PSI - Issue 28

Ping Zhang et al. / Procedia Structural Integrity 28 (2020) 1176–1183 P. Zhang et al. / Structural Integrity Procedia 00 (2019) 000–000

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field indicates that more strain has been produced in a broader zone ahead of the crack tip, making the crack propagate easily. Also, conflicting crack paths can occur when the area is controlled by multiple slip systems and increase or decrease the propagation rate. 4.2. Crack propagation path After the first extension, cracks continued to grow until they reach the XFEM domain boundary. The final crack paths along with the ΔICSS, which shows the difference of ICSS values between the last two crack growth increments, are depicted in Fig. 3 for [001] and [111] orientation at 24 °C and 650 °C. Interestingly, the numerical responses have many similarities to the experimental observation. For example, multiple deflections can be observed in [111] oriented samples, while only a few exist in [001] samples. On the other hand, all crack directions are also the same as experimental ones, corresponding to crystallographic directions. However, there is a mismatch regarding the amplitude of cracks. The numerical result in 650 °C [111] sample shows a smaller amplitude than the experimental one. Many reasons may account for this mismatch: (1) the effects of creep and oxidation at high temperature; (2) defects contained in the specimens; (3) multiple slip bands formed around the crack, which were observed in the experiment but not captured in this study.

Fig. 3. Experimental (Zhang et al., 2019) and numerical crack paths for [001] and [111] orientation at 24 °C and 650 °C.

We now look at the distributions of ΔICSS. It is noticed that higher intensity values are observed around the crack path and crack tip, caused by the stress concentration. The ICSS will accumulate around the crack tip and drive the crack to grow further. Also, the ΔICSS field differs significantly among the two orientations and temperature levels, showing the same trend as the ICSS distribution shown in Fig. 2b. Further, we track the evolution of ICSS values around the crack tip to examine the development of cracks with increasing loading cycles. Here, the [111] oriented sample at 24 °C was chosen for analysis as it experienced the most loading cycles in both experiment and simulation. In Fig. 4, a map of slip plane activity after 17, 20 and 23 loading cycles is depicted. The dominant slip plane, which has the highest ICSS, is indicated for each element. Four slip planes are represented by different colours and the crack growth is expected to follow the dominant one. It is noted that the specimen is mainly dominated by two slip planes. The �1� 11� slip plane (coloured green) will make a crack grow downwards at a 154.3° angle, measured with respect to the loading axis, while the �11� 1� slip plane (coloured blue) will result in a 19.9° upward crack path. At the 17 th cycle (Fig. 4a), the crack tip (point A) was located at the boundary of two domains and about to change its direction. Then the crack grew upwards within the blue area and reached a