13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- element. Here, the triaxiality value means the ratio between the hydrostatic stress and the von Mises equivalent stress, see Equation (2). σ σ = h Mises H (2) H is the triaxiality value for unit volume element. σh is the hydrostatic stress in the element. σMises is the von Mises equivalent stress in the element. The conclusions for triaxiality dependent behavior can be summarized as: the cohesive parameters are not pure material constants but dependent on the triaxiality conditions. With increasing the triaxiality value, the material maximum traction T0 becomes bigger but the material critical separation δ0 and cohesive energy Γ0 become smaller. Details about this investigation can be consulted in references [18-20]. When the triaxiality dependent behaviour is implemented into the CZM, the triaxiality value can only be obtained from the surrounding continuum element and has to be transferred to the cohesive element. 3. Extended CZM for fatigue fracture 3.1. Overview The ordinary TSLs just describe the material fracture failure under monotonic loading condition. For material fatigue fracture properties, other approaches need to be introduced. By reviewing some ideas from pioneers, a tentative method of Roe and Siegmund [13] is chosen as starting point. Considering the theory of continuum damage mechanics, a damage variable and a corresponding damage evolution law are introduced in the CZM following ideas of Scheider [8]. This cyclic CZM is used for fatigue fracture analysis. In respect to the fatigue fracture process, the important research topics focus on fatigue crack initiation life and fatigue crack growth rates analysis. In experimental investigation, fatigue crack initiation is usually tested using uncracked smooth specimen and fatigue crack growth is measured using pre-cracked specimen. The triaxiality conditions for these two standard specimens are totally different. When the CZM is applied for simulation of these two fatigue phenomena, it is necessary to take the triaxiality influence into account in the damage process. So, a triaxiality dependent cyclic CZM is now proposed. The model should be implemented to reproduce fatigue experimental phenomena which contain fatigue crack initiation and fatigue crack growth, just using a unique set of parameters. For simplicity, in this paper just mode-I fracture is considered. This means in the CZM just normal separation contributes to the damage. 3.2. Fatigue damage process With the damage variable D, the cohesive strength and normal stiffness of the cohesive element will degrade (Equation (3) and Equation (4)). ( ) ( ) 0 0 1 ⎡ ⎤ = − ⎣ ⎦ %N N H T T D (3) ( ) 0 1 2 1 δ = − = % % N N N T k k D (4)
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