Life prediction of corrosion-fatigue based on a new crack growth rate model with damage and the extended finite element method

•A new corrosion-fatigue crack growth rate model introducing damage is proposed.•A robust and efficient crack surface update method is proposed based on XFEM.•A fatigue life algorithm based on the cycle-by-cycle concept is developed.•The mixed-mode crack path and corrosion-fatigue life are accurately predicted.•The method is well applied to a typical ship structure.