PSI - Issue 13

Stanislav Seitl et al. / Procedia Structural Integrity 13 (2018) 1494–1501 Seitl et al./ Structural Integrity Procedia 00 (2018) 000–000

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Fig. 3. Geometries and dimension of the compact tension (CT) specimen and specimen used for S–N measurement. 3.2. Probabilistic models S-N curve – ProFatigue software The assessment of the S-N field can be performed in a probabilistic way using a Weibull model for minima as proposed by Castillo & Canteli (2001,2009): � � � � � ��� ����� � ���� �������� ������ � �� ; ���� � ������ � �� � (3) where B is a threshold value at the total lifetime, C is the endurance or fatigue limit for , and re the location, scale and shape Weibull parameters, respectively. The percentiles curves are hyperbolas sharing the asymptotes log N = B and log Δ = C , whereas the zero percentile curve represents the minimum possible number of cycles required to achieve failure for different values of log Δ . With the aim of facilitating the practical assessment of S-N field for the fatigue data handled in this work, the freeware software ProFatigue was used Canteli et al. (2014), which can be free downloaded from the website: http://www.iemesgroup.com/dowload. Crack propagation rate curve - ProPagation software Traditionally Eq (2) is used, as already mentioned, for modeling the crack propagation rate. A definition of the sigmoidal crack propagation rate curve as a cumulative distribution function of the Gumbel family for maxima or minima by normalizing the ∆K axis is proposed by Castillo et al. (2014) : ��� � ∗ ���� � � ∗ � ��� � �∗ � ���� � � ∗ � � ��� ����� � ����� � � � � ∗ ∗ � �� , ( 4) which depends on four material parameters  ,  ,  K th and  K up. In order to facilitate the practical assessment of fatigue crack propagation properties data handled in this work, the freeware software ProPagation was used, which can be free downloaded from the website: http://www.iemesgroup.com/dowload. 4. Results and discussion Results of experimental program performed at stress ratio R =0.1 for S355 J0 steel grade for two rolling directions, S355 J0 A and S355 J0 B, are shown in Fig. 4, along with the comparison between the fatigue results for P f =50% probability of failure using both Basquin and Weibull models. The stress  denotes the maximal stress value applied to each specimen. The values for P f = 50% provide an overview of the basic behavior of the S355 J0 steel grade. The results from ProFatigue are compared with those from the Basquin model, whereby Table 2 presents the parameters for the different approaches by applying the maximum likelihood method. In all studied cases, a similar description of the S-N curves was observed in the investigated fatigue regions for both bilinear Basquin’s and ProFatigue models, but not beyond this region where the discrepancies are notorious, due to the lack of failures in the lifetime range between 10 5 and 10 7 cycles for the S355 J0 A steel (Fig. 3(a)), and for N>10 7 cycles in the case of S355 J0 B steel (Fig. 4 b)).