13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- load, the results obtained by Sadananda and Shahinian and corresponding to the “steady” state regime are included in figure 5 to avoid the transient regime. Their results are also close to ours and to those of Gustafsson et al. [10], reinforcing our conclusion on the moderate effect of microstructure in this regime of crack propagation. The slope of the (da/dt)cr curves drawn in figure 5 is between 2 and 4. The temperature dependence is indicated in figure 6 where an apparent activation energy of the order of 300 KJ/mole is observed from our tests and Gustafsson et al. experiments [10]. This energy is close to the activation energy for oxygen grain boundary diffusion (274 KJ/mole) in nickel, as noted earlier. It is clear that the CCG rate behavior is also affected by oxidation and can be described as successive crack jumps over a critical distance (≈ Rvp) with lasting times of the order of the transition time ti defined earlier by Eq. 7. This simple approach leads to a predicted slope of the (da/dt)cr – K curves of 2(2n 2 – n-1) / (n-1), i.e. to a slope close to 4n for sufficiently large values of the exponent n. This predicted slope is much higher than the slope indicated in figure 6 which was found to be between 2 and 4. However this simplified approach is valid only when it can be assumed that the critical creep strain, εc (Eq. 7) is constant. This assumption is not valid when the tests are carried out under air environment. Results of CCG rate measurements under vacuum [27] showed that the slope of the (da/dt)cr – K curves was much higher (> 20) compared to those determined in air environment. These large values of the slope under vacuum are thus in better agreement with the predicted value of ~ 4n. This indicates that it is necessary to develop more sophisticated models when the material is tested under air environment. These models must include a variation of the critical creep strain ahead of the crack tip with oxygen grain boundary diffusion given by Eq. 4. Figure 5. Creep crack growth rate versus ΔK curves corresponding to regime B (see text). The results by Gustafsson et al. (diamonds) [10] and Pédron and Pineau (triangles) [5, 14] obtained under similar conditions and those reported by Sadananda and Shahinian (circles) [15] using fatigue precracked specimens are shown.
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