Interface Debonding Model and its Application to the Mixed Mode Interface Fracture Toughness

The aim of this paper is to investigate the mixed mode fracture toughness of an interface crack. The crack propagation is simulated by modifying a cohesive interface model proposed by Ma and Kishimoto (Ma, F. and Kishimoto, K. (1996). A Continuum Interface Debonding Model and Application to Matrix Cracking of Composites, JSME Int. J. Series A, 39:496–507). Based on the internal variable theory of thermodynamics, a continuum interface constitutive model relating interface traction with interface separation has been developed. By introducing an interface damage variable, an evolution equation was derived to characterize the degradation of interfacial rigidity with interface debonding. This constitutive relation is embedded at the crack tip of the interface and the propagation of the interface crack is simulated by the Finite Element Method. The results show that the fracture toughness and fracture boundary curves of dissimilar materials depend on the definition of the characteristic length included in the interface stress intensity factors. By changing the characteristic length properly and normalizing with the critical stress intensity factors, the intrinsic fracture boundary curve can be obtained. This curve can be considered as the fracture criterion based on the interface stress intensity factors. The relation between the fracture toughness and the phase angle is also influenced by the characteristic length. By changing the phase angle, the fracture toughness data is located on the same trend curve and the numerical results are well consistent with the analytical decohesion energy for all material pairs.