# Thermal Delamination Modelling and Evaluation of Aluminium–Glass Fibre-Reinforced Polymer Hybrid

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## Abstract

**:**

## 1. Introduction

## 2. Material Modelling Constitutive Equations

#### 2.1. Aluminium Material Modelling

_{y}, is expressed as [24]:

_{room}is the room temperature and T

_{melt}is the melting point of the aluminium. The fracture strain with the effect of pressure, strain rate and temperature is:

_{1}, d

_{2}and d

_{3}are the pressure effect constants, $\eta $ is the ratio between pressure and effective stress, d

_{4}is the strain rate effect constant and d

_{5}is the temperature effect constant.

#### 2.2. GFRP Material Modelling

_{1}and σ

_{2}represent the effective stress tensor components in respective directions, τ

_{12}represents the effective shear tensor, X

_{T}and X

_{C}are the longitudinal tensile and compressive strengths, Y

_{T}and Y

_{C}are the transverse tensile and compressive strengths, S

_{C}is the shear strength, E

_{A}and E

_{B}are the longitudinal and transverse Young’s modulus, G

_{AB}is the shear modulus, υ

_{BA}and υ

_{AB}are the Poisson’s ratio in respective directions, and β is the weighting factor for shear term.

#### 2.3. Cohesive Zone Modelling

_{N}are the normal direction peak traction and ultimate displacement. E

_{N}is defined as the Mode-I penalty stiffness.

_{T}are the tangential direction peak traction and ultimate displacement. E

_{T}is defined as the Mode-II penalty stiffness.

## 3. Finite Element Modelling

_{o}of 40 and 25 mm, respectively. The span length for the ENF test, L, is 50 mm. The results from experiments are shown in Table 3, where the slope, k, and peak loads, F

_{P}, are used in data reduction to obtain fracture toughness.

_{N}is calculated from [10]:

_{T}, is calculated from [10]:

_{P}, from Table 3 are converted into the respective fracture toughness required for cohesive parameters at each temperature. Peak traction stresses, σ and τ, are estimated empirically from compilations of previous literature on Mode-I and Mode-II interface strength done by Zhao et al. [14], where the values are similar to a literature review of aluminium and GFRP laminates. To acquire the cohesive properties at higher temperatures, a ratio approach between experimental data and cohesive properties was implemented in this study.

_{N}and E

_{T}, at higher temperatures are ratioed to the ratio of the slope, k, from a load–displacement curve based on Equations (11) and (12) [32].

_{I}is the slope for Mode-I and k

_{II}is the slope for Mode-II; x is the respective temperature based on the required parameter.

## 4. Numerical Results and Analysis

#### 4.1. Mesh Convergence

#### 4.2. Load–Displacement Curves and Model Validation

#### 4.3. Crack Initiation and Stress Distribution

## 5. Conclusions

- The validity of the FE model at each temperature is verified with a slope maximum difference within 5.73% for Mode-I at 110 °C and 7.26% for Mode-II at 70 °C.
- Crack front stress is concentrated in the middle for Mode-I, while stress is focused on the sides of Mode-II delamination. Results for 30 °C are characterised by a more fluctuating gradual stress variation for both modes.
- The stress distribution at 70 °C is very polarised, where all elements except the outermost one of Mode-I have practically similar peak stress, while the opposite is observable in Mode-II. A similar trend of more gradual stress variation can be discovered for 110 °C.
- DCB and ENF trends employed from experimental tests successfully obtain temperature-dependent cohesive zone properties.
- A Johnson–Cook material model with temperature dependency and Chang–Chang material model properties at each temperature ensured proper modelling of specimen bending and flexure.
- The validated temperature-dependent cohesive zone model demonstrates the applicability of the current methodology to analyse laminates at high temperatures.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 5.**Mode-I load–displacement curve validation between experiment and simulation at (

**a**) 30, (

**b**) 70 and (

**c**) 110 °C.

**Figure 6.**Mode-II load–displacement curve validation between experiment and simulation at (

**a**) 30, (

**b**) 70 and (

**c**) 110 °C.

**Figure 8.**Normalised Mode-I stress distribution along the crack front at (

**a**) 30, (

**b**) 70 and (

**c**) 110 °C.

Material Properties | ρ (kg/m^{3}) | E (GPa) | G (GPa) | ν | |

2869 | 72.8 | 27.36 | 0.33 | ||

Yield surface parameters | A (MPa) | B (Mpa) | n | C | m |

369 | 684 | 0.73 | 0.0083 | 1.7 | |

Failure parameters | d_{1} | d_{2} | d_{3} | d_{4} | d_{5} |

0.13 | 0.13 | −1.5 | 0.011 | 0 |

**Table 2.**Material properties of glass fibre-reinforced polymer (GFRP) for Chang–Chang failure criterion [28].

30 °C | 70 °C | 110 °C | |
---|---|---|---|

ν_{AB} | 0.321 | 0.335 | 0.239 |

E_{A} (GPa) | 37.12 | 36.94 | 30.73 |

E_{B} (GPa) | 9.75 | 7.65 | 2.65 |

G_{AB} (GPa) | 5.36 | 3.27 | 0.13 |

X_{T} (MPa) | 750.67 | 719.48 | 441.77 |

Y_{T} (MPa) | 58.40 | 52.88 | 20.79 |

X_{C} (MPa) | 816.53 | 658.42 | 551.52 |

Y_{C} (MPa) | 168.51 | 128.44 | 94.74 |

S_{C} (MPa) | 94.93 | 52.57 | 6.54 |

β | 0.5 | 0.5 | 0.5 |

Mode-I | Mode-II | |||||
---|---|---|---|---|---|---|

30 °C | 70 °C | 110 °C | 30 °C | 70 °C | 110 °C | |

k (N/mm) | 12.57 ± 0.15 | 12.47 ± 0.46 | 7.25 ± 0.08 | 239.97 ± 7.10 | 134.50 ± 1.91 | 91.97 ± 2.59 |

F_{P} (N) | 34.51 ± 2.42 | 22.04 ± 1.23 | 10.55 ± 0.16 | 297.3 ± 4.63 | 208.32 ± 10.48 | 74.97 ± 2.34 |

30 °C | 70 °C | 110 °C | |
---|---|---|---|

E_{N} (GPa) | 463.85 | 460.38 | 267.52 |

E_{T} (GPa) | 69.23 | 38.80 | 26.53 |

G_{IC} (J/m^{2}) ^{a} | 169.50 | 68.74 | 27.71 |

G_{IIC} (J/m^{2}) ^{a} | 166.70 | 147.00 | 28.31 |

σ (MPa) | 30.00 | 12.16 | 4.90 |

τ (MPa) | 45.00 | 40.09 | 7.72 |

Temperature | 30 °C | 70 °C | 110 °C | |
---|---|---|---|---|

k (N/mm) | Experiment | 12.57 | 12.47 | 7.25 |

Simulation | 13.24 | 12.46 | 7.66 | |

Difference (%) | 5.38 | 0.13 | 5.73 | |

F_{P} (N) | Experiment | 34.51 | 22.04 | 10.55 |

Simulation | 31.95 | 18.78 | 11.37 | |

Difference (%) | 7.42 | 14.76 | 7.83 |

Temperature | 30 °C | 70 °C | 110 °C | |
---|---|---|---|---|

k (N/mm) | Experiment | 239.97 | 134.50 | 91.97 |

Simulation | 249.85 | 144.27 | 95.63 | |

Difference (%) | 4.12 | 7.26 | 3.99 | |

F_{P} (N) | Experiment | 297.30 | 208.32 | 74.97 |

Simulation | 252.36 | 222.90 | 84.36 | |

Difference (%) | 15.12 | 7.00 | 12.53 |

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**MDPI and ACS Style**

Chow, Z.P.; Ahmad, Z.; Wong, K.J.; Koloor, S.S.R.; Petrů, M.
Thermal Delamination Modelling and Evaluation of Aluminium–Glass Fibre-Reinforced Polymer Hybrid. *Polymers* **2021**, *13*, 492.
https://doi.org/10.3390/polym13040492

**AMA Style**

Chow ZP, Ahmad Z, Wong KJ, Koloor SSR, Petrů M.
Thermal Delamination Modelling and Evaluation of Aluminium–Glass Fibre-Reinforced Polymer Hybrid. *Polymers*. 2021; 13(4):492.
https://doi.org/10.3390/polym13040492

**Chicago/Turabian Style**

Chow, Zhen Pei, Zaini Ahmad, King Jye Wong, Seyed Saeid Rahimian Koloor, and Michal Petrů.
2021. "Thermal Delamination Modelling and Evaluation of Aluminium–Glass Fibre-Reinforced Polymer Hybrid" *Polymers* 13, no. 4: 492.
https://doi.org/10.3390/polym13040492