PSI - Issue 37

R. Baptista et al. / Procedia Structural Integrity 37 (2022) 57–64 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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CTS specimen. Table 1 shows that SIF K II is zero for the initial crack length, therefore MTS criterion will predict crack propagation along the initial crack direction. Fig. 3 a) shows the resulting crack path when MTS criterion is considered, where crack propagation maintains the initial crack direction, maximizing K’ I (Fig. 3 e)). Increasing α to 15º, introduces mixed mode loading conditions. Table 1 shows that K I is slightly decreased, but K II increases to 2.7 MPam 1/2 . Fig 3 f) shows that the virtual SIF K’ I maximum value now occurs for a crac k propagation angle θ of 13.9º, leading to crack kinking. Once a new crack kinked plane has been formed, K II /(K I +K II ) ratio decreases to zero, as the MTS criterion predicts crack propagation along the direction where K’ I is maximum, Rozumek et al. (2018). Table 1 shows that increasing α will continue to increase initial crack propagation angle θ, according to the MTS criterion. Eventually, as mode II component in mixed mode loading conditions increases, crack propagation angles will diverge from MTS criterion predictions. Miao et al. (2018) experimental results show that for α>60º crack propagation occurs according to MSS criterion. Fig. 3 e) to h) show that θ increases from -70.5º to 0.0º , as α increases from 0º to 90º, maximizing K’ II value. Fig. 3 c) shows an MSS predict crack path when α=75º, and Fig 3 d) shows an MSS predict crack path for pure mode II loading. In this case, coplanar (in-plane shear-mode) crack growth was obtained. CTS specimen FCG simulations are in line with several authors experimental work, including Demir et al. (2018). For pure mode I or mixed mode loading con ditions the MTS criterion should be used, but if α>75º or high non proportional shear loads are applied, crack propagation occurs according to MSS criterion, Floros et al. (2019).

(b)

(d)

(a)

(c)

(e)

(f)

(g)

(h)

Fig. 3. CTS specimen FCG according to (a) MTS criterion with α=0º ; (b) MTS criterion with α=15º; (c) MSS criterion with α=75º; and (d) MSS criterion with α=90º; Virtual SIF K’ I and K’ II when (e) α=0º; (f) α=15º; (g) α=75º; and (h) α=90º .

Table 1. CTS specimen SIF K I and K II , SIF K II /(K I +K II ) ratio and MTS and MSS criteria crack propagation direction prediction.

α (degree)

K I (MPam

1/2 )

II (MPam

1/2 )

MTS (degree) MSS (degree)

K

K

II /(K I +K II )

0

21.9 21.2 19.0 15.5 11.0

0.0

0.00 -0.11 -0.21 -0.32 -0.45 -0.63 -1.00

0.0

-70.5 -56.2 -42.4 -30.1 -19.2

15 30 45 60 75 90

-2.7 -5.1 -7.2 -8.8 -9.8

13.9 26.8 38.6 49.5 60.0 70.5

5.7 0.0

-9.3

-10.1

0.0

FPB specimen also allows for pure mode I to pure mode II loading. When L 2 =L 3 , pure mode II loading is applied to the specimen. In this case the loads applied to the left and right rollers were 1.5 kN and 3.5 kN respectively.