# Moisture Absorption Effects on Mode II Delamination of Carbon/Epoxy Composites

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## Abstract

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## 1. Introduction

_{IIC}of the carbon/epoxy composites has decreased by 37.5% when compared to the unaged specimens. Davidson et al. [9] conditioned the thermoplastic particles toughened carbon/epoxy composites at 50 °C/95%RH for approximately 11 months as well. The G

_{IIC}was found to have deteriorated by around 20% when the specimens were tested in environments of –43 °C and 98 °C. As for eight-harness satin-weave glass/epoxy composites immersed in distilled water at aging temperature of 72 °C, G

_{IIC}has dropped by 55% and 40% in warp and weft directions respectively after around 4 months of immersion [10]. Zhao et al. [11] aged eight-harness satin-weave glass/bismaleimide composites in seawater for around 8 months. The authors discovered that Teflon insert specimens showed degradation in G

_{IIC}at aging temperatures of 50 °C and 80 °C for 22% and 32%, respectively. However, for precracked specimens, G

_{IIC}decreased by 18% at 50 °C but increased by 19% at 80 °C. Nash et al. [12] immersed non-crimp carbon fabric/benzoxazine composites in deionized water at aging temperature of 80 °C for nearly 4 months. Two types of benzoxazine were used, which were toughened (BZ9120) and untoughened (BZ9130) resins. In addition, two types of crack tip conditions were considered, which were non-precracked and precracked specimens. For non-precracked specimens, the authors discovered G

_{IIC}increased by 153% and 34% for BZ9120 and BZ9130 resins, respectively. As for precracked specimens, the authors found invariant G

_{IIC}for both resins.

_{IIC}throughout the aging period was not known. Recently, it has been demonstrated that mode I, II, and mixed-mode I/II fracture toughness varied at a different rate with respect to the moisture content [13]. Nevertheless, the study was limited to distilled water immersion. For aircraft applications, the highest humidity level is commonly taken as 85% relative humidity (RH) [14].

## 2. Materials and Methods

#### 2.1. Materials and Specimens

#### 2.2. Moisture Absorption Test

#### 2.3. Mode II Delamination Test

_{o}= 30 mm and half span length L = 50 mm. Specimens were taken out from the chamber to perform delamination tests at aging intervals of 4, 12, 27, and 156 days, which corresponded to the moisture content M = 0.23%, 0.42%, 0.61%, and 0.94%. Delamination tests were also carried out for specimens at dry condition. All tests were performed using a Shimadzu Universal Testing Machine (Shimadzu Corp., Kyoto, Japan) with the load cell capacity of 10 kN at 1 mm/min. At least three specimens were tested for each aging interval. All tests were performed at the ambient conditions.

#### 2.4. Date Reduction Scheme

_{IIC}was calculated using Irwin–Kies [17] equation

_{C}is the critical load, B is the width of the specimen, C is the compliance and a is the crack length. The compliance calibration model is described by [16]

_{2}and C

_{1}are constants fitted through C − a

^{3}plot. Substituting the derivative of Equation (2) into Equation (1) gives

## 3. Experimental Results and Discussion

#### 3.1. Moisture Absorption Curves

_{m}is 0.94%. To apply Fickian diffusion model [18], the slope of the initial linear region which is up to 60% of M

_{m}is fitted (Figure 3). The value of the slope (0.339) corresponds to $\left({M}_{2}-{M}_{1}\right)/\left[{\left(\sqrt{t}/h\right)}_{2}-{\left(\sqrt{t}/h\right)}_{1}\right]$ as described in Equation (4). The diffusivity D

_{z}= 2.56 × 10

^{−2}mm

^{2}/day is thus obtained using Equation (4).

#### 3.2. Mode II Fracture Toughness

_{IIC}values at different moisture levels. The G

_{IIC}values are calculated using Equation (3), where the C

_{2}values at different moisture content levels are displayed in Table 1. The maximum coefficient of variation (C.V) is 14% at M = 0.23%, which signifies a comparatively good repeatability of the tests. It is noticed that in general G

_{IIC}has been decreased upon moisture attack. In average, the G

_{IIC}values dropped by 15%, 18%, 23%, and 10% at M = 0.23%, 0.42%, 0.61%, and 0.94%, respectively. This could be due to matrix degradation that leads to interface weakening effect [11], and is commonly noticed as a result of moisture absorption [4,5,13,19,20,21,22]. The slight increment of the G

_{IIC}at M = 0.94% could be due to ductility enhancement due to matrix plasticization [12], which could have enlarged the fracture process zone at the interface [11]. It is worth noting that the matrix plasticization effect is also reflected in the global bending behavior of the composite, which is shown in Figure 6. Matrix plasticization leads to the softening of the material, and hence a lower stiffness is observed upon moisture absorption. Nevertheless, overall, it is apparent that moisture has degraded the mode II fracture toughness. Compared to the previous study on the water absorption effects on another type of unidirectional carbon/epoxy composite by immersion in distilled water at 70 °C, it is apparent that distilled water has a more severe effect than humidity. The maximum moisture content M

_{m}was 5.3%, which was accompanied by a drop of approximately 50% in the G

_{IIC}as compared to the dry specimens [13].

#### 3.3. Force–Displacement Curves

#### 3.4. Residual Property Model

_{IIC}with respect to moisture content M, the following residual property model (RPM) [3,6,13] is adopted

_{IIC}(M) is the residual mode II fracture toughness at particular moisture content, G

_{IIC,dry}is the dry property, G

_{IIC,min}is lowest mode II fracture toughness within the range of study, M is the moisture content, M

_{m}is the maximum moisture content, and ζ is the degradation parameter. This model assumes that the residual mode II fracture toughness is a function of moisture content only. The best-fit curve with ζ = 0.2918 is plotted as the solid line in Figure 4. The largest difference is found at M = 0.94%, with a 15% difference. This is due to the fluctuation in the trend, where a slight increment in the G

_{IIC}is noticed towards the end of the aging period. Nevertheless, the predicted G

_{IIC}is more conservative (lower than the experimental value), thus a lower predicted value with 15% difference is acceptable from the safety point of view. The same model is then applied for the stiffness (Figure 6), which is written as

## 4. Numerical Simulation

#### 4.1. Finite Element Model

#### 4.2. Lamina Properties

_{f}of each specimen is calculated using the equation

_{f}at each moisture content is listed in the second column of Table 2. It noteworthy that, for unidirectional laminates, E

_{f}is equal to the longitudinal modulus E

_{11}. The values in bracket indicate the C.V(%). Good repeatability is found, with a maximum C.V of less than 8%. The E

_{11}value estimated at dry condition is the same as reported in a previous study [15], where the same carbon/epoxy composite was used. Therefore, the same lamina properties reported in reference [15] are used for dry condition. As for the other lamina properties (transverse modulus E

_{22}, in-plane shear modulus G

_{12}, out-of-plane shear modulus G

_{13}, and G

_{23}) at wet conditions, they are estimated using the same ratio of the corresponding E

_{11}with respect to its dry value. The Poisson’s ratio (ν

_{12}) is assumed to be invariant with the moisture content [6]. It is to note that the transverse and shear properties are generally recognized to be sensitive to moisture attack [6]. However, since the bending behavior of the composite is dominated by E

_{11}, the accuracy of the transverse and shear properties are therefore not critical in this case.

#### 4.3. Cohesive Properties

_{u,s}is reached, damage is initiated (D = 0). Further increment in the separation results in the traction decrement, which signifies softening effect. When the traction is reduced to 0, the element is completely failed (D = 1). The area under the traction–separation curve corresponds to the mode II fracture toughness G

_{IIC}.

_{ss}, interface shear strength t

_{u,s}, and the mode II fracture toughness G

_{IIC}. G

_{IIC}is determined from the experiments or estimated using Equation (6). K

_{ss}at the dry condition is assumed to be 4.5 × 10

^{5}MPa/mm, which is the same value as the interface normal stiffness K

_{nn}used to simulate mode I delamination of the same composite [15]. It is common that the same normal and shear interface stiffness value is used for the same material [27].

_{IC}is the mode I fracture toughness and t

_{u,n}refers to the interface normal strength. In a separate study on mode I delamination of the same material, it was reported that G

_{IC}= 245 N/m at quasi-static loading. In addition, the interface normal strength t

_{u,n}= 35 MPa was found to be a good choice to obtain reliable simulation results [15]. Using Equation (9), the value of t

_{u,s}at dry condition is estimated to be 81 MPa.

_{IIC}are the estimated values from Equation (6) instead of the experimental values. The intention is to evaluate the accuracy of the predicated K

_{ss}(M) and G

_{IIC}(M) using the RPM.

#### 4.4. Simulation Results

_{IIC}values used in the simulation are the predicted values using Equation (6), and it is shown in Figure 4 that the fitted G

_{IIC}value at M = 0.94% is 15% lower than the experimental value. Therefore, it is reasonable to observe a larger difference in the peak load.

## 5. Conclusions

- The moisture absorption is well fitted using Fick’s law, with the maximum moisture content of approximately 0.94% and diffusivity of 2.56 × 10
^{−2}mm^{2}/day. - In general, mode II fracture toughness decreases with the moisture content. The maximum degradation is 23% at moisture content of 0.61%.
- The variation of the mode II fracture toughness is well fitted using the residual property model, with a 15% difference at the moisture content of 0.94%.
- The maximum difference between the experimental and numerical slopes is 10% under dry conditions. This signifies that the approach of estimating the lamina properties and interface shear stiffness used in this study is reliable.
- The difference between the experimental and numerical peak loads is less than 12.5%, except for the case at maximum moisture content of 0.94%. This indicates that the mode II fracture toughness values predicted using the residual property model and the methodology adopted to estimate the interface shear strength provide sufficient accuracy in predicting the mode II delamination behavior of the composite.
- The numerical results show that the damage is initiated in the interface during the early stage of loading. When the numerical peak load is attained, the first element has reached its total failure.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 7.**Three possible degradation trends of the residual property with respect to the moisture content.

**Figure 10.**Experimental and numerical force displacement curves at moisture content of (

**a**) 0%, (

**b**) 0.23%, (

**c**) 0.42%, (

**d**) 0.61%, and (

**e**) 0.94%, along with the evolution of the damage energy.

Moisture Content M (%) | C_{2} (×10^{−8} N^{−1}mm^{−2}) |
---|---|

0 | 5.57 |

0.23 | 5.65 |

0.42 | 6.18 |

0.61 | 5.82 |

0.94 | 5.35 |

**Table 2.**Lamina properties for the carbon/epoxy composite used in this study [15].

M (%) | E_{11} (GPa) | E_{22} (GPa) | G_{12} (GPa) | G_{13} (GPa) | G_{23} (GPa) | ν_{12} |
---|---|---|---|---|---|---|

0 | 103 (4.95) | 6.7 | 2.7 | 2.7 | 2.5 | 0.34 |

0.23 | 94 (2.90) | 6.1 | 2.4 | 2.4 | 2.3 | 0.34 |

0.42 | 86 (7.89) | 5.5 | 2.2 | 2.2 | 2.1 | 0.34 |

0.61 | 91 (0.16) | 5.9 | 2.4 | 2.4 | 2.2 | 0.34 |

0.94 | 99 (0.66) | 6.4 | 2.6 | 2.6 | 2.4 | 0.34 |

M (%) | G_{IIC} (N/m) | K_{ss} (MPa/mm) | t_{u,s} (MPa) |
---|---|---|---|

0 | 1322.75 | 4.50 × 10^{5} | 81 |

0.23 | 1121.90 | 3.94 × 10^{4} | 70 |

0.42 | 1083.24 | 3.83 × 10^{4} | 68 |

0.61 | 1055.34 | 3.76 × 10^{4} | 66 |

0.94 | 1019.01 | 3.66 × 10^{4} | 64 |

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**MDPI and ACS Style**

Wong, K.J.; Johar, M.; Koloor, S.S.R.; Petrů, M.; Tamin, M.N. Moisture Absorption Effects on Mode II Delamination of Carbon/Epoxy Composites. *Polymers* **2020**, *12*, 2162.
https://doi.org/10.3390/polym12092162

**AMA Style**

Wong KJ, Johar M, Koloor SSR, Petrů M, Tamin MN. Moisture Absorption Effects on Mode II Delamination of Carbon/Epoxy Composites. *Polymers*. 2020; 12(9):2162.
https://doi.org/10.3390/polym12092162

**Chicago/Turabian Style**

Wong, King Jye, Mahzan Johar, Seyed Saeid Rahimian Koloor, Michal Petrů, and Mohd Nasir Tamin. 2020. "Moisture Absorption Effects on Mode II Delamination of Carbon/Epoxy Composites" *Polymers* 12, no. 9: 2162.
https://doi.org/10.3390/polym12092162