PSI - Issue 13

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

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Table 2. Parameters of the Wöhler curves using the Basquin equation and Weibull distribution for S355 J0 steel grades. Basquin equation Weibull model Steel grade Rolling direction A B R 2    B C S 355 J0 A -70.83 1239.1 0.883 0.02 0.04 1.05 8.93 6.23 B -5.01 615.12 0.2183 0.04 0.06 1.02 8.46 6.28 According to the obtained results, the Weibull model as proposed in Castillo et al. (2001, 2009), Castillo et al (2014), provides more reliable results than the simple linear S–N approach with additionally probabilistic definition of the S-N field so that the former one, is recommended for practical applications in civil engineering structural analysis under fatigue, see Krejsa et al (2016) Krejsa et al (2017), Kala & Omishore (2016), Kala (2017).

a) b) Figure 4. Experimental results of the S-N field for and description of fatigue strength using Basquin and Weibull models for failure probabilities 50% Before the crack propagation rate measurement are evaluated and discussed, it should be noted that the stress intensity factor ranges in Eq. (2) for cracks in CT specimens can be computed according to ASTM E647 Standard. �� � � � √ � � ����� ����� � � ������ � ����� � ������ � � ������ � � ���� � � , (5) where  = a / W , a is the crack length, W is the specimen width, B is the specimen thickness and  F is the applied load range in the study case R =0.1. The crack length increment is calculated as an average value of two crack length measurements performed on both sides of the CT specimen during the test. In this study, the K -decreasing method according to the ASTM E647 was used to obtain the values near the threshold values. From this point, the constant load value was used for the estimation of the crack growth rate of the tested specimens in the Paris’ region. Figures 5a),b) and 6a),b) show the results of the experimental program of crack propagation rate performed for the S355 J0 steel grades for two rolling directions along with description of fatigue. The results from ProPagation for 50% probability of failure are compared with those from Paris’ model, whereby Table 3 presents the parameters for the different approaches by applying the maximum likelihood method. While the values of the exponent m that describe the slope of the curve, range between 2.0 and 7.0 for the most materials those values usually range between 3.0 and 4.0 for steel, see e.g. Klesnil Lukáš (1992) or Branco et al (2008). Since the evaluation with the ProPagation model requests the knowledge about the threshold and critical values of the stress intensity range, a parametric study was prepared for this assessment. The threshold value of stress intensity factor was preselected as being 1, 1.5 and 2 while the critical value of the stress intensity factor was assumed 100, 90, and 70, to cover all interval of possible variants. As shown in Table 3, the position parameter  is similar for all the cases whereas the scale parameter  varies from 3 up to 5.