# Bonding Behaviors of GFRP/Steel Bonded Joints after Wet-Dry Cyclic and Hydrothermal Curing
## 4 Interfacial Fracture Energy  
In the context of studies on FRP-to-concrete and FRP-to-steel bonded joints, the interfacial fracture energy, \(G_{f}\), is one of the most important indices to express the bonding behaviors [22]. However, in this study, the strength of the adhesive, GFRP materials, and interfacial strength decreased continuously with an increase in harsh curing duration, by which the failure mode of the specimens, after harsh aging transferred from a cohesive failure to an adhesive-steel interface debonding (for wet-dry cyclic curing) or delamination of GFRP (for hygothermal pretreatment). Different failure modes may affect the interfacial fracture energy \(G_{f}\), and therefore, it is inappropriate to calculate the interfacial fracture energy \(G_{f}\) through traditional methods.  
The output energy of the loading machine during quasi-static tensile testing is equal to the sum of three sources of energy: strain energy in the steel substrates, thermal energy, and energy in the bonding part. Assuming that the thermal effect was negligible, the energy in the bonded part, which could be regarded as the interfacial fracture energy (\(G_{f}\)) in this study, can be calculated by following equation:  
\[G_{b}=W-G_{s} \tag{1}\]  
where \(G_{b}\) is the energy stored in the bonded part before fracture occurred, \(W\) is the total output energy of the loading machine, and \(G_{s}\) is the strain energy of the steel substrate. \(W\) was calculated by measuring the area underneath the load-displacement curves, which is shown in Figure 11.  
Figure 10: Threshold values of strain curves.  
The strain energy in steel substrates was calculated by assuming a pure elastic tensile deformation of the steel substrates during the quasi-static tensile loading, and the elastic energy in steel substrates was calculated by Equations (2) and (3), as follows:  
\[G_{s}=\frac{1}{2}\varepsilon^{2}E_{s}V \tag{2}\]  
\[V=l\times A \tag{3}\]  
where \(G_{s}\) is the strain energy of the steel substrate, \(\varepsilon\) is the strain of the steel substrate (S-3), \(E_{s}\) is the Young's Modulus of the steel material, and \(V\) is the volume of the steel substrate. In addition, the parameters \(l\) and \(A\) are the length and area of the steel substrate, which were 300 mm (\(2\times 150\) mm = 300 mm) and 100 mm\({}^{2}\) (\(5\) mm \(\times\) 20 mm = 100 mm\({}^{2}\)), respectively. The calculated strain energy of the steel substrates for each specimen before failure occurred is shown in Figure 12.  
Based on the fracture mechanism of the bonding specimens during quasi-static tensile loading, the interfacial fracture energy of the specimens could be calculated through \(G_{b}\) by using Equation (1), as shown in Figure 13. Compared with the reference specimen, specimens cured in harsh environmental conditions showed a significant reduction in interfacial fracture energy, indicating the undesirable effect of the harsh environmental curing on the bond behavior. Figure 14 shows the normalized interfacial fracture energies of specimens cured in different conditions.  
Figure 11: Output energy of loading machine before fracture occurred.  
Figure 12: Strain energy of steel substrates before fracture occurred.  
According to Figures 13 and 14, by comparing the results of WD-[D]-20 (i.e., WD-30-20, WD-60-20, and WD-90-20) with the same curing temperature, lower interfacial fracture energy was observed for the specimen with longer curing, indicating that a more severe reduction of interfacial fracture energy could be introduced by longer wet-dry cyclic curing duration. Similar observations were found in test series of WD-[D]-40, WD-[D]-60, and HY-[D]-[T]. For WD-30-[T] (i.e., WD-30-20, WD-30-40, and WD-30-60) with the same wet-dry duration and different temperatures, the interfacial fracture energy \(G_{b}\) was reduced from 9.84 \(\AA\) (WD-30-20) to 8.17 \(\AA\) (WD-30-60), showing the negative effect of higher temperature. A similar degradation of interfacial fracture energy was found in HY series testing.