PSI - Issue 38

Hendrik Bissing et al. / Procedia Structural Integrity 38 (2022) 372–381 Hendrik Bissing, Markus Knobloch, Marion Rauch / Structural Integrity Procedia 00 (2021) 000 – 000

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Fig. 3 illustrates the influence of the hardening coefficient K’ (a) , the hardening exponent n’ (b), the two slope values of the strain-life curve b (c) and c (d), the Y oung’s modulus E (e), and the notch factor K t (f). All curves show inflection points that do not occur in theory, because the mathematical compatibility relations, Seeger (1996), of K’ and n’ with the other values b, c, σ f ’ and ε f ’ are neglected in this calculation in order to consider only one parameter while keeping the others constant. Large stress amplitudes affect the SN i curves for the parameter K’, n’ and c while the curves for the parameter b are mainly influenced by small stress amplitudes. Since the fatigue strength exponent b represents elastic material properties and the ductility exponent c represents plastic material properties, their effects in the corresponding stress regimes is expectable. The tensile strength f u does not affect the SN i curves, because its influence is considered within the calculation of the strain-life curve by using the compatibility equations, which are neglected in this study. However, the following observations can be made from the curves in Fig. 3: • The effect of the cyclic hardening coefficient K’ is considerably small and at first relevant for stress ranges higher than approximately 200 N/mm². • The effect of the cyclic hardening exponen t n’ is relevant for large stress ranges from approximately 150 N/mm², leading to differences in the applicable number of cycles of approximately one order of magnitude. • The regime between 150 N/mm² and 200 N/mm² of stress range, corresponding to approximately 10 5 number of cycles appears to represent the transition life N T where elastic and plastic strain-life curves intersect. • The fatigue strength exponent b has bigger influence than the ductility exponent c. Exponent b is significant for almost all stress amplitudes of real-world application, although the impact for small stress amplitudes is substantially bigger. • The Young’s modulus has almost no impact on the SN i curves. The crack initiation life N i is mainly governed by local plasticity and hysteresis loops. Hence, the Young’s modulus is of minor importance for the SN i curves. • The main influence for crack initiation life results from the notch factor K t . The shift of the curves for the quantile values shows a difference in applicable number of cycles of three orders of magnitude for all stress amplitudes. For the CPM, different application cases of the crack shapes exist that meet the requirements of butt-welded specimens, using rectangular cross sections, Fig. 4. In this subsection only the application case no. 3, Fig. 4c, is presented. The dimensions of all calculated specimens are bounded to 40 mm width and 10 mm thickness, which is essentially needed for the total crack propagation evaluation. The initial crack depth a 0 and the initial crack length c 0 are correlated in this investigation with c 0 = 10∙a 0 . This study uses the Paris law (Paris et al., 1963) as the crack propagation approach. The constant parameters are set to the mean of their probability distributions and the load is applied as tensional stress amplitude with R equal to 0 to follow the same procedure as for the SLA.

a) Appl. case 1

b) Appl. case 2

c) Appl. case 3

d) Appl. case 4

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Fig. 4. Possible application cases of the crack propagation method for butt-welded test specimens

Fig. 5 shows the effects of three selected parameters, parameter C of the Paris law (a), the lower boundary value of the Paris law ΔK 0 , and the initial crack depth a 0 (b). The plots show SN p curves for the crack propagation life