Abstract:An important characteristic of the interfacial constitutive model for the fracture initiation and propagation is different with macroscopic fracture criteria, which based on elastic or elastic-plastic analyses, In interfacial constitutive model, material strength, toughness, crack nucleation and propagation are all characterized by the local traction-separation relationship and the cohesive surface methodology. The five current main interfacial constitutive models were introduced. These interfacial model characters and the interface traction-separation relation were presented.