13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- Figure 5. Modified S-N curve according to the √area-concept proposed by Murakami. 3.3 Crack growth threshold evaluation Another appropriate data evaluation method is shown in [27, 28]. In the present work, this approach proposed by Döker is applied to small fatigue cracks assuming the fracture inducing inclusion sizes being identical with the initial crack length. Based on the linear elastic fracture mechanics, the threshold stress intensity factor ΔKth can be plotted vs. the load ratio R. As mentioned in [27], only positive R can be used and given the fact that no fracture inducing inclusions were visible for fractured specimen at R = 0.7 (see Fig. 4g) and h)), this approach is only applied for fatigue data of R = 0.1 and 0.5. Initially, ΔKth needs to be calculated. Assuming a circle shaped volume crack with the diameter of the crack initiating inclusion, Eq. (1) and Eq. (2) can be used as good approximations, where aincl is the mean size of all measured inclusions and ΔσD and σD,max are the corresponding fatigue strength values. (2) (3) According to [27], a ΔKth–R curve can be derived from the above values (continuous line in Fig. 6). The curve is separated into multiple sections described by different equations (see Fig. 6). Here, the two curves nearly overlap at negative R. For R < 0, the green dotted line is valid and the threshold value asymptotically approaches ΔK0. The red dotted line represents a downward oriented parabola which intersects with the positive R-axis at R = -1 and with the ΔKth –axis at ΔKth = Kmax,0. The different shape of the curves compared with [27] probably is due to the distinctly smaller crack length considered in the present study. Additionally, Fig. 6 shows the ΔK values calculated from the obtained fatigue test data using the stress amplitudes and the crack inducing inclusion sizes (blue diamonds). Note that for this evaluation only fractures close to the observed run-outs (see Fig. 3) were taken into account. Referring to the work of Grad et al. [29], ΔK was also calculated using the sizes of the ODAs found at R = -1 (green triangles).
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