{I}) fields obtained experimentally and numerically. Images a, b and c correspond to the experimental results, and the remaining ones to the simulations with the application of Puck’s failure theory; the images (

**a**,

**d**), (

**b**,

**e**) and (

**c**,

**f**) correspond to loads of 4.3 kN, 4.875 kN and 5.5 kN, respectively.

**Figure 6.**Stress–strain plot: experimental results and prediction of the effects of the seawater exposure for 0 and 900 immersion days.

**Figure 9.**Prediction of the concentration of seawater after 30, 60, 150, 400 and 900 days of immersion.

**Figure 10.**Stress–strain plot: model prediction of the effects of the seawater exposure for different immersion time.

**Figure 11.**Maximum stress against immersion time: numerical predictions and experimental results for 0 and 900 immersion days.

**Figure 12.**Seawater concentration after 900 immersion days with: (

**a**) all permeable surfaces; (

**b**) impermeable lateral surfaces; (

**c**) impermeable hole surface.

**Table 1.**Recommended inclination parameters for GFRP, adapted from [50], Composites Science and Technology, 2002.

${p}_{\perp \Vert}^{t}$ | ${p}_{\perp \Vert}^{c}$ | ${p}_{\perp \perp}^{t}and{p}_{\perp \perp}^{c}$ |

0.30 | 0.25 | 0.20 to 0.25 |

Failure Mode | Damage Value |
---|---|

Tensile fiber | ${d}_{ft}=1$ |

Compressive fiber | ${d}_{fc}=1$ |

Tensile matrix | ${d}_{mt}=1$ |

Compressive matrix | ${d}_{mc}=1$ |

$\mathbf{Saturation}\mathbf{Absorption}{\mathit{M}}_{\mathit{\infty}}(\%)$ | Slope k $(\times {10}^{-5}\mathit{d})$ | Thickness h (mm) | Mass Diffusivity Coefficient D $(\times {10}^{-8}m{m}^{2}/\mathit{d})$ |
---|---|---|---|

1.04 | 14.35 | 2.3 | 2.31 |

Nº | Maximum Load, F (N) | Maximum Displacement, δ (mm) |
---|---|---|

1 | 8969 | 2.87 |

2 | 9545 | 3.19 |

3 | 9155 | 2.33 |

Average | 9223 | 2.8 |

St. Dev. | 208 | 0.4 |

Nº | Maximum Load, F (N) | Maximum Displacement, δ (mm) |
---|---|---|

1 | 8380 | 2.69 |

2 | 7566 | 1.35 |

3 | 7475 | 2.16 |

Average | 7807 | 2.1 |

St. Dev. | 407 | 0.6 |

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**MDPI and ACS Style**

Vidinha, H.; Branco, R.; Neto, M.A.; Amaro, A.M.; Reis, P.
Numerical Modeling of Damage Caused by Seawater Exposure on Mechanical Strength in Fiber-Reinforced Polymer Composites. *Polymers* **2022**, *14*, 3955.
https://doi.org/10.3390/polym14193955

**AMA Style**

Vidinha H, Branco R, Neto MA, Amaro AM, Reis P.
Numerical Modeling of Damage Caused by Seawater Exposure on Mechanical Strength in Fiber-Reinforced Polymer Composites. *Polymers*. 2022; 14(19):3955.
https://doi.org/10.3390/polym14193955

**Chicago/Turabian Style**

Vidinha, Hugo, Ricardo Branco, Maria Augusta Neto, Ana M. Amaro, and Paulo Reis.
2022. "Numerical Modeling of Damage Caused by Seawater Exposure on Mechanical Strength in Fiber-Reinforced Polymer Composites" *Polymers* 14, no. 19: 3955.
https://doi.org/10.3390/polym14193955