PSI - Issue 2_B

Chretien Gaëlle et al. / Procedia Structural Integrity 2 (2016) 950–957

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Gaëlle Chretien et al. / Structural Integrity Procedia 00 (2016) 000–000

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Fig. 8. Evolution of crack opening with crack length at: (a) 20°C; (b) 400°C.

4. Non-propagation diagram 4.1. Kitagawa-Takahashi diagram

The Kitagawa and Takahashi (1976) diagram represents the evolution of propagation threshold in function of the crack length a. It is today the most used simple criteria to visualize the condition of non-propagation or the condition for self-arrest of cracks. It is built with the two main thresholds in fatigue: the classical fatigue limit and, the more recently introduced, the threshold stress intensity range. Black lines on figures 9 a and b stand for this criterion. The relation between these two thresholds is relatively simple: 0 0 LC th a. . . Y K     (2) With Y a geometry factor defined for CT specimen and a 0 the transition crack size defined according to expression 3. The a 0 value is a constant for a material in given conditions. 2 0 th LC 0 � . Y K .� 1 a     (3) As commonly admitted in literature, the effective SIF at threshold is similar for short and long cracks. Thus it is easy to consider that the nominal threshold for the different crack lengths can be determined thanks to equation 4. a. . Y � K � a � K �.� R 1 � � a � � K � a � K �.� R 1 � � a � K eff th op C S, nom th eff th op C S, nom th              (4) The evolution of the stress range at threshold Δσ th with the crack length of the residual crack during machinings and the crack length of the propagated short cracks is plotted at 20°C and 400°C on figures 10 a and b respectively. Data appear to be near the nominal threshold line when the crack becomes long. For short crack, a bend is observed at the transition between the two main thresholds. 4.2. El Haddad criterion Several other experimental studies have been undertaken to model this domain. El Haddad et al. (1979) were the first to propose a model that take into account the curvature by adding a term a 0 to the crack length. Thus the expression of the SIF range at threshold becomes: 0 th th � a a .� . . Y � a � K      (5)