# Investigation of Debonding Effect in Internal Replacement Pipe System Under Lateral Loading
## 2 Finite Element Analysis
### Internal Replacement Pipe (IRP) System Modelling and Validation
#### 2.2.3 IRP System Validation  
A nonlinear static structural FEA approach is utilized to effectively depict and simulate the material nonlinearity exhibited by the IRP. To achieve this objective, the full Newton-Raphson solution procedure, a widely recognized iterative method for addressing nonlinear problems, is employed [18,19]. The FEA model accommodates substantial deformations and plasticity, ensuring a realistic representation of the IRP system's behavior under varying load conditions. Figure 7 and Table 5 are a comparative analysis of load and displacement across various locations of the IRP system using FEA and experimental techniques. The findings demonstrate a favorable agreement up to a low load level of 21.4 kN (4.8 kip). At this point, a difference of 8% and 15% between the FEA and experimental results was observed for locations situated 43.3451 mm (1.7065 inches) and 591.8327 mm (23.3005 inches) away from the midspan, respectively. However, as the load magnitude increases, the disparity between the two methods amplifies. At the maximum load of 69.1 kN (15.5 kip), the difference increases to 20% and 26% at the respective locations mentioned earlier. In Figures 8 and 9, it is evident that at the maximum load of 69.1 kN (15.5 kip), a higher level of shear stress is observed within the adhesive layer situated between the host pipe and the IRP when compared with the pull-off stress, i.e., 28.75 MPa (4.17 ksi) versus 15.08 MPa (2.19 ksi), respectively. The shear stress is particularly prominent in the region adjacent to the discontinuity edge when compared with the pull-off stress. An analysis of Figure 7 reveals a distinct pattern in the unloading curve of the experimental sample, possibly indicating the occurrence of debonding in the adhesive layer between the host pipe and the IRP. This is evident from the noticeable decrease in strength during the unloading phase, suggesting the presence of structural weakening. The divergence in FEA and experimental results at higher levels of load is attributable to the debonding phenomenon occurring in the adhesive layer. Figure 6: Meshing configurations for IRP system deflection. Figure 8: Shear stress results on the adhesive layer of the 12.7 mm (0.5 inch) discontinuous IRP system at a maximum load of 69.1 kN (15.5 kip) (magnified 18 times). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Load kN (kip)**} & \multirow{2}{*}{**Locations inch**} & \multicolumn{2}{c}{**Deflection, mm (inch)**} & \multirow{2}{*}{**Difference (\%)**} \\ \cline{3-4}  & & **FEA** & **Experiment** & \\ \hline
21.4 (4.8) & 1.7065 & 0.897 (0.035) & 0.975 (0.038) & 8 \\
23.3005 & 0.526 (0.021) & 0.617 (0.024) & 15 \\
69.1 (15.5) & 1.7065 & 3.922 (0.154) & 4.925 (0.194) & 20 \\
23.3005 & 2.116 (0.083) & 2.855 (0.112) & 26 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of FEA and experimental results for the 12.7 mm (0.5 inch) discontinuous IRP system. Figure 7: Validation of load-displacement relationship in the 12.7 mm (0.5 inch) discontinuous IRP system. Figure 10 displays the equivalent stress on the IRP within the 12.7 mm (0.5 inch) discontinuous IRP system under the maximum load of 69.1 kN (15.5 kip). It can be observed that the highest equivalent stress, reaching 29.2 MPa (4.2 ksi), occurs at the bottom section of the IRP\({}^{\prime}\)s discontinuity opening. Notably, this value remains below the strength of ALTRA10, which is 79.4 MPa (11.5 ksi). Consequently, it can be inferred that the IRP has not experienced failure up to the maximum load of 69.1 kN (15.5 kip). A series of tests were performed on a generic epoxy material. Those results showed that the epoxy had a pull-off strength of 19.58 MPa (2.84 ksi) and a shear strength of 4.95 MPa (0.72 ksi), resulting in an approximate ratio of 4:1. This significant disparity between pull-off and shear strengths indicates that shear stress is the predominant factor contributing to the failure of the adhesive layer.