PSI - Issue 43

Lucie Malíková et al. / Procedia Structural Integrity 43 (2023) 264–269

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Lucie Malíková et al. / Structural Integrity Procedia 00 ( 2022) 000 – 000

propagation direction. It should be noted that although the crack is loaded in mode I, because of the presence of the corrosion pit in its very near neighbourhood a small amount of loading mode II is also presented. Therefore, some kinking from the original crack propagation direction can occur. The kinking angle was calculated from the following mathematical conditions of maximum tangential stress   : = 0 , 2 2 < 0 . (2) The results obtained are presented and discussed in the following section. Let’s remind the dependence of the criterion on the radial distance from the crack tip, where it is applied. In this work, the criterion was applied at the distances of 0.1, 0.5, 1 and 1.5 mm. 3. Results and discussions As commented above, a mutual comparison of the stress intensity factors K I and K II was performed in order to verify the results of the ODM. The first terms of the Williams power series, A 1 and B 1 , are directly related to the stress intensity factors according to the following relations: = 1 √2 and = − 1 √2 . (3) The results can be seen in Tab. 1 for both loading modes. The values correspond perfectly for K I and are acceptable for K II for most of the crack lengths considered.

Table 1. Values of the stress intensity factors calculated via ODM and CINT and their mutual difference.

K I [MPa·m

1/2 ]

K II [MPa·m

1/2 ]

a [mm]

diff [%]

diff [%]

ODM

CINT

ODM

CINT

0.05 0.25

0.44 2.86 6.92

0.44 2.86 6.93

0.13 0.11 0.11 0.03 0.08 0.10 0.12 0.11

0.10 0.68 1.32 1.68 1.32 0.80 0.09 0.20

0.10 0.71 1.39 1.80 1.46 0.96 0.29 0.07

2.91 4.41 4.86 6.70 9.63

0.5

1

15.66 23.74 31.40 48.15 70.98

15.65 23.72 31.37 48.09 70.90

1.5

2 3 4

16.52 69.81

178.67

The dependences of the further crack propagation angle on the crack length are presented in Fig. 2. The individual curves were calculated via the multi-parameter form of the MTS criterion considering 1, 2, 4, 6 and 10 initial terms of the Williams expansion when the tangential stress was approximated. The MTS criterion was applied at four various radial distances and therefore, four various plots are introduced. From the dependences, the following can be summarized: • It can be clearly seen, that when only the first terms of the Williams expansion, i.e. the stress intensity factors, are considered, the results are independent of the radial distance. This is a well-known phenomenon. • The results show that the corrosion pit can affect the crack propagation only when the crack is short enough. Otherwise, the crack propagates in its original direction, perpendicularly to the applied stress. • The curves show that nearly in all cases the largest kinking angle occur for the crack of the length 0.25 mm. • The number of the higher-order terms considered in the MTS criterion has an important effect on the crack propagation angle. The values of the angle are decreasing with the number of the higher-order terms considered.