13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- crack growth is very similar. One possible reason for this diversity is from the influence of the model dimension. In experiment, the specimen is a three dimensional model, but in simulation a two dimensional model is used. The calculation about the energy integral ΔJ is bigger for two dimensional problems than for three dimensional problems. The other possible reason is from the new CZM. This numerical model may express the real cyclic process inaccurately. 5. Conclusions CZM is a very robust numerical tool for material fracture analysis. It is simple enough for theoretical understanding and practical application. For the material monotonic fracture, the implementation of the CZM is particularly mature. But for fatigue fracture analysis, the application is just in developing. In this paper, according to the pioneers’ idea [13], a triaxiality dependent cyclic CZM is proposed. This model can be applied for various triaxiality conditions, and only one set of unique material damage parameters is used. In the very low cycle fatigue regime, using the triaxiality dependent cyclic CZM in fatigue crack initiation and fatigue crack growth simulation, the reasonable comparison results between experiment and simulation can be obtained. However, this new CZM is still in a testing process. Many improvements and developments need to be done in the future. More materials should be chosen in the simulation to validate the new CZM. The cyclic process for the CZM needs more discussions, especially in unloading and compression period. The format of the damage evolution law maybe modified. The triaxiality dependent behavior in the whole cyclic process needs much more investigations. Acknowledgements Author would like to thank Dr. Ingo Scheider from Helmholtz-Zentrum Geesthacht, Institut für Werkstoffforschung, for providing many helpful suggestions in cohesive zone model application. References [1] D.S. Dugdale, Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids, 8 (1960) 100-104. [2] G.I. Barenblatt, The mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics, 7 (1962) 55-129. [3] A. Hillerborg, M. Modéer, P.E. Petersson, Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research, 6 (1976) 773-782. [4] A. Needleman, A continuum model for void nucleation by inclusion debonding. Journal of Applied Mechanics, 54 (1987) 525-531. [5] A. Needleman, An analysis of decohesion along an imperfect interface. International Journal of Fracture, 42 (1990) 21-40. [6] V. Tvergaard, J.W. Hutchinson, The relation between crack growth resistance and fracture process parameters in elastic-plastic solids. Journal of the Mechanics and Physics of Solids, 40 (1992) 1377-1397. [7] H. Yuan, G.Y. Lin, A. Cornec, Verification of a cohesive zone model for ductile fracture. Journal of Engineering Materials and Technology, 118 (1996) 192-200. [8] A. Cornec, I. Scheider, K.H. Schwalbe, On the practical application of the cohesive model. Engineering Fracture Mechanics, 70 (2003) 1963-1987. [9] I. Scheider, W. Brocks, Simulation of cup-cone fracture using the cohesive zone model. Engineering Fracture Mechanics, 70 (2003) 1943-1961.
RkJQdWJsaXNoZXIy MjM0NDE=