In this study, the effect of the designed arrangement of TSW defects in graphene on cohesive zone law between polyethylene (PE) and graphene is investigated using the molecular dynamics simulation. The traction-separation relationship including the peak stress and work of separation in mode I and II fracture is derived by the quasi-static decohesion test of PE-graphene bilayer structure. Since the surface roughness and the magnitude of the locally rippled configuration of the graphene is readily affected by the sequence of pentagon and heptagon and their spatial orientation, we considered both the density and the in-plan orientation of the patterned TSW defects. In mode II fracture test, the work of separation of PE/graphene nanocomposite is significantly improved by the designed TSW defects.