A Cohesive Fatigue Model Based on the S-N Diagram

The relationship between fatigue life and fatigue crack propagation rate is explored with a new cohesive damage model. The parameters of the model are obtained from idealizations of S-N diagrams used in engineering design. The model is based on the hypothesis that both stable tearing damage and damage due to cyclic loading are representations of a density of microcracks and, therefore, a single damage variable can describe the state of damage. This assumption implies that the quasi-static cohesive law that describes tearing is also the envelope of the fatigue damage. Fatigue damage within the cohesive envelope is assumed to accumulate at a rate that depends on the displacement jumps. The fatigue model was implemented as a UMAT subroutine for Abaqus cohesive elements by adding fatigue damage accumulation to a cohesive model based on the Turon quasi-static cohesive law. The analyses were conducted using a simplified cyclic loading procedure in which the maximum applied load is kept constant and the computational expense of cycling the load is avoided. The predicted propagation rates for a double cantilever beam (DCB) specimen were compared to experimental results for IM7/8552 graphite/epoxy tape.