PSI - Issue 28

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

1180

5

an acceptable level of computational expense. Then, we propose that the critical ICSS value for 650 °C is related to that for 24 °C through 0  and s  as

ICSS ICSS

  

  

24 C 

24 C 

1 2



s 

24 C 

(8)

.

0





650 C 650 C  



s 

65 C 0 

0

The CP model was calibrated against the experiments of [111] orientated samples at both 24 °C and 825 °C by following Zhang et al. (2020) . Then, parameters were linearly interpolated for the crack growth simulation at 650 °C. Only 12 equivalent octahedral slip systems were considered as no adequate evidence of the activation of cubic slip systems was reported in FCC crystals (MacLachlan et al., 2001). All parameters utilised are provided in Table 1.

Table 1. Parameters of the CP model at 24 °C and 650 °C Parameters C 11 /MPa C 12 /MPa C 44 /MPa n

0   /sec

0 /MPa 173.5 155.4

τ s /MPa

τ 0 /MPa q αα q αβ c /MPa d

-1

h

24 °C

174030 147435

77380 72590

118520 108461

10 0.00001 10 0.00001

266.5 194.2

216.8 176.3

1 1

1 1

200 200

2 2

650 °C

4. Results and discussion 4.1. ICSS distribution around the crack tip

By applying the CP model to the sample tested at 24 °C and 650 °C, the ICSS value of each octahedral slip system at the crack tip was analysed before the first crack extension. It was found that different slip systems were activated depending on orientation and temperature, and this distinction can be significant. For instance, in the [001] oriented sample at 650 °C (Fig. 2a), the asymmetric butterfly-shaped patterns around the tip for two selected slip systems differ clearly in terms of intensity and spatial distribution. On the other hand, when comparing the results between samples of different orientations at the same temperature, nearly all slip systems were activated in the [111] orientation while only four major ones were active in [001] orientation.

Fig. 2. (a) ICSS distributions of two selected slip systems around the crack tip in 650 °C [001] sample; (b) distributions of the highest ICSS around the crack tip for both orientations at 24 °C and 650 °C.

Moreover, by taking the highest ICSS among all slip systems at each integration point, which is the damage criterion used in this paper, the distribution of the highest ICSS is illustrated in Fig. 2b for all samples. The contour shapes produced are related to the sample orientation and the slip system being activated. The [001] samples show a highly asymmetric distribution while [111] samples exhibit a more symmetric pattern. Besides, whether the field will be concentrated around the crack tip depends on the crystal orientation but also temperature. It is noted that the 24 °C [111] and 650 °C [001] fields are more concentrated around the crack tip, whereas the 24 °C [001] and 650 °C [111] are rather dispersed. These distributions could affect both crack growth paths and rates. For instance, a more scattered