PSI - Issue 51

Michael Horvath et al. / Procedia Structural Integrity 51 (2023) 95–101 M. Horvath et al./ Structural Integrity Procedia 00 (2022) 000–000

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3.3. Application of the methodology to arbitrarily shaped casting imperfections After initial set-up and proof of the TCD method functionality, the linear-elastic methodology is extended to assess the fatigue strength of arbitrarily shaped spatial imperfections. Based on the planar projections depicted on the derived radiographs, the fatigue strength factor K f is evaluated for each imperfection according to a preceding study (Horvath et al. 2022). The relation between K f and the critical distance L M ( N f ) follows an exponential function, given by Equation (4), where the parameters a , b , c and d depend on the defect geometry itself. � �� � ����������� � �� � ������������ � �� � �� (4) Utilizing the proposed exponential function, numerical efficiency of the assessment methodology is significantly increased, as individual simulation runs within the iterative main loop are not necessary anymore. The fatigue assessment results of defect-afflicted cast steel specimens are depicted in Fig. 4(a) for load ratio R = -1 and in Fig. 4(b) for R = 0.

Fig. 4. Fatigue assessment results of defect-afflicted cast steel specimens: (a) R = -1; (b) R = 0.

For each specimen, two radiographs are assessed by the numerical TCD-framework. Thus, two fatigue life cycle numbers are evaluated for each sample. The lower cycle number if denoted as conservative result, whereat the higher cycle number is referenced as non-conservative fatigue datapoint, compare to Fig. 4. The majority of predicted fatigue life values is above the S-N curve for a probability of survival of P S = 97.5%, which serves as design limit curve in accordance to the common guideline FKM (Forschungskuratorium Maschinenbau) (Rennert et al. 2012). Thus, the applied TCD methodology depicts a well-applicable engineering-feasible tool to assess the fatigue behaviour of imperfective cast steel components. 4. Development of a strain energy density-based fatigue assessment methodology The basic aspect of the strain energy density concept states that fatigue life results of arbitrary geometrical features merge into a uniform scatter band (Schuscha et al. 2020). This implies that plain and notched specimens should lead to identical SED values at the same number of cycles to failure. Following this consideration and the basic idea of the implemented TCD-framework, a relationship between the control radius R c and the number of cycles to failure N f is proposed. Based on the analytical calculation of the elastic SED (Lazzarin and Berto 2005), a calibration procedure of the relationship of control radius to load cycle number R c ( N f ) is carried out, utilizing the generalized S-N curves of plain and notched specimens with a notch opening angle of 2  = 45°. The iterative validation procedure is