13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- (7) where β is a constant. In Eq. 7, εc may be strongly dependent on oxidation as underlined by Diboine and Pineau [25] (see their figure 9). The parameter C can be evaluated from the tests performed by Pédron and Pineau [5, 14] at 650°C. These tests suggest that ti ≈ 10 s for K = 25 MPa.m1/2 leading to C ≈ 9.109 (t in s, K in MPa.m1/2). Moreover the critical distance Xc, must be lower than the calculated creep zone size, Rvp given by [24]: (8) with G = 10-8 for Rvp (m), t (h) and K (MPa m1/2) [25]. The parameter G increases with temperature. This leads to Rvp ≈ 10 µm at 650°C, which is close to the grain size of our material. These calculations indicate that, within a first approximation, ti could be calculated from Eq. 7 with Xc equal approximately to the grain size or from Eq. 8 written as Eq. 9: (9) The transition time ti in Eq. 1 can thus be evaluated with two expressions (Eqs 7 and 9). However it appears to be difficult to establish a definite model for the FCGR behavior in regime A in the absence of more detailed measurements of ti and variations of εc with time. The third term in Eq. 1 can be determined using the FCGR behavior in regime B which is purely time dependent (Figure 3). The creep crack growth (CCG) regime (tm >> ti) has been investigated by a number of authors (see e.g. [5, 15, 25]). However, the test procedure used by these authors is completely different from ours. They start from a fatigue precrack and then maintain the load constant. This procedure does not allow investigating the initiation and the propagation of a crack in a continuously creep-oxidation damaged material. Our test procedure allows us avoiding the tail of the curves observed in most CCG rate measurements reported in the literature. An attempt was made to model these transient curves observed in stainless steel [26]. These tails lead to an apparent threshold in K which is load and time dependent, as clearly shown elsewhere [25]. In our tests the CCG rate component is simply obtained by noting that for long tm the third term in Eq. 1 is much larger than the two other ones. This means that the CCG rate, (da/dt)cr at a given temperature, can simply be obtained using Eq. 1 with long hold times only (3600 s at 550 °C, 1200 s at 600 °C and 650 °C). The results are shown in figure 5 where test results by Gustafsson et al. [10] obtained with long hold times (2160 s) have also been included. A good agreement between both sets of results is observed which suggests that crack propagation in regime B is not too much dependent on microstructural details. The results obtained by Sadananda and Shahinian [15] are also included in figure 5 but, as these authors have investigated the propagation of a fatigue precrack under constant
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