# 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 Crack Development
Crack development of interfaces when the shear displacement is 10 mm in the unbonded condition, 50% partially bonded condition and fully bonded condition are presented in Figures 7-9, wherein the red line is the interface, and the red dots represent cracks. For unbonded interfaces: (1) when the normal stress is 1 MPa, almost no cracks appear; (2) when the normal stress is 2 MPa, only a small number of cracks appear on the right side of the interface; (3) when the normal stress is 3 MPa, obvious cracks appear on the interface, and there are distributions in many regions with a small number of cracks; (4) when the normal stress is 4 MPa, cracks are uniformly distributed in most of the interface; (5) when the normal stress is 5 MPa, cracks are uniformly distributed in all the regions. Hence, the number of cracks increases significantly with increasing normal stress the more uniformly they are distributed on the interface. Figure 7: Crack development of interface in unbonded condition (the red region means the distribution of cracks). It can also be observed that cracks occur on the upper side of the interface, i.e., in the lower strength block. For the higher strength block, cracks rarely occur. Cracks in the unbonded state are mostly generated by friction degradation due to friction interlocking of particle bulges on both sides of the interface. Meanwhile, the particles of higher strength block have stronger cohesion and thus have higher resistance to internal locking damage, which is the reason why cracks are more likely to occur on the upper block. Moreover, the  
Figure 8: Crack development of interface in 50% bonded condition (the red region means the distribution of cracks). Figure 9: Crack development of interface in fully bonded condition (the red region means the distribution of cracks). cracks basically appear near the interface and show no tendency to develop internally. This is because the generation of cracks is just the disappearance of particle friction interlocking, and the shapes of interfaces become flatter, reducing the possibility of further particle friction interlocking. The development of cracks in the 50% bonded binary interface is presented in Figure 8. Compared with the failure of the unbonded binary interface, its cracks are obviously increasing, and the distribution is more complicated. When the normal stress is 1 MPa, the cracks are distributed on the upper block of the interface and concentrated around the bonded part, and cracks develop upwards. At the normal stress of 2 MPa, cracks still appear mainly in the bonded region at the interface, but they also begin to appear at the boundary between the bonded and unbonded portions, with a tendency to expand further to the unbonded portion. When the normal stress is 3 MPa, cracks are no longer concentrated only in the bonded region of the interface but are also distributed in the unbonded region. There are also obvious long cracks, which initiate from the boundary between the bonded and unbonded regions. Meanwhile, a small number of cracks appear inside the upper block. At the normal stress of 4 MPa, the main features of the fracture distribution are similar to those at the normal stress of 3 MPa, while the cracks inside the upper block further increase. When the normal stress is 5 MPa, the crack distribution is also similar to that at 3 MPa or 4 MPa, and the cracks in the upper block show a tendency to penetrate along the extension direction of long cracks in the lower block. During shearing, the unbonded portion of the interface comes into contact with the damaged surface created by the bonded portion. Since the contact surface is not smooth, new shear degradation is bound to occur, leading to the generation of new cracks. In the process, the upper block produces a large number of cracks due to its low strength. Stress concentrations occur at the boundary between the bonded and unbonded regions at the interface, which produces large bending moments and tensile stress at high normal stress, leading to long cracks in the lower block.