PSI - Issue 5

U. Zerbst et al. / Procedia Structural Integrity 5 (2017) 745–752 U. Zerbst et al./ Structural Integrity Procedia 00 (2017) 000 – 000

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At this background, the fatigue limit is defined as the stress level below which all these cracks are arrested. An example is provided in Fig. 1(b). At higher cyclic stresses one or more cracks will propagate, however, now at the short crack propagation stage which means that (i) the linear elastic  K concept is not applicable because the crack size is in the order of the plastic zone size and (ii) initially there will be no crack arrest phenomenon. This will gradually develop during this second crack propagation stage. Note that the build-up of the plasticity-, roughness- and oxid-induced crack closure effects can also cause crack arrest and, if the cracks are initiated at notches the decrease of the notch stress away from the notch root will also contribute to this. When the crack closure effects are fully developed, they become crack size independent and the cracks have reached the long crack propagation stage. Also at this stage, crack arrest may occur below a certain cyclic stress level now represented by the long crack fatigue crack propagation threshold  K th,LC .

Fig. 1. (a) Stages of fatigue crack propagation; (b) Crack arrested within a grain after c. 10 8 loading cycles, according to Beretta et al. (2009). Fig. 2 shows the crack propagation stages in terms of a Kitagawa-Takahashi diagram (Kitagawa & Takahashi, 1976) but modified by Miller (1993) for the growth of microstructurally short cracks. Note that the curve defines crack arrest. As can be seen, the endurance limit is given by two criteria, a cyclic stress and a crack size d. The existence of this crack size does not only provide a justification for the application of fracture mechanics to fatigue life and strength, it also gives, schematically, the size of the initial crack, namely d.

Fig. 2: Kitagawa-Takahashi diagram (Kitagawa & Takahashi, 1976) as modified by Miller (1993).

Short crack propagation Most frequently the fatigue life is largely controlled by the propagation of short cracks. Although they overlap with respect to their size, it is common to distinguish between mechanically and physically short cracks. The size of a mechanically short crack refers to the order of the size of the plastic zone surrounding it. The consequence is, that the linear elastic  K concept cannot be used for characterizing the crack driving force of mechanically short cracks. Instead, parameters such as the cyclic J integral have to be used. These can be determined by numerical analyses or analytically, extending approaches such as the EPRI method or the Reference stress method to cyclic loading. For a detailed discussion see Tchoffo Ngoula et al. (2017). Here, an approach of the second group shall be briefly introduced as it was used by Zerbst et al. (2011). The cyclic J integral is determined by an equation