# Numerical Analysis for Shear Behavior of Binary Interfaces under Different Bonded Conditions
## 3 Shear Mechanical Behavior under Different Bonded Conditions  
### Influence of Bonded Conditions on Shear Stress-Shear Displacement Curve  
In order to study the influence of bonded conditions on the shear behavior of the binary interface, the variations of shear stress-shear displacement curves of binary interfaces under different bonded conditions are firstly analyzed, which are shown in Figure 2.  
Figure 2: The shear stress–shear displacement curves of binary interfaces under different bonded conditions. (**a**) Bonded ratio = 0%; (**b**) bonded ratio = 25%; (**c**) bonded ratio = 50%; (**d**) bonded ratio = 75%; (**e**) bonded ratio = 100%.  
Figure 2a shows that the stress-displacement curves of the binary interfaces under the unbonded condition are in the standard shear-slip state. The slope of the stress rise before the peak remained almost constant, and the stress rise slowed down near the peak with a certain degree of yielding. It showed no significant stress drop in the post-peak, and the residual strength was stable and almost equal to the peak strength. The stress-displacement curves of the binary interfaces in the fully bonded state can be seen in Figure 2e. There was a good linear relationship between shear stress and shear displacement as the stress rose, and no obvious yielding occurred around the peak. After the peak, the curves show a more pronounced stress drop due to the decrease in load-bearing capacity. However, there was a small increase in the curves throughout the stress-decrease section, which is attributed to the fact that the model has not completely failed, and the failure surface was not penetrated. With further loading, the shear stresses of the model tended to decrease in general. In the residual stage, the stress appeared to steeply rise and fall. The misalignment of the failure surface causes the model to form a structure favorable to the temporary load bearing. Although the failure surface was completely penetrated at this time, it cannot maintain long-term stability in the shear process.  
Figure 2b-d show the stress-displacement curves of the binary interfaces under 25%, 50% and 75% bonded conditions, respectively. The curves of partially bonded binary interfaces are closer to that of the unbonded binary interface regarding the shape before the peak, while the post-peak performances are similar to that of fully bonded binary interfaces, which indicates a gradual transformation. For 25% bonded interfaces, the curves show obvious plastic near the peak stress, which fades as the bonded agree increases. Meanwhile, the peak displacement changes accordingly. Specifically, the peak displacement is approximately 2.5 mm at 25% bonded interfaces, 2.0 mm at 50% bonded interfaces, 1.5 mm at 75% bonded interfaces and 1.0 mm at fully bonded interfaces. This can be attributed to the fact that the bonded interface has a good overall elastic deformation capacity, so the stress can basically be maintained to grow linearly before the peak. The unbonded interface may produce localized sliding before the peak, which causes a reduction in shear stiffness, and the rate of stress rise slows down. Additionally, the unbonded region is also equivalent to a crack, which acts as a guide for the development of fractures in the shear process. As a result, the curves of binary interfaces with 25% bonded are flatter in the residual stage.