13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- In Fig. 4b) for R = -1, an ODA is visible in the region directly above the inclusion. Such structures could be observed in several specimens for R = -1, but were never found in samples fatigued at higher load ratios. Examples are given in Fig. 4d) and f). Some uncertainty remains in this observation because ODAs are generally very difficult to detect in this steel. In [19], microstructural investigations were performed via focused ion beam technique (FIB) and SEM of cross-sections perpendicular to the fatigue crack surface close to the crack initiating inclusion. The results showed the presence of a nanocrystalline area around the inclusion only for R = -1. Based on this observation, a possible reason for the R-dependency of the highest observed number of cycles to failure is given in [19]. Furthermore, there is a change of the fracture surface profile with increasing load ratio. At higher load ratios, the fish-eyes become more distinguished and a step-like transition develops between the fish-eye and the residual fracture which indicates the occurrence of cyclic creep and plastic deformation. As shown by displacement measurements of the specimens during the fatigue tests in [19], increasing load ratio leads to higher total mean strains, i.e. plateau values of 0.4% and 4.5% for R = 0.1 and R = 0.5, respectively. At R = 0.7, steady cyclic creep occurs during the entire test. Additional fatigue tests at high stress amplitudes were performed showing weak cyclic softening of this steel in accordance with [26] for a similar kind of 12% Cr steel. The dominance of cyclic creep on deformation and failure at R = 0.7 corresponds to the fracture surface depicted in Fig. 4g) and h) showing a “tensile test like” cup-cone fracture without any distinct fatigue features. However, it should be noted that even at this high load ratio fatigue lives clearly above 107 have been reached. For the fish-eye fractures at other load ratios, inclusion sizes and compositions as well as the area of the fish-eyes were determined by SEM and EDX. For all fractures, the crack initiated at oxide inclusions in the middle of the fish-eye with compositions either CaO·Al2O3 or MgO·Al2O3. However, the crucial factor for fatigue life is the diameter of crack inducing inclusions, following a normal distribution and ranging from 16 µm up to 45 µm in this test series. To consider the inclusion size dependency on fatigue life, the √area-concept of Murakami [9] was applied. The √area-parameter represents the inclusion size perpendicular to the applied maximum stress, which is treated equivalent to a fatigue crack of equal size. By means of fracture mechanics, this leads to Eq. (1) for the fatigue strength: (1) HV is the hardness of the material and α a material constant describing the influence of load ratio. C is 1.56 for internal defects and 1.43 for subsurface cracks, respectively. At first, the material constant α for the R-dependency of the fatigue limit needs to be determined from the slope of the fatigue strength vs. (1-R)/2 curve. In the present case, α is 0.546. In the next step, σa/σW can be plotted against the number of cycles to failure in a linear graph (Fig. 5). In this plot, the huge scatter of the S-N curves could be reduced to less than one order of magnitude, so the fatigue data of load ratios from -1 up to 0.5 can be described in a single curve in a fatigue life range of more than four orders of magnitude. The Murakami approach is convenient for describing the curve both in the HCF and the VHCF-regime and independent of load ratio. Thus, the α-parameter of 0.546 seems to be accurate for describing the dependency of fatigue strength on load ratio of the present material. An evaluation of the R = 0.7 data and a deeper analysis of the obtained α value is given in [19].
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