A phase-field fracture model for creep-fatigue behavior

A phase-field fracture model for creep-fatigue behavior is proposed. The fatigue and creep behavior are simulated by modifying the free energy functional through a total degradation function that diminishes fracture toughness with the accumulation of the relevant history variable. Specifically, strain energy density and creep strain serve as the chosen fatigue and creep history variables, respectively. To model the creep-fatigue interaction, we propose several total degradation function formulations comprising fatigue and creep degradation functions. Numerical experiments demonstrate the capability of our model to reproduce the strain-lifetime relationship and crack growth behavior under creep-fatigue loading conditions with varying hold times. Moreover, we simulated examples of plates with holes, demonstrating the capability of our model for complex crack paths.