Stochastic Calibration of a Cyclic Cohesive Zone Model Through Monte Carlo Analysis

Fatigue induced crack propagation is still an open issue, relevant to many engineering applications. Cyclic loading produces damage accumulation at a local­ized region which results first in the formation of micro-cracks and finally leads to the creation of macro-cracks. The modeling of fatigue induced crack propagation can be done according to different approaches, such as the Paris law, where the rate of crack growth is dependent on fracture mechanics parameters, e.g., the stress intensity factor or the strain energy release rate. Other approaches are the empirical methods, typically S-N approach and the micromechanical models describing the accumulation of damage based on material microstructure changes. Another approach involves the definition of phenomenological models where the fatigue crack growth is described by adopting cohesive zone laws. In this paper a damage-based irreversible cyclic cohesive zone model is adopted, where damage healing is considered during the fatigue damage evolution. The model presents different parameters, some of which are characterized by a large variability, do not possess a precise physical meaning and then they are not amenable to direct measurement. In this context, this paper aims to provide a robust procedure for the calibration of these model parameters, based on a Monte Carlo stochastic approach. Indications regarding the minimum number of experimental measurements are also provided, to support the planning of tests setups for laboratory investigations. Finally, the definition of a well posed inverse problem allows an efficient identification of all the sought model parameters reducing then the experimental costs.