PSI - Issue 19

Jean-Gabriel SEZGIN et al. / Procedia Structural Integrity 19 (2019) 249–258 Jean-Gabriel Sezgin et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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Considering the values of the FCG acceleration ratio in the [10 -3 Hz; 10 Hz] frequency range, it was assumed that N air /N H >> 1, which led to the expression (6). The relevance of this assumption was then retrospectively verified. ln ( ) = − ln + ln 0 (6) As observed on Figure 7, the IG fraction depended on the test frequency. By assuming that an IG fraction of zero translated the non-occurrence of the time-dependent mechanism, the value of 0 was deduced from the results of the fitting in Figure 7 and this value was found to be equal to 134 Hz. In the literature, some models exist to take into account such a combined mechanism: the superposition model (Chen and Wei 1998; Landes and Wei 1969; Wei 2002; Wei and Gao 1983) and the process competition model (Amaro et al. 2014; Austen and Mcintyre 2014). In the present study, the mechanisms were combined in regard with the fraction of IG fraction noted hereafter α . The superposition model relies on a linear combination of expressions (1) and (3) translating the time dependent and cycle dependent mechanisms respectively. As a result, the FCG rate and FCG acceleration ratio are expressed by (7) and (8) (with the nomenclature introduced in Figure 8). ( ) + = (1 − ) ( ) + ( ) = ( ) + (1 − ) ( ) + ( ) (7) ( ) + = {(1 − ) ( ) + ( ) }/ ( ) = (1 − ) ( ) + ( ) (8) The process competition model consists in combining the time and cycle dependent mechanisms, (2) and (4) respectively, by considering a pondered harmonic combination (9). ( ) − 1 + = (1− ) ( ) + ( ) (9)

Figure 8 – Decomposition of the FCG acceleration ratio into two mechanisms in terms showed on different diagrams. The S - N diagram (a) shows the different regimes. The d a /d N – Δ K diagram (b), obtained by rotation of (a), shows the mechanisms. Effect of test frequency on the H-enhanced FCG acceleration (c) shows the combination of the mechanisms of cycle- and time-dependence properties. Figure 9-a) compares the results obtained by the superposition and the process competition models to the experimental values. In the graph, the elementary cycle- and time-dependent mechanisms were respectively represented by a dashed line with diamond shaped markers and dotted line with cross shaped markers. The results of the superposition and process competition models were respectively marked with green triangles and black squares linked by solid lines and the experimental results with blue circles. The graph showed that neither the superposition model nor the process competition model firmly supported the decomposition of the FCG acceleration ratio into two elementary mechanisms. The first one led to an unbounded behaviour, whereas the later one led to the FCG acceleration ratio almost equal to the cycle-dependent mechanism (the HISCG mechanism). These facts suggest that the cycle- and time-dependent crack growths do not occur individually but interact with each other since the present H-assisted FCG acceleration was accompanied by QC and IG. Taking into account these situations, the third model was then proposed to predict more accurately the experimental results. Considering the elementary mechanisms expressed in (2) and (4), the proposed model, hereafter called interaction model, is expressed in (10). ( ) + = ( ) 1 − ( ) (10)