Abstract: In this article, based on irreversible thermodynamics, a damage evolution equation of fractional form is constructed. Furthermore, effective strain and effective stress are introduced into the study of pipeline connection assemblies under the condition of axial symmetry. By means of the theory of conservative integral, the series of power function is derived to express the relation between the stress and fatigue life under repeated loading with constant amplitude. The material parameters are obtained by the results of the fatigue test of axially symmetric specimens. Based on APDL which is the further development of the platform of ANSYS, a damage mechanicsfinite element method is employed. The fatigue crack initiation life for standard titanium alloy TC6 specimens is predicted, and the result is consistent with that of the experiment. The fatigue crack initiation life for pipeline connection assemblies is also predicted. The fatigue crack propagation path is analyzed and the fatigue crack propagation life is predicted. This research provides a feasible way to predict the fatigue lives of structure members by means of damage mechanics.

Key words: damage mechanics, finite element method, fatigue life, ANSYS, second development