A cohesive zone model for fatigue crack growth in quasibrittle materials

Abstract

A cohesive zone model for fatigue crack initiation and growth in quasibrittle materials is proposed in the present paper. While bulk material is modeled to be linearly elastic, the softening material in the cohesive zone and cracks are modeled to be internal singular surfaces in the elastic body. The interactions of the singular surfaces are described in a cohesive force law and a Coulomb-type friction law if in contact. The cohesive zone material is modeled to accumulate damage not only along the damage locus but also along an unloading path underneath it, enabling a simulation of fatigue damage and crack growth without the ad hoc imposition of a law of growth rate within the cohesive zone model. The maximum principal stress criterion is used to advance a tip of the cohesive zone in the direction of the maximum principal stress when it reaches the critical value of material strength. The physical crack tip is grown as a natural process of debonding of the cohesive zone under cyclic loading, which, in contrast, may be subcritical with energy dissipation less than the material toughness under static loading. The boundary value problem formulated for fatigue crack growth incorporating the cohesive zone model is nonlinear due to the history dependence of the cohesive zone, and is solved efficiently using the iterative single-domain dual-boundary-element method of successive over-relaxation. It is demonstrated through examples that the present model is capable of predicting fatigue crack initiation as well as growth in a unified way. It is also shown that the cohesive zone model is more advantageous and flexible in handling fatigue cracks under arbitrary loading than the classical singularity-based fracture mechanics approach.