13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- Figure 13. Reaction force versus loading-pin displacement for CT specimen The crack opening behavior due to displacement of the top and bottom pins is observed in Fig.12. Before crack propagation begins to occur, the cohesive zone begins to form, as shown in Fig.12(a) and (b). Once a critical displacement is reached, crack propagation is seen in Fig.12(c) and (d). It shows the expected linear relationship between loading-pin displacement and reaction force in Fig.13. More complex fracture mechanics problems can be analyzed through combining the cohesive law derived from MD simulations and finite element method. 6. Conclusion (1) Molecular dynamics simulations under a special configuration have been performed to study the mechanism of α-Ti under tensile loading condition, and the EAM/alloy potential used in LAMMPS is certified by melting point verification. (2) Crack tip successively emitted dislocations along crystal orientation [2110]and[2110]respectively for loading direction[0110]. The phenomenon continued in the whole process of loading. With the emission of dislocation, crack tip moved forward slowly and the crack blunting phenomenon is obvious at crack tip. In the process, we also find that HCP→BCC phase transformation near the crack tip for α-Ti via CNA. It is obvious that twin occurred for α-Ti under loading direction[0001]. Dislocation and twin are two kinds of principal mechanisms for α-Ti. The deformation mechanisms of α-Ti are included in the T-S curve derived from MD simulations. (3) The traction-separation relation of α-Ti with crack is characterized via MD simulations. The parameterized cohesive traction-separation relation under tensile loading condition at room temperature to simulate the crack propagation behavior of CT specimen composed of α-Ti in a FEA. The curve obtained through our simulation is agreement with predictions from linear elastic fracture mechanics, showing the expected linear relationship between loading-pin displacement and reaction force. It shows our methodology is feasible. Our study may provide several novel ideas for simulating complex fracture problems based cohesive laws used in FEA. Acknowledgements This work was supported by the National Defense Basic Scientific Research Program of China through the contract of B1520132013 and the Fundamental Research Funds for the Central Universities through the contract of 2010SCU21014 and NSAF through the contract of 10776023. References [1] J.D.Matthew, Jr. Titanium-A Technical Guide. ASM INTERNATIONALTM Metal Park, 1988. [2] C Leyens, M Peters. Titanium and Titanium Alloys. WILEY-VCH GmbH & Co. KGaA. Weinheim, 2003. [3] S J Plimpton. Fast parallel algorithms for short-range molecular dynamics. J Comput Phys 1995;117:1–19. <http://lammps.sandia.gov/>. [4] J Li. AtomEye: an efficient atomistic configuration viewer. Modell Simul Mater Sci Eng 11 (2003) 173.
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