Critical gas turbine components, often fabricated from nickel-based superalloys, need to withstand significant loading, high temperatures as well as an oxygen-rich environment. Predictions of the material behavior are crucial in the design process of such components. Polycrystalline nickel-based superalloys experience a shift from transgranular ductile fracture to intergranular brittle fracture when exposed to a combination of high temperature, oxygen-rich environment and tensile mechanical loading. The change of fracture mode is accompanied by an increase and subsequent saturation of the crack growth rate. [1] To account for this phenomenon, we have proposed a thermodynamically consistent fully chemo-mechanically coupled modeling framework for intergranular fracture. [2] Therein, a coupled cohesive finite element formulation is employed for modeling the grain boundaries. The modeling framework allows for mixed-mode loading/unloading scenarios and a crystal plasticity model is adopted for the grains. In order to study crack growth rates, it is crucial to propagate cracks far through the polycrystals. Upon crack propagation an increasing part of the grain boundaries is exposed to the environmental oxygen concentration. We formulate a moving boundary condition for oxygen flow from the environment into open edge cracks. The moving boundary condition is based on penalizing concentration gradients in fractured regions of the structure. It handles both edge as well as interior cracks (resulting e.g. from material defects) in monotonic and cyclic loading. Numerical experiments are performed on 2D polycrystalline structures. We show that the model can qualitatively predict the increase and saturation of crack growth rates for increasing environmental oxygen pressure levels in cyclic loading. It is further demonstrated that the model can propagate cracks initiating at the edges past interior cracks, while propagating the environmental oxygen concentration to the crack tip. [1] Molins R., Hochstetter G., Chassaigne J., Andrieu E. Oxidation effects on the fatigue crack growth behaviour of ally 718 at high temperature. Acta Materialia, Vol. 45 (2), pp. 663-674, 1997. [2] Auth K.L., Brouzoulis J., Ekh M. A fully coupled chemo-mechanical cohesive zone model for oxygen embrittlement nickel-based superalloys. Journal of the Mechanics and Physics of Solids, Vol. 164 , pp. 104880, 2022.