Three-dimensional crack closure model under thermomechanical fatigue loading

Understanding the three-dimensional (3D) effects of thermomechanical fatigue (TMF) crack closure is crucial for high temperature damage tolerance design in complex structures. However, the coupling interaction between temperature variation and mechanical loading brings a great challenge for predicting the TMF crack closure and growth. Here, a plasticity-induced closure model is proposed for 3D TMF cracks. Firstly, the yield stress ratio concept is employed to quantify the combined effects of high temperature and fatigue loading. Based on this, boundary conditions for 3D cracks under TMF cycle loading are described using the thin plate sheet method. Subsequently, the size of reversed plastic region and the opening-stress level are theoretically obtained using the complex function method. Theoretical results indicate that the yield stress ratio influences the reversed-to-forward plastic ratio, and the opening-stress ratio exhibits a positive correlation with yield stress ratio and a negative correlation with 3D constraint level. Under various combinations of constraint states, stress levels and TMF phases, the predicted opening-stress ratios demonstrate strong agreement with those from the existing simulations. By directly applying the proposed theoretical model, experimental part-through crack growth rate curves under TMF conditions can be unified into a fundamental baseline.