PSI - Issue 7

F. Fomin et al. / Procedia Structural Integrity 7 (2017) 415–422 Fedor Fomin and Nikolai Kashaev/ Structural Integrity Procedia 00 (2017) 000–000

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(2002). Hereinafter, the term ODA is used for this region of the fish-eye. According to SEM observations, ODAs have fracture surfaces that are quite different from those of the white smooth area. Very rough fibrous morphology composed of a large number of facets was observed within ODA, as shown in Fig. 2(d). No ODAs were observed in our research at stresses higher than 700 MPa, i.e., when the fatigue life is shorter than approximately 100,000 cycles. This result leads us to conclude that, apparently, ODA formation is caused by early stage short fatigue crack growth. In the present study, it was found that the theoretical model based on the plastic zone at the crack tip reported by Zhao et al. (2011) was in accordance with the quantitative fractographical analysis. In the model, we assume that the formation of ODA is completed when the plastic zone size at the crack tip is equal to the characteristic size of the material, which in our case is equal to the average width of the martensitic plates d = 0.7 ± 0.2 µm (Fomin et al., 2017). For mode I crack under the plain strain conditions, the reversed plastic zone size at the crack tip R p is given by Y  is the yield stress (Anderson, 2005). SIF range for the internal penny-shaped crack can be estimated according to Anderson (2005) as ∆� = (2/�)∆�√�� , where ∆σ is the stress range and a is the crack length . Using Equation (1), the radius of the internal crack for which the plastic zone size is equal to the average grain size can be found. Fig. 3(a) shows the relationship between the ODA radius obtained from fractographical analysis and the applied maximum stress. It can be seen that the ODA radius tends to decrease as the maximum stress increases. This result is in good agreement with the theoretical model represented by two curves corresponding to the boundaries of grain size deviations (0.5 and 0.9 µm). The described model may also explain the much rougher morphology of the ODA area. When the crack is located in the ODA zone, crack propagation step per cycle is smaller than the martensitic lath, so that the crack is searching for the most favourable path and is significantly deflected. As a result, the fracture surface comprises many facets and is characterized by a relatively rough topography (Fig. 2(d)). In the smooth area outside the ODA, crack propagation step per cycle is larger than the martensitic plate, the crack is less deviated, and the fracture surface is smoother (Fig. 2(c)). 2 1 , 6 2  p Y K    R       (1) where ∆K is the stress intensity factor (SIF) range and

Fig. 3. (a) Relationship between the ODA size and applied stress; (b) SIF range at the periphery of ODA as a function of maximum stress. The stress intensity factor range at the edge of the rough area ∆ K ODA can be calculated using the ODA size obtained from fractographical analysis. As shown in Fig. 2(b), the ∆ K ODA values range from 6.9 to 9.2 MPa√m and increase slightly with increasing peak cyclic stress. For comparison, SIF threshold value for long cracks ∆ K th,LC for fine lamellar Ti-6Al-4V found by Wagner and Lütjering (1987) is also shown in Fig. 3(b). It is clear that ∆ K values at the periphery of the ODA are quite close to the ∆ K th,LC values albeit slightly higher. 5. Analytical model It was revealed by fractographical analysis that all cracks observed in the current study were nucleated at the pores, which can be regarded as notches within the FZ. It is well-known that the size of the notch strongly affects the approach applicable for the fatigue life assessment. It was found from the fracture surface observations that the pore diameter at