13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- As for 2 c IK x σ π = , singularity exists at 0 x = . In order to obtain vacancy concentration at crack tip, the IK is given firstly, and the effective scope of the local stress effect is seted as 1.5a, where 0.02mm a= is half the length of the crack. Then the value at 1.5 x a = is calculated, as seen in Fig.4, the value is compared to the corresponding value in Fig.3, it can be found that the difference between the two results is no more than 1%. So the value at 1.5 x a = is selected as the initial value for the calculation. Then the value at crack tip can be calculated through multiple numerical iteration. The results are plotted in Fig.4. According to the results, it can be observed that the range of values of ( 0) xρ ≈ is 0.75: 1.2, the range of δ is 0.65: 1.1( ( ) 0 0 x ρ ρ ≈ − ). Based on the chemical formula of non-stoichiometric GDC ( 4 3 3 2 0.8 0.2 1.9 Ce Ce Gd O x x δ + + + − − − ), it can be concluded that the value of δat crack tip is 0.4 when the local stress effect is considered. The corresponding chemical formula of GDC is 3+ 3+ 20.8 0.2 1.5 Ce Gd O . After the multi-scale simulations is completed, the fracture toughness is 0.5142MPa m. Compared to the fracture toughness of Ce0.8Gd0.2O1.9 (20GDC) ( 0.9493MPa m ), it is reduced by 45.83%. So, in the process of production and application of the material, the local stress effect should be specially focused. 5. Conclusion In the work, the coupling theory of the electrolyte in the working environment is presented. In order to study the local stress effect, the electrolyte membrane with crack is selected, and the mechanical behavior of the membrane is studied by using a multi-scale method. According to the simulated results, it can be found that when micro crack exists in the electrolyte membrane, the stress at crack tip is much bigger, and the concentration of oxygen vacancy at crack tip is severely affected. Based on the simulated results, the fracture toughness of the model is decreased to 0.5142MPa m when the local stress effect is considered in the working condition, it is reduced by 45.83% compared to the uncoupled value (0.9493MPa m). So, in the process of production and application of the material, the local stress effect should be specially focused. Acknowledgements This work is supported by National Natural Science Foundation of China (10972066), the Foundation of Excellent Youth of Heilongjiang Province, and the Research Fund for the Doctoral Program of Higher Education of China (20122302110020). References [1] P. Datta, P. Majewski, F. Aldinger, Study of gadolinia-doped ceria solid electrolyte surface by XPS. Mater Charact, 60 (2009) 138-143. [2] J Roa, E Gilioli, F Bissoli, Study of the mechanical properties of CeO2 layers with the
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