Configurational forces in a phase field model for the cyclic fatigue under complex situation
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During the last decade, the phase field fatigue model has been introduced as a powerful method to capture the most important fatigue properties under complex loading and reproduce the crack evolution path in an efficient fashion. However, it is still hard to understand the details of the phase field model for fatigue fracture. The reason for this difficulty is that the phase field model is based on an energetic formulation. The total energy of the body establishes a variational principle. Therefore, it is desirable to understand the phase field model in an energetic way. In this spirit, we borrow the concept of configurational forces and examine the energetic driving forces of the phase field model. The advantage of the configurational force framework is that it is based on the material manifold itself. It is shown that the phase field model contains different types of energetic forces, which contribute to the crack propagation in a certain manner. Generally speaking, when the configurational forces point in the same direction as the crack progresses, it accelerates the crack propagation; otherwise, it hinders further crack extension. Lastly, we show that the proposed tool of configurational forces complies with Griffith energy criterion; thus, the onset of a crack happens when the total configurational force on the crack tip vanishes.