PSI - Issue 52

Lucie Malíková et al. / Procedia Structural Integrity 52 (2024) 376–381 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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2.2. MTS fracture criterion When the crack behavior shall be assessed, a fracture criterion needs to be used. In this paper, the classical one parameter form of MTS criterium was utilized. This criterion is based on the fundamental idea that a crack will propagate in the direction where the tangential stress range    reaches its maximum, see Erdogan and Sih (1963). This condition can be written mathematically as: ∆ =0 , 2 ∆ 2 <0 . (1) If the tangential stress component is expressed via the stress intensity factor ranges  K I and  K II , an explicit form of Eq. 1 can be derived as follows: = arctan −2∆ II ∆ I +√∆ I 2 +8∆ I 2 I . (2) By means of Eq. 2, the crack deflection angles for 400 different configurations were calculated (10 corrosion pit depths × 10 initial crack lengths × 4 initial crack inclination angles). Let’s note that configurations with positive and negative  value give the same results only with opposite sign. 3. Results and discussion In the following section, selected results of the performed study are presented. The dependences of both the stress intensity factor ranges and the crack deflection angles on the normalized crack length for various corrosion pit depths are introduced in Fig. 3. Let’s note that in order to capture the effect of the cross -section weakening, the normalized crack length was assumed as ( a + D )/ W . Results for initial crack inclination angles  = -15° and - 45° were chosen. Let’s note, that the specimen configuration with a perpendicular crack (  = 0°) served for validation of the numerical model correctness and it can be concluded that the model works well, and a perpendicular crack does not try to deflect to any direction. The dependences in Fig. 3 enable to formulate the following conclusions regarding the stress intensity factor ranges: • The mode I stress intensity factor range  K I is generally higher for less inclined cracks (the highest values are obtained for a specimen with a perpendicular crack), and the opposite result was observed for  K II . • The curves obtained for  K I and  K II become coincident for longer cracks for all initial crack inclination angles investigated – the corrosion pit plays no role for long cracks. • If the crack is very short (about a few tenths of millimetres), the weaking of the cross-section through the corrosion pit increase both  K I and  K II values with increasing corrosion pit depth;  K I and  K II values are approximately twice as large when comparing the corrosion pit with the depth of 0.1 and 1.0 mm for all the initial crack inclination angles investigated (except for the case of a perpendicular crack). • On the other hand, when the values of the stress intensity factor ranges are compared for the same value of the normalized crack length, then deeper corrosion pit corresponds to lower  K I and  K II . The values of the crack deflection angles estimated via MTS criterion can be seen in Fig. 3c and 3f and the effect of the corrosion pit size can be assessed like: • Generally, the results correspond to the expectation that the crack during its propagation tries to deflect more or less into the direction perpendicular to the loading, i.e.  ≈ -15° when  = -15° and  ≈ -45° when  = -45°. • Considering that although the values on y-axis on both plots are different, but both of them displays the range of 5°, it is obvious that the corrosion pit size affects little bit more the more inclined cracks.