PSI - Issue 19

Jan Papuga et al. / Procedia Structural Integrity 19 (2019) 405–414 Author name / Structural Integrity Procedia 00 (2019) 000–000

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the range of potential critical distances in advance nor he has so many results of different notch types, the conclusion is that the prediction quality is inferior to the classic nominal notch approach. The output of one more calculation configuration is provided in Tab. 7 - the case when the critical distance is zero and maximum stress at the notch is used ( L CD =0mm variant). The output is obviously conservative, and even in the better variant using Mises stress the minimum error is close to 20%. The relevance of such output in the common engineering practice is questionable. Table 5. Results of the nominal stress solution using Peterson’s or Buch’s formulas for K f determination. Optimized a by Peterson (Eq. 4) Optimized A by Buch (Eq. 5), h =0 mm a 2.16 0.31 1.15 A 1.6 1.22 1.45  QS S u /K t S u S u / K f  QS S u / K t S u S u / K f Maximum  FI [%] 28.6 35.4 26.6 26.0 27.4 18.4 Minimum  FI [%] -50.8 -34.4 -34.2 -18.9 -41.1 -19.0 Range of  FI [%] 79.4 69.8 60.8 44.9 68.5 37.4 Average  FI [%] 2.7 3.4 4.2 1.5 -1.2 0.2 St. dev. of  FI [%] 17.6 16.5 17.6 10.9 14.7 9.1

Table 6. Differences in obtained critical distances for various versions. Critical distances [mm] obtained by the calibration for all notch types

Number of cycles for which the critical distance value is derived

Critical distances [mm] derived from  K th

Lowest values

Highest values 

Lowest  K th 

Highest  K th 

Mises 0.075 0.068 0.063 0.059 0.053 0.050

PS1

Mises 0.914 0.670 0.529 0.418 0.414 0.455

PS1

0.146 0.134 0.126 0.118 0.109 0.102

2.451 1.268 0.771 0.571 0.646 0.708

0.075 0.044 0.029 0.019 0.011 0.007

0.534 0.442 0.383 0.331 0.273 0.237

20 000 50 000 100 000 200 000 500 000

1 000 000

Table 7. Results of the TCD approaches using the  K th dependency to derive the critical distance, zero critical distance ( L CD =0 mm) or the calibration (calibr.) based on data of one unnotched and one notched specimen. GM refers to geometric mean (arithmetic mean of logarithms), PS1 to the first principal stress when used as the equivalent stress. Min  K th Mean  K th Max  K th L CD =0 mm calibr, min calibr, GM calibr, max Eq. stress Mises PS1 Mises PS1 Mises PS1 Mises PS1 Mises PS1 Mises PS1 Mises PS1 Maximum  FI [%] 66.2 78.8 49.5 64.1 23.3 40.1 68.7 80.3 56.3 60.5 25.4 22.8 0.1 0.1 Minimum  FI [%] 2.9 18.8 -35.8 -15.1 -46.0 -30.8 17.2 30.6 -0.2 -0.1 -44.4 -35.5 -53.9 -44.3 Range of  FI [%] 63.3 59.9 85.3 79.3 69.4 70.9 51.5 49.7 56.5 60.6 69.8 58.3 54.1 44.4 Average  FI [%] 35.4 49.5 8.0 25.1 -15.2 2.7 43.4 56.0 25.0 28.7 -7.3 -4.1 -26.1 -18.7 St. dev. of  FI [%] 15.8 13.2 23.9 20.9 21.9 20.9 13.0 11.5 18.2 18.3 22.1 18.5 18.9 14.9 The comparison of various RSG approaches is available in Tab. 8. The Stieler variant is essentially conservative with quite conservative mean error value, but it can lead also to non-conservative results. The IABG method is better balanced around zero relative error, and the typical output is also given graphically in Fig. 3. The scatter is lower than by those TCD approaches providing similarly balanced output. The Eichlseder solution seems to be slightly inferior to IABG. An interesting output is obtained from the FKM approach, which is essentially conservative in both variants of equivalent stress. Even the minimum  FI value is conservative, while the maximum  FI value is still quite low -