PSI - Issue 2_A

Abhishek Tiwari et al. / Procedia Structural Integrity 2 (2016) 690–696 Author name / Structural Integrity Procedia 00 (2016) 000–000

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Table 2. Statistical details of MC analysis of grouped datasets Total no. of tests Valid tests K JC Eq (MPa m 1/2 ) T 0 ( 0 C)

Std-Dev-1

Std-Dev-1

Gr-1 Gr-2 Gr-3 Gr-4

15 15 12 12

9 9 8 8

80.62 81.22 75.8 67.33

-125 -115 -105 -99

28.86 24.35 20.62 18.7

43.27 43.27 48.18 48.18

The Master Curve analyses of the four grouped dataset shows a systematically increasing T 0 with increasing crack depth. The increasing constraint which causes otherwise non-critical cleavage initiators such as carbides to trigger cleavage by developing high stress field explains the result. Also the matrix helps under higher constraint by allowing decohesion and micro-crack formation in the active volume ahead of crack tip. The constraint due to changing crack depth is measured by calculating Weibull traixiality as explained earlier. The active sampled volume is calculated using method described elsewhere (Tiwari et al., 2015) for a/W ratio of 0.3, 0.4, 0.5, 0.6 and 0.7. The behavior of active volume is plotted against K JC calculated from load-load line displacment response of simulated model in Fig. 3. The K JC vs. V* is fitted using power relation as shown in Eq. (2).  ) ' ( 0 K Z V V JC    (2)

It can be seen in Fig. 3 that the fitting parameters of Eq.(2) show a systematic trend with crack depth.

Fig. 3 Curve fitting of active volume calculated according to Eq.(10).

The Weibull triaxiality calculated in the active volume is plotted for different a/W models with corresponding K JC in Fig. 4. The behavior of Weibull triaxiality shows, for investigated geometry, an increasing constraint trend with increasing crack depth. However, for a/W of 0.5, 0.6 and 0.7 the q W response is close especially for 0.5 and 0.6 a/W values. The importance of fitting parameters of Eq. (2) and q W is further investigated by comparing with T stress and change in T stress associated with change in a/W . The T stress for TPB geometry is calculated by the polynomial correlation given by Wallin et al., as shown in Eq. (3).

T

4 1.13 5.96 ( ) 12.68 ( ) 18.31 ( ) 15.7 ( ) 5.6 ( ) W a W a W a W a W a             3 2

, TPB stress

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(3)



YS