# Parameter Study of Interfacial Capacities for FRP–Steel Bonded Joints Based on 3D FE Modeling

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## Abstract

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## 1. Introduction

## 2. Bonding Materials

#### 2.1. Material Properties of GFRP and Steel

#### 2.2. Tensile Test of the Adhesive Specimen

## 3. Tensile Property of GFRP–Steel Specimen

## 4. Finite Element Model

#### 4.1. The Geometry of the Finite Elements

#### 4.2. Validation of the FE Model

## 5. Parametric Studies

#### 5.1. Effect of FRP Elastic Modulus

_{f}= 10 Gpa, 50 Gpa, 100 Gpa, 200 Gpa, and 400 Gpa were adopted in this study; the other parameters of the model were set as shown in Table 1 and Figure 3a. The results of the numerical simulation analysis are listed in Table 2 and Figure 9 and Figure 10.

_{f}= 10 Gpa, 50 Gpa, 100 Gpa, 200 Gpa, and 400 Gpa) under a 22.48 kN tensile loading. According to Figure 9, it was found that the elastic modulus of the FRP could significantly affect the normal peeling stress distribution of the bonding layer. The normal peeling stress distribution of the bonding layer was more uniform for the specimens bonded with FRP materials with a higher elastic modulus. The minimum value of the normal peeling stress was calculated as −3.80 Mpa for the FRP with an elastic modulus of 10 Gpa; as the elastic modulus of the FRP increased, the ultimate value of the normal peeling stress increased gradually. The changes in the extreme normal peeling stress showed that the stress concentration at the end of the bonding layer decreased with an increase in the FRP plate stiffness and that the bonding strength of the joint could be improved accordingly [14]. Furthermore, for the FRP with 10 Gpa, the variation range of the normal stresses of the adhesive layer was −3.80~2.44 Mpa, whereas the variation range of the bonding condition for 500 Gpa was −1.28~2.22 Mpa.

#### 5.2. Effect of FRP Thickness

#### 5.3. Effect of Bonding Length

#### 5.4. Effect of Bonding Thickness

#### 5.5. Effect of Adhesive Stiffness

## 6. Conclusions

- When taking into account that the thickness of the bonding layer of the bonded specimen was relatively small, the stress results (for the interface peeling stress and the von Mises stress) of different calculating paths of the bonding material were very close. Therefore, path II (through the middle layer of the bonding layer) was used as the subsequent stress analysis path.
- The study of different FRP stiffnesses (elastic modulus and thickness) showed that the normal peeling stress and von Mises stress distributions in the bonding layer were more uniform in the specimens bonded with more rigid FRP materials, while the FRP with a higher stiffness was more conducive to eliminating the stress concentration in the adhesive layer.
- An increase in the bonding length could effectively reduce the stress concentration in the adhesive layer. When considering the manufacturing costs, we recommend a bonding length of 90 mm for double-strap bonded specimens.
- A difference in bonding thickness likely may not affect the nonuniformity of the interface peeling stress. However, a change in the bonding thickness can affect the equivalent stress remarkably; with an increase in the bonding thickness (from 0.5 mm to 2.5 mm), the extreme value of the bonding layer stress decreased gradually.
- The elastic modulus of the adhesive layer had a significant influence on the peeling stress of the bonded specimen. The peeling stress on the left side of the bonding layer was more sensitive to the stiffness of the adhesives; bonding materials with a higher elastic modulus were more likely to cause stress concentration in the bonding zone. This research included a detailed analysis of the influence of various bonding parameters on the tensile behaviors of FRP–steel double-strap bonded structures; however, when considering the relatively complex failure mechanisms of bonded composite structures, a more profound experimental analysis (including different bonding parameters and conditions) is required. It is worth noting that this study was aimed at the bonding stresses of FRP–steel double-strap bonded joints based on a linear elastic assumption and cohesive failure mode; therefore, the failure mechanisms of FRP–steel composite specimens composed of nonlinear materials with other failure modes (except for cohesive failure) require further research.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**The GFRP–steel double-strap joints and the tensile test graph. (

**a**) Dimensions of the GFRP–steel double-strap joints; (

**b**) raw materials and test loading graph of the double-strap joint.

Mechanical Parameter | GFRP | Adhesive * | Steel |
---|---|---|---|

Young’s modulus, Mpa | 15,400 (longitudinal direction) 6850 (transverse direction) 7630 (thickness direction) | 213.24 * (Secant Young’s modulus) | 204,000 |

Strength, Mpa | 291.1 (longitudinal direction) 125.3 (transverse direction) 144.6 (thickness direction) | 18.85 * | 291.3 (Yield stress) |

Poisson’s ratio | 0.37 | 0.40 (According to product manual) | 0.3 |

Elastic Modulus of FRP Plates/Gpa | Ultimate Peeling Stresses for Path II/Mpa | Von Mises Stresses for Path II/Mpa |
---|---|---|

10 | −3.80 | 16.96 (left)/6.15 (right) |

50 | −1.95 | 11.02 (left)/9.25 (right) |

100 | −1.61 | 10.09 (left)/9.84 (right) |

200 | −1.41 | 9.59 (left)/10.18 (right) |

500 | −1.28 | 9.29 (left)/10.41 (right) |

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**MDPI and ACS Style**

Liu, J.; Yuan, Y.; Wang, L.; Liu, Z.; Yang, J.
Parameter Study of Interfacial Capacities for FRP–Steel Bonded Joints Based on 3D FE Modeling. *Materials* **2022**, *15*, 7787.
https://doi.org/10.3390/ma15217787

**AMA Style**

Liu J, Yuan Y, Wang L, Liu Z, Yang J.
Parameter Study of Interfacial Capacities for FRP–Steel Bonded Joints Based on 3D FE Modeling. *Materials*. 2022; 15(21):7787.
https://doi.org/10.3390/ma15217787

**Chicago/Turabian Style**

Liu, Jie, Yu Yuan, Libin Wang, Zhongxiang Liu, and Jun Yang.
2022. "Parameter Study of Interfacial Capacities for FRP–Steel Bonded Joints Based on 3D FE Modeling" *Materials* 15, no. 21: 7787.
https://doi.org/10.3390/ma15217787